-
Notifications
You must be signed in to change notification settings - Fork 1
/
Copy pathDifferent_Initial_Conditions.nb
1578 lines (1560 loc) · 77.7 KB
/
Different_Initial_Conditions.nb
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
(* Content-type: application/vnd.wolfram.mathematica *)
(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)
(* CreatedBy='Mathematica 12.0' *)
(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 158, 7]
NotebookDataLength[ 77779, 1570]
NotebookOptionsPosition[ 76537, 1543]
NotebookOutlinePosition[ 76878, 1558]
CellTagsIndexPosition[ 76835, 1555]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[
RowBox[{"Quit", "[", "]"}]], "Input",
CellChangeTimes->{{3.8071800437060566`*^9, 3.8071800446834955`*^9}, {
3.809461449770506*^9, 3.809461451227523*^9}},
CellLabel->"In[37]:=",ExpressionUUID->"b7630cf4-ff71-4ecc-8c14-c3ae62a4932c"],
Cell[CellGroupData[{
Cell["\<\
Our model settings to see how the initial conditions change the outcome of \
the model:\
\>", "Text",
CellGroupingRules->{"GroupTogetherGrouping", 10000.},
CellChangeTimes->{{3.8125301364301248`*^9, 3.812530169515755*^9}, {
3.812530268653805*^9, 3.8125302828232956`*^9},
3.812530800881503*^9},ExpressionUUID->"ec55524c-8c60-4f5f-9350-\
1709875a8d16"],
Cell[BoxData[{
RowBox[{
RowBox[{"Kill", "=", "10"}], ";"}], "\n",
RowBox[{
RowBox[{"tmin", "=", "7"}], ";"}], "\n",
RowBox[{
RowBox[{"Amin", "=", "0.95"}], ";"}], "\n",
RowBox[{
RowBox[{"Sp", "=", "1000"}], ";"}], "\n",
RowBox[{
RowBox[{
RowBox[{"Ss", "=", "5000"}], ";"}], "\n"}], "\n",
RowBox[{
RowBox[{
RowBox[{"T", "[", "t_", "]"}], ":=",
RowBox[{"4.75", "+",
RowBox[{"14.09", "*",
RowBox[{"Sin", "[",
RowBox[{
RowBox[{"0.01057", "*", "t"}], "+", "0.3018"}], "]"}]}]}]}],
";"}], "\n",
RowBox[{
RowBox[{
RowBox[{"Aw", "[", "t_", "]"}], ":=",
RowBox[{"0.97", "+",
RowBox[{"0.0001", "*", "t"}]}]}], ";"}], "\n",
RowBox[{
RowBox[{
RowBox[{"Growth", "[", "t_", "]"}], ":=",
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"T", "[", "t", "]"}], "-", "tmin"}], ")"}], "^", "2"}], "*",
RowBox[{"(",
RowBox[{
RowBox[{"Aw", "[", "t", "]"}], "-", "Amin"}], ")"}]}]}], ";"}], "\n",
RowBox[{
RowBox[{
RowBox[{"Growth2", "[", "t_", "]"}], ":=",
RowBox[{"0.5", "*",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"T", "[", "t", "]"}], "-", "tmin"}], ")"}], "^", "2"}], "*",
RowBox[{"(",
RowBox[{
RowBox[{"Aw", "[", "t", "]"}], "-", "Amin"}], ")"}]}]}], ";"}], "\n",
RowBox[{
RowBox[{
RowBox[{"S", "[", "t_", "]"}], ":=",
RowBox[{
RowBox[{
RowBox[{"G", "[", "t", "]"}], "*", "s", "*",
RowBox[{"(",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"G", "[", "t", "]"}], "+",
RowBox[{"a0", "*",
RowBox[{"B", "[", "t", "]"}]}]}], ")"}], "/", "Sp"}], ")"}]}], "+",
RowBox[{
RowBox[{"G", "[", "t", "]"}], "*", "k"}]}]}], ";"}], "\n",
RowBox[{
RowBox[{
RowBox[{
RowBox[{"P", "[", "t_", "]"}], ":=",
RowBox[{
RowBox[{"M", "[", "t", "]"}], "*", "d1"}]}], ";"}],
"\[IndentingNewLine]"}], "\n",
RowBox[{
RowBox[{
RowBox[{"P2", "[", "t_", "]"}], ":=",
RowBox[{
RowBox[{"A", "[", "t", "]"}], "*", "d1"}]}], ";"}], "\n",
RowBox[{
RowBox[{
RowBox[{
RowBox[{"S2", "[", "t_", "]"}], ":=",
RowBox[{
RowBox[{
RowBox[{"B", "[", "t", "]"}], "*", "0.01", "*",
RowBox[{"(",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"B", "[", "t", "]"}], "+",
RowBox[{"b0", "*",
RowBox[{"G", "[", "t", "]"}]}]}], ")"}], "/", "Sp"}], ")"}]}], "+",
RowBox[{
RowBox[{"B", "[", "t", "]"}], "*", "k"}]}]}], ";"}],
"\[IndentingNewLine]"}], "\n",
RowBox[{
RowBox[{"sp1", "=",
RowBox[{
RowBox[{
RowBox[{"G", "'"}], "[", "t", "]"}], "\[Equal]",
RowBox[{
RowBox[{
RowBox[{"Growth", "[", "t", "]"}], "*",
RowBox[{"G", "[", "t", "]"}], "*",
RowBox[{"(",
RowBox[{
RowBox[{"(",
RowBox[{"Sp", "-",
RowBox[{"G", "[", "t", "]"}], "-",
RowBox[{"a0", "*",
RowBox[{"B", "[", "t", "]"}]}]}], ")"}], "/", "Sp"}], ")"}]}], "+",
RowBox[{"P", "[", "t", "]"}], "-",
RowBox[{"S", "[", "t", "]"}]}]}]}], ";"}], "\n",
RowBox[{
RowBox[{"sp2", "=",
RowBox[{
RowBox[{
RowBox[{"M", "'"}], "[", "t", "]"}], "\[Equal]",
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"Growth2", "[", "t", "]"}], "-", "Kill"}], ")"}], "*",
RowBox[{"M", "[", "t", "]"}], "*",
RowBox[{"(",
RowBox[{
RowBox[{"(",
RowBox[{"Ss", "-",
RowBox[{"M", "[", "t", "]"}], "-",
RowBox[{"a0", "*",
RowBox[{"A", "[", "t", "]"}]}]}], ")"}], "/", "Ss"}], ")"}]}], "+",
RowBox[{"S", "[", "t", "]"}], "-",
RowBox[{"P", "[", "t", "]"}]}]}]}], ";"}], "\n",
RowBox[{
RowBox[{"sp3", "=",
RowBox[{
RowBox[{
RowBox[{"B", "'"}], "[", "t", "]"}], "\[Equal]",
RowBox[{
RowBox[{
RowBox[{"Growth", "[", "t", "]"}], "*",
RowBox[{"B", "[", "t", "]"}], "*",
RowBox[{"(",
RowBox[{
RowBox[{"(",
RowBox[{"Sp", "-",
RowBox[{"B", "[", "t", "]"}], "-",
RowBox[{"b0", "*",
RowBox[{"G", "[", "t", "]"}]}]}], ")"}], "/", "Sp"}], ")"}]}], "+",
RowBox[{"P2", "[", "t", "]"}], "-",
RowBox[{"S2", "[", "t", "]"}]}]}]}], ";"}], "\n",
RowBox[{
RowBox[{
RowBox[{"sp4", "=",
RowBox[{
RowBox[{
RowBox[{"A", "'"}], "[", "t", "]"}], "\[Equal]",
RowBox[{
RowBox[{
RowBox[{"Growth2", "[", "t", "]"}], "*",
RowBox[{"A", "[", "t", "]"}], "*",
RowBox[{"(",
RowBox[{
RowBox[{"(",
RowBox[{"Ss", "-",
RowBox[{"A", "[", "t", "]"}], "-",
RowBox[{"b0", "*",
RowBox[{"M", "[", "t", "]"}]}]}], ")"}], "/", "Ss"}], ")"}]}],
"+",
RowBox[{"S2", "[", "t", "]"}], "-",
RowBox[{"P2", "[", "t", "]"}]}]}]}], ";"}],
"\n"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"all", "=",
RowBox[{"{",
RowBox[{"sp1", ",", "sp2", ",", "sp3", ",", "sp4"}], "}"}]}], ";"}], "\n",
RowBox[{
RowBox[{"init1", "=",
RowBox[{"{",
RowBox[{
RowBox[{
RowBox[{"G", "[", "0", "]"}], "\[Equal]", "10"}], ",",
RowBox[{
RowBox[{"M", "[", "0", "]"}], "\[Equal]", "3"}], ",",
RowBox[{
RowBox[{"B", "[", "0", "]"}], "\[Equal]", "500"}], ",",
RowBox[{
RowBox[{"A", "[", "0", "]"}], "\[Equal]", "500"}]}], "}"}]}],
";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"init2", "=",
RowBox[{"{",
RowBox[{
RowBox[{
RowBox[{"G", "[", "0", "]"}], "\[Equal]", "300"}], ",",
RowBox[{
RowBox[{"M", "[", "0", "]"}], "\[Equal]", "3"}], ",",
RowBox[{
RowBox[{"B", "[", "0", "]"}], "\[Equal]", "500"}], ",",
RowBox[{
RowBox[{"A", "[", "0", "]"}], "\[Equal]", "500"}]}], "}"}]}],
";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"init3", "=",
RowBox[{"{",
RowBox[{
RowBox[{
RowBox[{"G", "[", "0", "]"}], "\[Equal]", "800"}], ",",
RowBox[{
RowBox[{"M", "[", "0", "]"}], "\[Equal]", "3"}], ",",
RowBox[{
RowBox[{"B", "[", "0", "]"}], "\[Equal]", "500"}], ",",
RowBox[{
RowBox[{"A", "[", "0", "]"}], "\[Equal]", "500"}]}], "}"}]}],
";"}]}], "Input",
CellGroupingRules->{"GroupTogetherGrouping", 10000.},
CellChangeTimes->{
3.8071800602935467`*^9, {3.8071802258336563`*^9, 3.807180226337388*^9},
3.807180347193081*^9, {3.807180518817112*^9, 3.8071805190149965`*^9},
3.807180925219217*^9, {3.8071810484811854`*^9, 3.8071810525438566`*^9}, {
3.8071811276292076`*^9, 3.80718113327697*^9}, {3.8071853463059654`*^9,
3.8071853519747143`*^9}, 3.8071855879277287`*^9, {3.8071856479485846`*^9,
3.807185710191349*^9}, 3.807185745875059*^9, {3.8071858151987743`*^9,
3.807185817006732*^9}, {3.8081242561854305`*^9, 3.8081242833585587`*^9}, {
3.808124500612605*^9, 3.8081245301376467`*^9}, 3.808130469917739*^9,
3.8125301488970733`*^9, {3.812530426105364*^9, 3.81253042753758*^9},
3.8125308008825026`*^9},
CellLabel->"In[1]:=",ExpressionUUID->"12f82992-d552-4f00-ae09-1c50cc3b400e"]
}, Closed]],
Cell[BoxData[""], "Input",ExpressionUUID->"f4476171-1513-4bc0-aa91-c9228580455a"],
Cell[CellGroupData[{
Cell[BoxData[{
RowBox[{
RowBox[{"scen1", "=",
RowBox[{"{",
RowBox[{
RowBox[{"a0", "\[Rule]", "0.5"}], ",", " ",
RowBox[{"b0", "\[Rule]", "0.4"}], ",",
RowBox[{"k", "\[Rule]", "0.01"}], ",",
RowBox[{"d1", "\[Rule]", "0.05"}], ",",
RowBox[{"s", "\[Rule]", "0.001"}]}], "}"}]}],
";"}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"sol1", "=",
StyleBox[
RowBox[{"NDSolveValue", "[",
RowBox[{
RowBox[{
RowBox[{"{",
RowBox[{"all", ",", "init1"}], "}"}], "/.", "scen1"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"G", "[", "t", "]"}], ",",
RowBox[{"M", "[", "t", "]"}], ",",
RowBox[{"B", "[", "t", "]"}], ",",
RowBox[{"A", "[", "t", "]"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"t", ",", "0", ",", "200"}], "}"}]}], "]"}], "Program"]}],
StyleBox[";", "Program"]}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"sol2", "=",
StyleBox[
RowBox[{"NDSolveValue", "[",
RowBox[{
RowBox[{
RowBox[{"{",
RowBox[{"all", ",", "init2"}], "}"}], "/.", "scen1"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"G", "[", "t", "]"}], ",",
RowBox[{"M", "[", "t", "]"}], ",",
RowBox[{"B", "[", "t", "]"}], ",",
RowBox[{"A", "[", "t", "]"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"t", ",", "0", ",", "200"}], "}"}]}], "]"}], "Program"]}],
StyleBox[";", "Program"]}], "\[IndentingNewLine]",
RowBox[{
RowBox[{"sol3", "=",
StyleBox[
RowBox[{"NDSolveValue", "[",
RowBox[{
RowBox[{
RowBox[{"{",
RowBox[{"all", ",", "init3"}], "}"}], "/.", "scen1"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"G", "[", "t", "]"}], ",",
RowBox[{"M", "[", "t", "]"}], ",",
RowBox[{"B", "[", "t", "]"}], ",",
RowBox[{"A", "[", "t", "]"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"t", ",", "0", ",", "200"}], "}"}]}], "]"}], "Program"]}],
StyleBox[";", "Program"]}], "\[IndentingNewLine]",
RowBox[{"Show", "[",
RowBox[{
RowBox[{"ParametricPlot", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"sol1", "[",
RowBox[{"[", "1", "]"}], "]"}], ",",
RowBox[{"sol1", "[",
RowBox[{"[", "3", "]"}], "]"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"sol2", "[",
RowBox[{"[", "1", "]"}], "]"}], ",",
RowBox[{"sol2", "[",
RowBox[{"[", "3", "]"}], "]"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"sol3", "[",
RowBox[{"[", "1", "]"}], "]"}], ",",
RowBox[{"sol3", "[",
RowBox[{"[", "3", "]"}], "]"}]}], "}"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"t", ",", "0", ",", "200"}], "}"}], ",",
RowBox[{"PlotRange", "\[Rule]",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"0", ",", "1000"}], "}"}], ",",
RowBox[{"{",
RowBox[{"0", ",", "1100"}], "}"}]}], "}"}]}], ",",
RowBox[{"PlotStyle", "\[Rule]",
RowBox[{"{",
RowBox[{"Blue", ",", "Black", ",", "Red"}], "}"}]}], ",",
RowBox[{"AspectRatio", "\[Rule]", "1"}], ",",
RowBox[{"PlotLabel", "\[Rule]", "\"\<Phase portrait\>\""}], ",", " ",
RowBox[{"AxesLabel", "\[Rule]",
RowBox[{"{",
RowBox[{"\"\<GMO\>\"", ",", "\"\<Wild\>\""}], "}"}]}]}], "]"}], ",",
RowBox[{"StreamPlot", " ", "[",
RowBox[{
RowBox[{"{",
RowBox[{"GMO", ",", "Wild"}], "}"}], ",",
RowBox[{"{",
RowBox[{"G", ",", "0", ",", "20"}], "}"}], ",",
RowBox[{"{",
RowBox[{"B", ",", "0", ",", "4"}], "}"}], ",",
RowBox[{"StreamScale", "\[Rule]",
RowBox[{"{",
RowBox[{"Tiny", ",", "Automatic", ",", "10"}], "}"}]}], ",", " ",
RowBox[{"StreamStyle", "\[Rule]", "Pink"}]}], "]"}]}],
"]"}], "\[IndentingNewLine]",
RowBox[{"Plot", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"sol1", "[",
RowBox[{"[", "1", "]"}], "]"}], ",",
RowBox[{"sol2", "[",
RowBox[{"[", "1", "]"}], "]"}], ",",
RowBox[{"sol3", "[",
RowBox[{"[", "1", "]"}], "]"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"t", ",", "0", ",", "200"}], "}"}], ",",
RowBox[{"AxesLabel", "\[Rule]",
RowBox[{"{",
RowBox[{"\"\<t\>\"", ",", "\"\<N\>\""}], "}"}]}], ",",
RowBox[{"PlotStyle", "\[Rule]",
RowBox[{"{",
RowBox[{"Purple", ",", "Magenta", ",", "Pink"}], "}"}]}], ",",
RowBox[{"PlotRange", "\[Rule]", "Full"}], ",",
RowBox[{"PlotLabel", "\[Rule]",
RowBox[{"Style", "[",
RowBox[{"\"\<Different starting populations of RootPatch\>\"", ",",
RowBox[{"FontSize", "\[Rule]", "20"}]}], "]"}]}], ",",
RowBox[{"Frame", "\[Rule]",
RowBox[{"{",
RowBox[{"True", ",", "True", ",", "False", ",", "False"}], "}"}]}], ",",
RowBox[{"FrameLabel", "\[Rule]",
RowBox[{"{",
RowBox[{
RowBox[{"Style", "[",
RowBox[{"\"\<Time (days)\>\"", ",",
RowBox[{"FontSize", "\[Rule]", "14"}]}], "]"}], ",",
RowBox[{"Style", "[",
RowBox[{"\"\<Population GMO\>\"", ",",
RowBox[{"FontSize", "\[Rule]", "14"}]}], "]"}]}], "}"}]}]}],
"]"}], "\[IndentingNewLine]"}], "Input",
CellChangeTimes->{{3.807180080529944*^9, 3.807180209160219*^9}, {
3.8071809600204124`*^9, 3.8071809783439026`*^9}, {3.807181095599572*^9,
3.8071810986138444`*^9}, {3.80812428915536*^9, 3.8081243254955945`*^9}, {
3.8081243702507253`*^9, 3.808124389530169*^9}, {3.8081244337977324`*^9,
3.8081244621347513`*^9}, 3.8081302921715937`*^9, {3.8084025454051466`*^9,
3.8084025741919317`*^9}, {3.8084033319999228`*^9,
3.8084033563789415`*^9}, {3.809461385467534*^9, 3.8094614732853374`*^9}, {
3.8095351303857307`*^9, 3.8095351633947525`*^9}, {3.8095352093949566`*^9,
3.809535245539126*^9}, {3.8125308352625103`*^9, 3.812530947861585*^9}},
CellLabel->"In[39]:=",ExpressionUUID->"85a90bc1-2112-4a8b-ad15-d843eb11409c"],
Cell[BoxData[
GraphicsBox[{{{{}, {},
TagBox[
{RGBColor[0, 0, 1], AbsoluteThickness[1.6], Opacity[1.], FaceForm[
Opacity[0.3]], LineBox[CompressedData["
1:eJwl2Hk8lN/7P3BLWqgsyVIke7KFskYvkqXsIcqSbFmyRJR9prLMYO5JpNKm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"]]},
Annotation[#, "Charting`Private`Tag$4251#1"]& ],
TagBox[
{GrayLevel[0], AbsoluteThickness[1.6], Opacity[1.], FaceForm[Opacity[
0.3]], LineBox[CompressedData["
1:eJwd13c8lW8bAHBEMipCKrKSET9JQkkuO6SorLRLJBJKGec5nSPrrEdLRmU0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"]]},
Annotation[#, "Charting`Private`Tag$4251#2"]& ],
TagBox[
{RGBColor[1, 0, 0], AbsoluteThickness[1.6], Opacity[1.], FaceForm[
Opacity[0.3]], LineBox[CompressedData["
1:eJwl1Xk8VPv7AHCkDdlK9kjITouUJU+SyBLKVgiFiNwupdKcmTNRZnO6lQpd
FUWSm5A13SKkm1JEiKhk30IS8n3m95t/zuv9es2cz+dZZ3VAhGugkICAgKCg
gAD/+f8fFvzfA+gge518sPVXPNgfSlC3dKcDS+vD4uiJeCCUymhkGB2qPQ2v
tfXGw/Jzi+ckkujg+XEyKe5tPMTn/zJz+06Hg70b151Miwf1kvCwSlcGcE3X
6fdZxYNDa7q9w2ISFma2x5sS5yGizbx12XEm7JS4v6vsaRycnA0k6zhxICm9
1Mt2dSyI+eg0OxrEg9xZ/0vu/zAh8IFm+3wwG9b+VR75yY2Egn/Cbz1I5kJU
H8fBzIUEh7Jsu6I0LnRIjMYmOZAwaLbHp/weF0w8fi/y2U7C8elZ8nkpF0qs
w8bnjUjoq55qetzKhYpick2+GAl7B1JTtyvw4J2XUFJNFQNeXsphDV/hwe6T
Icphzxhg0etnmpjKgy8y4+PS5QzYvfRI/aYMHkz43MkILmCAW/6caOgjHuiJ
C93RT2eA9J52HW4DD64RzoLrSAZI1PLeXhNPAIsymU+OlgwQiXjvyiUS4OY+
390TpgxQ4d3vq45LABMV64rUTQyQfS+dPsFNAOEaq8l5fQaMyl49q5WSABpr
LRMnlRjAeRm7ZaAwAU7Wm1bTpuiQdsqkKHMgARoNorq9R+hQV1ck+HMsAapD
Zdg2PXSYGbvz2ORnAvzbqbDStJkOomqd92OFKeAWFm7ILKLD6CfRViclCq7z
mPsrTtNh941DC2NsKahlxUceiKTD9ttysdmOFDQdOzq3FPtgnqZ4/YUrBZNW
RzXifeiQ2u4s9cKbgpZnznP62+jQtcnr/ocIClSUwlpsRemQLMIb0b5IQbrd
vlUNwnT4d0RTSvYKBd1naCXhvwnY2TPgNpJEAa2TdaNxjID8Xoay/y0KXJQN
y8JbCPAIlByzfUDB4SPrskeyCTCT+l2mVUOB6vKhZdkZBIywI7iltRQ0p+nE
nLxFALlpxHXzKwo2fr43aHeVAN612ompenxfjar+y7ME+PT0OLNaKJhbGv1d
jk7Agjhr5pk2Chpasq+cPk1AfMrRjd7tFAx2WzWdOEbAZvWEqK5OCj5vrfd1
8yPg3pnfuot6KIhuj/Kw8Cbgi8F2eb9eCmKL+qo2e+L5kVH7MvsoyLjwaWuo
MwF+Aq9dfw9gfn1O+N90IIBldtpefIiC48JFev22BFTYVcuJDWM8jqo9xdsI
cJx1LXk7QsHslpFui60EPAkiGpNGKbAv9H7QZEqAuKGCq/MYBUd279511oQA
jZ4q90l01Xqpsu0bCTg18GEJ6zsFy/JIYbl1BGilh1Ci41hva5q2gAEB4eaU
FA29/2aG3qwOAUkJFwvb0YZO8uJiWgRIHtLO1J+gYI9YxCtDDQIyyGyxcPRn
sAgKViOg0vuY5HX00sBVrXkqBGRn97eVoo1uOqlLKxPgHZyTVIvelJuzNU4B
828sefwFmsgTWyMmh+fnhCUVocOfm/+XIUOATpDS+qtop4oRI7flBCim3QoN
RrsROvayUtgPm69EaKFfRqaJD4ljPlOHw1vxvt8qZiOaxAhw7rp+kR/PJ07H
wQYRAnIlLolIoy/LdXV8WUIATfSL0DXMh2ikX8PixQQkskOyJNBpYVvWWS4k
YK54pd4pzJ+bnX4vawEBg4kNxY2YbyXHuZ4eQQKuqbJoamhHq0OqXgIErM3a
cjcA62OWa0xv/00DZf9TwYlYv3+sXoxEzdFA40xGXynWl93j6KMyS4O8tZI+
DYMUPOT+zPv4iwbGfy0c7cB+EMyeaLs/TQPPXX317f0U1FXWPqN+0kDx7lmD
euwfc+Jv+7gpGkQKrDEpxP6alQ/14/2gwTWpWbkL2H/lTdo9mZM0qEjaLuT7
jYI/1RuqGydocM7SfLVqNwUDKdNfl6MHLofebvqC89w/oh44TgPr9akl5GcK
8uqbQl58p0FwOCNhdRcFdsveXLFA614vdS78RMHTn5prXo3R4I/jmVleHRTE
PSiRDkUrF2jljH+kYFF7nL0smnu5gh6L8zNv7JLfMEqDmSXPd4i1Yj9EdBne
QN9ZcGYN5wP2k8Vsxil0zYktFoLNFHj8Xv87AD2icKTo6HsKvhhx5Pejybb5
Rw0NFNgu3PfRHx3abO1t9A7zJzShHY3+eCKuLhbneUduTncyWlRtmf7b1xS8
t2z+/gpdMro+VaaOgrKcoQ3L8H6Xn5pYu/5HQau4LXs/2uaY27bzuC88Qau5
CB3Qc6OoAPfJAZX6mdUYf8xi3drWKgpkWWRLElqjUOTadCUFh/5Y76KC+Qtq
9LORqqDgtUyhVR769YWgydVPKbgbkMxzxXyLTtVX6T7BeYVwKQGsT4y02weD
xxSIX3ucU4o+PZzpqFtKweOSRTnuWN8t8sZfJAspUHg2/MoE63+peNzqVz7u
S7Uxugb2x0Lhydj2hxRcuSkqpzlDgyOd5/Qu5lAwLSnoUjxPgzfNNw8V3abg
Xk+O/S/sT9/dX40i0ygQML9RtVOIAO5LeKt9k4Jqn/IsYez3OyPVAvEpFKgX
eLgIiRIguzlGWxT38469T9qHcD5P5xqbWxOYb7NP8s04v+En6leWxmA8dgVJ
tUoE5ATMh+mdwn0lNNpYq4r7ysl9YFEUzpfvpb0btAlYnFmclxiC83ru53mO
Gc6n4sUi/b0YjxJNRh/32RjPc8bUhQIhW+eRJiBgz02pgh1O2D9CtS1WNgRM
mb/p3oP/P0s/FHWdcCHgjaP3OzdzCrCRDHVDCEgJF5ZfoE7B7b/NCx5eJ6B7
61M2+3sCHOv6+vWTGB0WbvbvJ6kEaLP7rN/UToeVj8rdQj/z4Cov6PELWwbu
7/R3iU48KD3eUxuczACftXOixVVceBBWHaTSyoDpytoDFZ5c2FTHkTmwgoTo
5NlfKeMc6FaQcyq2JuG+flv8jVQOtOz95OB5hITnxjemFPdxQKU0eccBigQB
ovtSuTwH1I5+fOh1n4TCp3Asq5sNU0uOrIisIWHFocn60gI2HAxzMnLtIEFw
efuINYcN2VdT7Z+PkjBxJ9mxLIQNLYnGCwSFmHDrKy/GZRcblAPO6bySYILk
SdtxtXVs8GPmxR5UZALRJtEwrsiGewV16oKaTDhjaZTJXsKGs50HxrYYoHP3
qZ+dZkGUz2OTP4yZwF68v8NzkAVdb1VW9Joyoddv/WDgZxacT243Sd/KBJ2z
cVmZbSzQ1ut7arGNCcXBVm0Lm1mQft4oxxq9wutz1XQTC2qUZmLt0YuY+U1D
6Au+SlOe6OeXvoU2oZ9q3+z+E707KMYnC+2gu3EwDS2+ozzUHf0DXqSPoy0b
eap171ngFJIm+BNt2jn4pgp9RGW5/SyaGgy88wT9LbX0prAVEyxWp1fkoonT
6h4r0BuKPKuvoHu7to4aoms/eo2HoB99jVu8AW04yhUORNtfCBDZhH7U/tnM
D33P9uM7M/TygWklD/Ry8bqjNujXu3ru2qBLQ5nvPND9M669euhMr1XJXmg3
e9phHbTqKXmn/eiKZo9lWvz7lujF+KL/UFetWoOWu2g9cQAtt0biw2r0EtEy
L3801ZYroYo+5FjZdxBd+kN8SAl9//XeFYHo91dfXVREDx+w1g1C8yIsfRTQ
Mu1/GQSjVyofdpBHzwhZrDqMHjbe6SeHjlm54xffqgYd12TRyZZZFSHosEmD
HyvRvhmHo0PRl2LMTvL9359MuSNoj9yFKnz3vJq8w/eps1S/DD9/H5+phKGL
v7a28m36sjuO7+bKvhG+aeV+H/i+KvlEm/97smOdbDi6pNQrnm97N08rvuce
PhHl36fTrsGLb41vw/l823y95cP3mM0gg39/hkOlI9/qz4v/5Md3+d4mHb5p
ju4sfvznNWe+88978q76OT8/Pr0Sd/nO2i6moYxWlIuy43uO0rq3Cl3TrtnM
j4eWqbyXn+/pl1FF/PiFppJWqqNZVuIifLPENQw10Qqj3235+YLcC2H8erry
kjn8fIOLlLs+OtXIXp1frwyr4S+b0f2rjqe588/LfjHozs/Xv49eGqCFGVcq
/0E3Su88oIv2762WLERvGIz+uBZttrCaVY6+7ph7QRUdsnjb/Ct+/yRYd0qi
G1pTfw6h09S2KQxh/89q3tDajPPSYu0wcAl9LCsqhT9vkX1mR5KBCYlpTr/b
P+D3C91Uqi2YoLu0/2hABwv8X+kma29hwgtpaSGbHqzPrrwclw1MWPIrKuPU
dxYEhCYGiehhfhasDTkowAZbVRmPbWpMUPBNdpVczobVAWaD2rLYH1T3HhMt
NrjL+xk/XcKEc9Hts3nb2XB3KCWidYoEn60hxcMH2dABnSt2dpOQ7u/LDDzP
Bq3VbUqJdSRkWT2WzMN998Bb/sFf+STE7D5tEveNDQxR44M1iSSUjEleLlbh
gNNXIrYygoSjG5a2TR7mAD3a9EfvDhLmouf7J0s4kDP/fNsqdGN5tAW9jAMT
jdXTrriPBxQ9i5eWc4AbrXu/1IqEP27X66s95YC9yHeJs5Z4/nipgX81B0a0
ZA5NbSZBsXvXGbkGDniZ36kM1cXzk3d9jRzigNsT19tcHRIiTGYD1Uc4sMCm
sTNHm4Qw5ZSNTaMc8I1rDhteS0Le5vwSiwl83wX9f4PVScgJj2UrzeB9i1sa
TZVJuLHtl4vCUi7csUkwcVUi4c0vM81OES7UiDkPHVYkQSheeH+mGBceKkW7
XJYn4VSBS88WSS6IHDXo+yxDQmVWwaMIWS5YrZ1qmsD/H1NJsfsgz4V3DYIr
FqF/bAgXXa7IhRvZQdGa0iQYbPSWeLyKC1cmff82liLhUFd1wUVVLly3S5Gw
lsT3S83Xhqpx4c1Wep2LBAkzL4OdrdW5YPhepNlXnIT+ZYK2Kppc+B8+n5DY
"]]},
Annotation[#, "Charting`Private`Tag$4251#3"]& ]}, {}}, {}},
AspectRatio->1,
Axes->{True, True},
AxesLabel->{
FormBox["\"GMO\"", TraditionalForm],
FormBox["\"Wild\"", TraditionalForm]},
AxesOrigin->{0, 0},
DisplayFunction->Identity,
FrameLabel->{{None, None}, {None, None}},
FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
ImagePadding->All,
Method->{
"DefaultGraphicsInteraction" -> {
"Version" -> 1.2, "TrackMousePosition" -> {True, False},
"Effects" -> {
"Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2},
"Droplines" -> {
"freeformCursorMode" -> True,
"placement" -> {"x" -> "All", "y" -> "None"}}}}, "ScalingFunctions" ->
None},
PlotLabel->FormBox["\"Phase portrait\"", TraditionalForm],
PlotRange->{{0, 1000}, {0, 1100}},
PlotRangeClipping->True,
PlotRangePadding->{{0, 0}, {0, 0}},
Ticks->{Automatic, Automatic}]], "Output",
CellChangeTimes->{{3.807180158620488*^9, 3.807180179676414*^9}, {
3.807180210179633*^9, 3.8071802321310735`*^9}, 3.807180351059868*^9,
3.8071805489948063`*^9, 3.807180929701643*^9, 3.807180983755803*^9,
3.807181056333684*^9, 3.807181100206931*^9, 3.8071853618602448`*^9,
3.8071856002236814`*^9, {3.807185635657634*^9, 3.8071857497548304`*^9}, {
3.808124391540022*^9, 3.8081244387404833`*^9}, 3.8081301972611895`*^9,
3.808130293830285*^9, 3.8081304746651134`*^9, 3.8084033200147753`*^9,
3.8084033572414308`*^9, 3.8094614757583423`*^9, 3.8095351656985683`*^9, {
3.809535229177951*^9, 3.8095352467752447`*^9}, 3.812530840302534*^9, {
3.812530926500535*^9, 3.812530950288211*^9}},
CellLabel->"Out[43]=",ExpressionUUID->"89c68c5a-b348-4f12-93be-1a98ba7da7ab"],
Cell[BoxData[
GraphicsBox[{{{}, {},
TagBox[
{RGBColor[0.5, 0, 0.5], AbsoluteThickness[1.6], Opacity[1.],
LineBox[CompressedData["
1:eJwV13c81V8YB3AVUfILZVRE9t4k4X7MjFJJ2XyvebOiSPa9V4WGlQYpI2WU
UlJRRpRKaWiLkpUmyY78jr/u6/26565znvs8n7PGa5e973wODo7P8zg45h6l
0mbOnV39wtinMd+eg0MGN3kUJYIZV2hpvYtPfBGQwd19l4sUGPW0eScr0gKl
ZNCsEea/kPGMxvuf6mSDiQweHmmzGvX/RPMuDIv/lCCDRwaJ1T/8B2kSgjlT
HQtkcdFwWbzulSFaxgRjmaGQLH5/8MkLL/tNa+9bV/5UThbxK3m6h/P/0JIL
Xsqm28ji5Ek7/8Gj47RPVd9D07Nk0ZLxIWzAf5ZWV2y3+ruWHJJPnXh0TJMD
urVrRm5ukIMKg+aifYUDWSPfTte7yWE3d0bM7rJ5EPw2z4WVJId/Fjp1Q/kL
cFda8mzHJzmINkWb/TzKjYtXfOv8cuVhU8tt1++/FNPqMc7XrBShOes1Kjy0
FDbN8vBgKOKIpOdTaUN+JAolvPFJVkS4V02Ewz1+OFYLxR14pAjz/tB7Va8E
8Ej3j4LqFiV0/+yk7xtdhoTAsf+6dynjTerhqvR1y3FWBTVFx5XRor5uUWnc
ctz1KPn5/LYyroVlVbznEsLTf9pcAYtUwBq1mTUQFkZm3diOO6UqkJy5mTuj
J4qH23/7v51VxfKzvkNCMaLo8N636bqKGnhoy8zV6kXxa1t+0RIXNQwyQ757
bFiBEHm1cp0baqjjlDVocFyJtUaJnw+Eq8N9SeZb9j4xVJot5Fc9oIFWPr1F
nO6SUNdqETljr4U2W8FTT2MlcUn1mR5vqBbepfySy86VxFVBh/P3jmqhl6vY
XK1DEp3v8s+ItWhhekaE6eS6Buz1OjWRltpQ+jU5dslZCs+rtVNy7HSgofLm
QGSUFHZtqCuXCtOBXsC15abZUrh6jkeRM0sHpv0BWm/fSUGpv3rF23YdOH/8
EDzPSRodK94Fvg/SRfLT2t7tO2QgM2rxDOf0kLokZ4/kXhnYrOiW6nyshyyb
vfO/H5fBd9evgb0jeshrVpNkvpaBXmZ4u77VWtyoy3Mtc5CFt3WjsPjIWvRd
ZrX9s5eD7Czj4HyvdTBNs2go3qwAtZ0/+V/nG4Jpc720LUQB71tSMmLfGaKO
S/rYzFEFbJb1+1HDbwSDWA6/bU8U4MNdlrUg0QjaO2/zzpK6+ahr/noyxBgy
ZpqOO0yVkPRc4riYNuD1Lw8suhJ+2ol/EnMA8qv/U7rEVILgxyV9+yIAMY0f
0/PqlTDQP15uVQ0IiRcXlq9XxvfWcE6GhQkWjov94tRVQTS/5Z5boaYwv3b4
rbqDCl7YHdPnOmUKdvBUg8seFQSVi9y+W2+Kfz1vj1VcVUGMcNGBNH4zjD/P
XOempoqXvxt4Ltw0w0AZz4FKeTUoWn+r5xW3gJxfZMhHSzX4zAwt5NxoAZ81
/Y6L/NRw7h8PbX+MBbpONil5FqmhIz9AVbrDAu/3xz9fvEYdwmd3XFhcZAlf
9Sk+TT4NfFGpMlmyxQobPySdF12tgVHOR8/WHLWCTpKQEYe6BqYDVjlNtliB
85NG0LMtGshbPbx5wsoahan+LcFZGghWvKEcZ2eDTz9fHSxbpYkeKkvxN2sj
mrO9VmeqaGL81s0GjycbcdliqCrKSBPUWn3eapFNiD/D22flqYmlo8NatKub
ILbJ1OxLoSaCuQOtegbt4Hzpyqy0khZOfQ2eFXy2BXAyOsm7XgvNHDuyqOkt
UOB8rPbHVgtRB+wOGCptxYRrv3tjsBZq8+3rzidtxQle8TvUVS20ONoX7rS2
x8uAQ/vO6GvjdjnTd+W3bagRFuU/YK2NxNXFDrxrHFDYeL44yEUbSwTPj55z
csDulXffrI/VBk3ndU7bIwfwt4zrtNdr464U03Dr9e3YpOj7W3iDDq77mj9U
uuiIqcMRtzt36OC5ll7BpwFHlPw6cKDITweOC0Mi1ss7gfP6hRVaB3VwSUM6
6cd5J9QYD5hsuq8Dle5LdfYXnSHnEJiZaKaL0YzEHwJvXfHqRoybzTZdLB1Z
mHNNwg2sFUfkBLx10egU8HDRTjd0fLxUc5atC441Wmc/zrjh2M5f3dV3ddGe
Xymvq+EBjoQw7SGaHizKTFdxu1G4/Jk1c2OzHsrrO5hqBym4mmc+iPPUg+lk
wPfrFRRuLKp05U3Qw36x7KmPC+kIyhpJlKvTg/basdbim3S8L4185Wa4FovP
PM77o+SNa6/iIh7p66M4VeexwA4/lBzw8eq21ofMK5M2qXQ/nNWz3fzXRR/c
dTfzjrX44dApUUXVOH3EJTf4p8Ef3m6VHel39ZGV7zr/kQYDy3sHzJxs1oE3
NTOvRzIAe/9sE/ziagA5K4bGaq0QBBUZzM4GGZB63/vlTngIvLav+SEab4DI
3etmo2+GwO7mr/s2+QZYuiE0z8ZoF+RjUqIu9xoguV++dlQmFO/m13dFBK9H
JrfHZbpWGNYLKl3hTDDE+Uvh7HjLPXg6z+VRa5ohDnmEV0X57QH1O6XnBOkr
w5JLg5wP7sH+519FFBsN8epmYeHd+2R9ailzE5cRxqIqe5abhYPiVbQ/cdgI
uaztxa/0IjA85RTkmWsE130drGMOEdj/LfmgQrkRPMKGleV2R6D00UBNzVMj
FFuVJDddIuuTSqQ/CRhDffiMxUOJvdjPqTAqf8oYLzI3dXpM74XwiOPS3yXG
CAtt37lAJBIlPUmKNdXGiFjv5R6mGYnWxi/uGz8YI9R+2Yti30gIs4qbQ1fT
sDRGuif8cSRKZ+ROVRfRcH241Hf7kX3w/5t5hpQhnKL+XTrXHYUsux9NURRw
etVZ3VcjUWgosPi2iQH4BGSPv1wYDVGrCb2xSGANzXCFqVI0Hma5P7c8CUjA
p+1TSDQU1RQWDLwG+A5JF9IHo7GDxVK80wk8eCB/8cK/aLBftW9O7wN+M49e
q+eLQXv00Vz9UUDAYoPaLuUYHHowrJuy3AR1G0wsn/rE4DtVy1DaZoJKmw+v
ep7FQPS6cNo/FxOERPomnuiIgTl3aFWblwk+8J8Nlf4ag9xyqfkxu03wflHA
5dZ5sdg4lXT6cYYJBmKENu/SjEX5MfunQc9NkKNSymV+KBbt/RdH8M4Eb6r8
Nj7JisVCA65VQl0mCFp8PUg3LxYeXTf9awdNoFN85N3Fylj8pyo+77+lpghc
IX5c50MsdjV/0b6yyRSX3k8G8snGoQGXAlV2mEIx5duPVLU48N8OPVfqYUre
p07iz9o4VFyZFCzaZYqqrZXhvjZxGD7FO3wqwxQmj5WY/4LjsDdQvYL92hRt
VW0a3hVxaO7782W2k8yJx09zzG/FQYS6JRHXb4ouw2MHlzbE4ZaDSVrkuClm
TI77ez+Lw6TRtpCgFWYofxtcwfczDrH8kSo73M3w2rlsuEYmHk8Orfd56WsG
68VqdE/leIhzceRuCTFD21p667BmPOomk3ltE8ywoFih7YtxPDh6cr7RCsxw
jmZUIOgUj8SquhLFPjMcTqscLU6KxyGXhbIzQeaIyHOyi+6Mh7HGkrGv4eZo
Kri7Tb47Hr+5BB+8iTWHHr79etwfD6er4jsrjpgj3oUROj0YD1ke3XLvS+YI
kW6n/ZuXgIYqb92W7+Zw/RE9nSeTgDH+uxYnAyzwKyi/SNg3AWX9zcL7d1uA
x12D7xcjAe53nnwJjbYAh2OSVUNQAu75v0uxOWQBMdM81vbwBGTUDbbOlFrg
U9D+r+aJCVAJWr3D56sFonjWN1rkJ8D7QYyfJsMSIk0X7TTfJsDHUM5ubJcl
Tgvb1+9qT4Df1ee6tyMtIe408rasMwGM07JcFkmWqLa/LSvSm4CQXc/OOV2w
hEKwpcKjoQREi0h/Tui1hBTy3j7hZCLTv8X1KbUB2d3jV1PFmLjLvWJroLMV
IopUkoOsmOg/p2bznm5F8lrM+9fWTCyBudmGACs0H6+cMrJlwmnfLl3pGCs0
ajGvL7ZjYnDg/ooPuVYIrb+47sQ2JsRbdnfbdFkhsKKPJ9KDiagjT/Yo+Vuj
qco7KWAPE5oCzBNfw20QJMr1mZ7DRA3PW4UHsTZYJrSrde9pJkw51G4X7bdB
A8+qyUO5TDgMfvjkmWWDLMW7AlfPMrG3da3im0obtHtwe44UMnEnZfB247AN
Br0V5ztdZMJqvufn06G2ONYwpH7qNhPUHyMVu6CNGBg1WibRzkTB2fti40ft
cHzmuLDnchYqUw0+tNlvwS2Dwh23zFkIrzHacmbjVqS/63ZwCmShvuX8cIqr
PZ50ydp6prGwc8O62p1O26AVml7pfImF3BLNqsAABwh7G4jsecBCxp9aVmjk
duiNf9Ky/8hCf1nEXsbuHZAx4Nl0b4iFe5aZp9hsR2RrHpg/bz4b8za3d6cx
ydzNCFV9spQNDpMb8/KjnNEzrnHQexUbLuZfWt7FOeMld0NXBvH1DaJZAmxn
dNJurWwgZthFyyUecsZMKZ+qmBgbL1yNbf1OO6Oh/taTNuLCvc1ZKrXOWLdh
wQKD1WyYX3ojX83hAjGHs/lDkmwki4xvaktyQTSrSG6eHBtZDx/2NB52QVTG
U1lZ4ryonKjKNBf0KvLzWhPf+GB0PuukCxbmzk9OJ+7L2z+9o9gFgu2sjavl
2TBVELz4odkFDjxTC3UV2JjWV+Xp43LFxd/t+zYrsRHq4t04nuhK+lP173Vq
bPyX963LMNkVIir/aboQX+oJm2UdcYXPZwmHaOIvQUzDJcddoUkrtKgh9kg4
c0Pygis+uC94q6/Oxsait2XWD11RMmJbo6HBhsIv22Onl7ih/NqHal4tNpq1
Xl7t4neD8oVwpgKxT6TLc1khN2RfuK9sQZzHsZOvQtwNzPYyjXhi4WUHk+6p
uSFHaOPIL2JO/YaYn1vc4FTGv/OxNhufWTo+tONusMvQ1A/VZUNO+L/U0Gw3
6F5OV0khDij7crPgjBtW+IRzFxKPtOXwcl5wg+WFztCXxDwy8yof3nAD406n
oK4eG2rNrfPs37mhJjfz1B/i6MX+eT6r3HFOw/qFuz4b9Wfx6LiEO/ZYTuTv
IebUXvmnWdodamLvHFOIj7q2WiqquON4iGnMdeL8S9q/fhq6Q3bhhuxF69h4
YMdhFOnhjk2fNuhdIV5+LLs9pcAdJ57HLR8wYGPx62Uvdp93B2UdnDFJzCGS
+sC11B07lKwmF69n42cO+7rqVXcotz5KUSVuLgxMfdHgjqbfbpfDiPddMzJd
0eWOAdWTPGPEnS8+l5as9sDOlnHhQUM2Xi1zy8+Q8sBpI4fxGeKW7W9ORMt5
oLF1unGJEamn9y2JG9U8QHtsKKZEnP650n3IyAOuTU1vvIlNfx8Q0Hf3AJ/y
2pCXxBf4laIenPbAzOvZteeMyf71O09w5ntAafNQWgXxzdspkaZFHli1qOdZ
LfFDv68RtZc8UEbr4H5H/O1Oye7KWg8ksn2deGlsqO6UD8r75AGHf3zxwcQ3
jB2/d/R4oEGR7hhFbLw8KWDlgAfu1H8UPUBsV9/POD7kgcIAH4dc4lChC76H
53mSc31T/oj4+l0Zz0hpTxQWa/6QABuGJx0+Xpf3hNEmfWsl4vtB+92HlT1R
JHs4VYf4jUiva7COJ25prW6zIh4PPufkbeGJh6nKRqHEBiul7Df7e8LphF9R
DXHj4NYXRwI90feHJ6mJ2PY+a0vLLk/oXBW0f0LsFvrZzmKfJy6PehV0Esc3
59uuT/FEeKa47Czx3d0SFvIXPaF5W7rRyISNqdHBdLErntgp7n3ZnFgnqqFD
oNITFQdkDtoSlyTQw6drPLHmg+aEE3H6kXPnXrR4Iu7Hkf7dxNQF+fmx3zzx
Mv3Xj0LiHMWJTWG/PEGXr8goIX516WG237AnlLpm11wmtqrcqbl1yhOHTW25
qolFu7ZrLOOiwG9U8KaVePbHSc+B5RQCn10p+kOcq8bk6hGmsGPTofkTxPqh
jIudohRmsydtp4l3/9EfbxOjkBR+soDTlI3+yfeptTIUth1747icOHF9o84t
OQpVke6CosSScWXt1xQo+FyJvrWK2IUjRq5EhcLk4X0PpIifLhSry9ShsPdF
4pA6caAVp89RPQp9HvXc2sQ8h34sStanYJmbsViP2JSvdnucIYWL3ybb1hN/
sjv/N9KYgvbHtFPGxLHpRwt2g8IJlTvWJsQ3lnn89DenELr/bYgl8bbtlse8
LCncpzV3WxEPnVBb525FwbnJxtSWWGnl7H77jRQ6/Zff20x8VjJfzMiBQq/7
uTZH4v8OaT5U3UFhSswyx5k44U/jntVOFLYGWNm5ElPNfS2zruT7ZQfEeBA/
V4/cO+ROwftxyognsUk2j9RnTwo0IW4XOrFUkHJUozeFBzdXfvMmznx9R6bS
l4I4d8VyX+IFNLvn5/wplC8oVPYjDi/5FJO1k8Ld94Nq/sS9AmHyBwIpCNGy
VzOIHWLmv4wIJq9vPjM15/u9x+L9dlE4mzPduJNYz05WyTGMQk9BVWQA8YWb
N15v2EOB8+UD0UBi4TVWLP0ICvc+al2Yc9Kh9yqKkRQ2Wo1JBBFP/Al4t4Jc
EMR5BQ7OmeE+nbg4hkKpQOK7Ob9rPqr+N5bCOX1bkWBiaw2JD9/jKaQu2mk6
55rsioMdTAo2Szuc56y0wFSrlU3B4F+h+5xzgl521u6n0NJQu2nOvG98Ui6T
e+oDA2WlOcfSxnTykikInPw2PPd5P0qSutIOUdhe8Ld4zm6CK44wj1A42Opm
PefWmLK1YankvB/xvZ37PcZ963vo6RRsX/FtnfNlu9ZU+0wKrSGuN+f2Y/Ut
DwOzLAr2R8cWzTltzVCf9gkKw886reb2j+MwK0PmFIV3qvzhc/sbOiJoJJRD
6o999PDceXS5Fw1w5VIoG92WNndeWx/oZo2doZA34ZUwd55aOU7f3xZQUFnh
KDN33oULvp14eI6C/9d17+fqYVlwjGn1eQrvi+nRFPEI7Wx2TimF+gdRLHdi
n1J1i8MXKYi9YHyZq7fXgneHYspJ/eaeXOcyV+99PRvcr1IYOXatcAex3OaI
P5sqKXDtOl3tQHzy1sI84yqyP5ca7tgT7zusOCZRTe79h24l2REPjNQU8N+m
sOhJyuaNxM4eGzfNqyXr92QssCE20NxV1N1A6j8NGhbEZTkcW142kv2V7Ssx
JV7Fmfm36R6FtG23+UA8/ea6/fmHFK5tmzhtQFwbO8XBeE6eX3WoRY147Er/
ELuNQkmRkKcysUZPW9eZV+T/stKkQ564yPpiw8t3FCSv7UmXJD4k7MakfaYw
WMDbxU98z9oq1KWHwmiHb/US4plYHSqij9RH75YYnrnz6VmCi18pGHu+uDVL
+teOitpZ4WHSrxyMV/6c6689pYOaIxQmOrvXDhA/Ej7xaeMYBSt3buMeYsO4
kHr2FIWnTvcWvCeWspFI+DWfjszkp+FNxIM9zH/3l9FhtnX22zFiBZHgX11C
dEQf35t2lNjLxvnjXxE6isLMxZKI31Ro1mmK0bFgUcevKOI7cd1xZ2To4J4q
jfQwmcuH5jPhunT0z6wXkiZutNH4mbaWjkTZl0ariP/GiXWWraPjPe2Y3TLi
kN6RO11GdAynMhUWEDtcPR+70ZKOkwI3az+T+bPGlnta2pGOgStXAnKIdV6b
ta10pmNKR6Eqg9jSk1ki4EoHf97Vb8nEAXsmHWY96IjQ/CYcSXz99Pfydj86
0rkK9tjPrf/xzDNjLx33Xyes55pbf/RU07/jdKzZdueXC5nHsSKvs0dP0vHM
w+T4ZuLUAoHQH9l0aD8OkTMnrqw6JNZ+ho7GgFs8qsTTnbERVefpqHc482SG
5IU0Nbp8UBUdHZO77E4TX3+mePj9KzpWRkhLNM/lFem756fe0OH42qj3BnFg
pFPDqvd0NClfSysmlpJIGnXvpKPPKjU7mTgtpNezu48O0dXx+6yJA/jydL6P
kf19a+vRTPKRpO3yj9OiXnhxKzT/EslT02cvToiv8oL9kwjZHOK3w6bLaOJe
mI4STk8iTs0Js2Kt8cLWL7zCXsR/vz69xqXkhXLJ5b1CxG+SU5L+W++FyMoG
9j6S7440/9OQdPfC+YMT2YokDyKsX1Pc0ws/Y/j0hYhHVj3VWkn3Qlm1ax0H
sVvYGZ3lvl5YO5Gc+JbkS1UxQ32eYPL+4dGDicRPw6JoQ7Fe4P5P3erdWjb4
xUc2NeR6Ychx5bMQkmeP7fkaQHV4QY9jVflWkp9XWkaHbfvoheSXJaVriQtF
efdZdnkhu7b4qDjxtVqVAyq9Xghu6ub9SvL3c+7QvInvXjDUCe2ay+f/5Y69
TP/rhfwLcj3nNUl93ltgdHelN/JWM0Q+k/tArNDqpVLO3ljSJOa7WIX026uL
XGiu3gh94G78RZn0U7vRIjd3b1Sw1k00EdcffGJwku6NKsYpvjji+RPRfksC
vGF1NKv2J7mvJLW/rR2L9oanWaH8I0UyD/Mygh7nekM44UCLP7nvlCpytYR3
eaOlv2C7iRQbbWImf4O7vXE58tgrUeLppXEq/r3eSNXX1h1aQ/Lj2Eiq84A3
tJusT58lHmns3WY85A135p7JSXIfg9u9Tm4OHyw5ljpcJkHmV2ri7xwJH9A2
mMeOkvvcwpF5K+56+GC/NN93RREy/ypOpfZSPli86LDrqDAb34PVOXm8ffCJ
ZV/UQPz8i9ugnb8PMhnxdTuIcz7cvN+xywdFVUuXsYRIfm4K3j3BJH7HUn66
jPSjzPeP1c/5QG9KIsWan41ijavxZ7/4ILROUaeBh/y/hX5P3vzqA50pAX02
sc6URsSL7z6IFvXiNyduaKoI5BzygcL4H6MH3OT776hwCpjwwZC67qHHC0l+
iruipbfIF/IVLm2POcm8flTe36rki9k1ZnvLONhQ9Cqzmwn2xaLhgKD2cRY+
WFdf2/7dFxzdOgIb+lhoOxetStvjB90pmvDxVhYmKrcaSg37oc9v7+WMShZm
b+2uOhjij9cLzG0eHGfBVsPSInbUH18nNzObdrHwwF19Z+AeBlad+js8YMGC
oDfj9pkIBqaHWo1XE3swCvieRzJQV5M1Zm/OwtjuZdd0Yhnoi9hfWmPKgkzy
+NTMfgY21PjyJdJYYF6rP5J+ggGDF8e9xvVZMODeUlFVzYCJXktTgDILB5ek
zB+4zcCrIY2iI0osvBBodFhZxwCvUWdXuSILDDGdyfhGBjgZC4J/ybNwUlPU
1OoxA637a+r9ZVgYce162d7BQNjOe28MxFkAfYUc3ycGdquvXWcvxsJhP/t9
tM8M/LumNchYxYJU2D2xoj4G/lSGb8tawcLWgyW+wb8Y6L149Hu3EAu5hz/f
zBtiIL/96fuR5SwMpK9c3DbMwDquW8ILiZmnj1zWG2fgY2BYtJwgC0/y73Ps
nGRAMuBKvq4ACyIX/tmf/svAV6foZeb8LHhdXHu+dYZB5r9h29alLFyuCB2f
nWUgJMS0w+M/Fv4HHihkog==
"]]},
Annotation[#, "Charting`Private`Tag$4311#1"]& ],
TagBox[
{RGBColor[1, 0, 1], AbsoluteThickness[1.6], Opacity[1.],
LineBox[CompressedData["
1:eJwV13c81V8YB3BFUSgVkpXkZyXzGpkfElJJSLbvNXKFrGRf7lU0hNJSUlah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