-
Notifications
You must be signed in to change notification settings - Fork 0
Expand file tree
/
Copy pathtutorial_database.bib
More file actions
815 lines (739 loc) · 29.6 KB
/
Copy pathtutorial_database.bib
File metadata and controls
815 lines (739 loc) · 29.6 KB
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
% This file was created with JabRef 2.10.
% Encoding: UTF-8
@article{Otsuka1991,
author = {Kenju Otsuka and Jyh-Long Chern},
journal = {Opt. Lett.},
keywords = {},
number = {22},
pages = {1759--1761},
publisher = {OSA},
title = {High-speed picosecond pulse generation in semiconductor lasers withincoherent optical feedback},
volume = {16},
month = {Nov},
year = {1991},
url = {http://ol.osa.org/abstract.cfm?URI=ol-16-22-1759},
doi = {10.1364/OL.16.001759},
abstract = {A novel method for producing high-speed picosecond optical pulses fromsemiconductor laser diodes that uses incoherent optical feedback is proposed.The incoherent optical feedback provides a successive pulselike modulation incarrier density and drives the system to a self-sustained pulsation state whoserepetition rate is determined by relaxation oscillations.},
}
@article {Wang2015,
AUTHOR = {Wang, Hongbin and Jiang, Weihua and Ding, Yuting},
TITLE = {Bifurcation phenomena and control analysis in class-{B} laser
system with delayed feedback},
JOURNAL = {Nonlinear Dynam.},
FJOURNAL = {Nonlinear Dynamics. An International Journal of Nonlinear
Dynamics and Chaos in Engineering Systems},
VOLUME = {79},
YEAR = {2015},
NUMBER = {4},
PAGES = {2421--2438},
ISSN = {0924-090X},
MRCLASS = {34H20},
MRNUMBER = {3317453},
DOI = {10.1007/s11071-014-1822-2},
URL = {http://dx.doi.org/10.1007/s11071-014-1822-2},
}
@Article{Bogacki1989,
Title = {A 3 (2) pair of {R}unge-{K}utta formulas},
Author = {Bogacki, Przemyslaw and Shampine, Lawrence F},
Journal = {Applied Mathematics Letters},
Year = {1989},
Number = {4},
Pages = {321--325},
Volume = {2},
Owner = {maikel},
Publisher = {Elsevier},
Timestamp = {2016.02.02}
}
@article{Engelborghs2001,
AUTHOR = {Engelborghs, K. and Luzyanina, T. and In 't Hout, K. J. and
Roose, D.},
TITLE = {Collocation methods for the computation of periodic solutions
of delay differential equations},
JOURNAL = {SIAM J. Sci. Comput.},
FJOURNAL = {SIAM Journal on Scientific Computing},
VOLUME = {22},
YEAR = {2000},
NUMBER = {5},
PAGES = {1593--1609},
ISSN = {1064-8275},
CODEN = {SJOCE3},
MRCLASS = {65L60 (65L20)},
MRNUMBER = {1813288},
MRREVIEWER = {J. C. Butcher},
DOI = {10.1137/S1064827599363381},
URL = {http://dx.doi.org/10.1137/S1064827599363381},
}
@article {Farmer1982,
AUTHOR = {Farmer, J. Doyne},
TITLE = {Chaotic attractors of an infinite-dimensional dynamical
system},
JOURNAL = {Phys. D},
FJOURNAL = {Physica D. Nonlinear Phenomena},
VOLUME = {4},
YEAR = {1981/82},
NUMBER = {3},
PAGES = {366--393},
ISSN = {0167-2789},
CODEN = {FDNPDT},
MRCLASS = {58F13 (34K99)},
MRNUMBER = {657740},
MRREVIEWER = {Richard C. Churchill},
DOI = {10.1016/0167-2789(82)90042-2},
URL = {http://dx.doi.org/10.1016/0167-2789(82)90042-2},
}
@article {Giannakopoulos2001,
AUTHOR = {Giannakopoulos, Fotios and Zapp, Andreas},
TITLE = {Bifurcations in a planar system of differential delay
equations modeling neural activity},
JOURNAL = {Phys. D},
FJOURNAL = {Physica D. Nonlinear Phenomena},
VOLUME = {159},
YEAR = {2001},
NUMBER = {3-4},
PAGES = {215--232},
ISSN = {0167-2789},
CODEN = {PDNPDT},
MRCLASS = {92C20 (34K18 34K60 37G15 37N25)},
MRNUMBER = {1868527},
MRREVIEWER = {Tom{\'a}{\v{s}} Gedeon},
DOI = {10.1016/S0167-2789(01)00337-2},
URL = {http://dx.doi.org/10.1016/S0167-2789(01)00337-2},
}
@Article{Glass1979,
author = {Glass, Leon and Mackey, Michael C.},
title = {PATHOLOGICAL CONDITIONS RESULTING FROM INSTABILITIES IN PHYSIOLOGICAL CONTROL SYSTEMS*},
journal = {Annals of the New York Academy of Sciences},
volume = {316},
number = {1},
publisher = {Blackwell Publishing Ltd},
issn = {1749-6632},
url = {http://dx.doi.org/10.1111/j.1749-6632.1979.tb29471.x},
doi = {10.1111/j.1749-6632.1979.tb29471.x},
pages = {214--235},
year = {1979},
}
@book{Hassard1981,
AUTHOR = {Hassard, Brian D. and Kazarinoff, Nicholas D. and Wan, Yieh
Hei},
TITLE = {Theory and applications of {H}opf bifurcation},
SERIES = {London Mathematical Society Lecture Note Series},
VOLUME = {41},
PUBLISHER = {Cambridge University Press, Cambridge-New York},
YEAR = {1981},
PAGES = {v+311 pp. (microfiche insert)},
ISBN = {0-521-23158-2},
MRCLASS = {58F14 (34C25 58-04 73J10 76E30)},
MRNUMBER = {603442},
MRREVIEWER = {Ralph Abraham},
}
@Article{Humphries2012,
AUTHOR = {Humphries, A. R. and DeMasi, O. A. and Magpantay, F. M. G. and
Upham, F.},
TITLE = {Dynamics of a delay differential equation with multiple
state-dependent delays},
JOURNAL = {Discrete Contin. Dyn. Syst.},
FJOURNAL = {Discrete and Continuous Dynamical Systems. Series A},
VOLUME = {32},
YEAR = {2012},
NUMBER = {8},
PAGES = {2701--2727},
ISSN = {1078-0947},
MRCLASS = {34K18 (34K13 34K28 39B12)},
MRNUMBER = {2903986},
MRREVIEWER = {Ana Paula S. Dias},
DOI = {10.3934/dcds.2012.32.2701},
URL = {http://dx.doi.org/10.3934/dcds.2012.32.2701},
}
@Article{Hutchinson1948,
Title = {Circular causal systems in ecology},
Author = {Hutchinson, G Evelyn},
Journal = {Annals of the New York Academy of Sciences},
Year = {1948},
Number = {4},
Pages = {221--246},
Volume = {50},
Owner = {maikel},
Publisher = {Wiley Online Library},
Timestamp = {2016.01.23}
}
@MastersThesis{Janssens2010,
Title = {{On a normalization technique for codimension two bifurcations of equilibria of delay differential equations}},
Author = {Janssens, Sebastiaan},
School = {Universiteit Utrecht},
Year = {2007},
Address = {the Netherlands},
Url = {http://dspace.library.uu.nl/handle/1874/312252},
note = {\url{http://dspace.library.uu.nl/handle/1874/312252}}
}
@Article{Kaplan1974,
AUTHOR = {Kaplan, James L. and Yorke, James A.},
TITLE = {Ordinary differential equations which yield periodic solutions
of differential delay equations},
JOURNAL = {J. Math. Anal. Appl.},
FJOURNAL = {Journal of Mathematical Analysis and Applications},
VOLUME = {48},
YEAR = {1974},
PAGES = {317--324},
ISSN = {0022-247x},
MRCLASS = {34K15},
MRNUMBER = {0364815},
MRREVIEWER = {S. P. Hastings},
}
@Book{Kuznetsov2013,
AUTHOR = {Kuznetsov, {\mbox {Yu.A}}},
TITLE = {Elements of {A}pplied {B}ifurcation {T}heory},
SERIES = {Applied Mathematical Sciences},
VOLUME = {112},
EDITION = {Third},
PUBLISHER = {Springer-Verlag, New York},
YEAR = {2004},
PAGES = {xxii+631},
ISBN = {0-387-21906-4},
MRCLASS = {37Gxx (34-04 34C23 37-04 37M20)},
MRNUMBER = {2071006},
DOI = {10.1007/978-1-4757-3978-7},
URL = {http://dx.doi.org/10.1007/978-1-4757-3978-7},
}
@InProceedings{Liu2013,
Title = {Bogdanov-{T}akens bifurcation of a delayed ratio-dependent {H}olling-{T}anner predator prey System},
Author = {Liu, Xia and Liu, Yanwei and Wang, Jinling},
Booktitle = {Abstract and Applied Analysis},
Year = {2013},
Organization = {Hindawi Publishing Corporation},
Volume = {2013},
doi = "10.1155/2013/453402",
url = "http://dx.doi.org/10.1155/2013/453402",
note = "\url{http://dx.doi.org/10.1155/2013/453402}"
}
@InCollection{Roose2007,
AUTHOR = {Roose, Dirk and Szalai, Robert},
TITLE = {Continuation and bifurcation analysis of delay differential
equations},
BOOKTITLE = {Numerical continuation methods for dynamical systems},
SERIES = {Underst. Complex Syst.},
PAGES = {359--399},
PUBLISHER = {Springer, Dordrecht},
YEAR = {2007},
MRCLASS = {37M20 (34K18 65P30)},
MRNUMBER = {2359338},
MRREVIEWER = {Tatyana Luzyanina},
DOI = {10.1007/978-1-4020-6356-5_12},
URL = {http://dx.doi.org/10.1007/978-1-4020-6356-5_12},
}
@Article{Samaey2002,
AUTHOR = {Samaey, Giovanni and Engelborghs, Koen and Roose, Dirk},
TITLE = {Numerical computation of connecting orbits in delay
differential equations},
JOURNAL = {Numer. Algorithms},
FJOURNAL = {Numerical Algorithms},
VOLUME = {30},
YEAR = {2002},
NUMBER = {3-4},
PAGES = {335--352},
ISSN = {1017-1398},
MRCLASS = {34K18 (34C37 37M20 65P40)},
MRNUMBER = {1927509},
DOI = {10.1023/A:1020102317544},
URL = {http://dx.doi.org/10.1023/A:1020102317544},
}
@Article{Shampine1997,
AUTHOR = {Shampine, Lawrence F. and Reichelt, Mark W.},
TITLE = {The {MATLAB} {ODE} suite},
NOTE = {Dedicated to C. William Gear on the occasion of his 60th
birthday},
JOURNAL = {SIAM J. Sci. Comput.},
FJOURNAL = {SIAM Journal on Scientific Computing},
VOLUME = {18},
YEAR = {1997},
NUMBER = {1},
PAGES = {1--22},
ISSN = {1064-8275},
CODEN = {SJOCE3},
MRCLASS = {65Y15 (34-04 34A50 65L05 65L06)},
MRNUMBER = {1433374},
DOI = {10.1137/S1064827594276424},
URL = {http://dx.doi.org/10.1137/S1064827594276424},
}
@Unpublished{extensionsDDEBifTool@JanSieber,
Title = {Extended systems for delay differential equations
as implemented in the extensions to {DDE}-{B}if{T}ool},
Author = {Jan Sieber},
URL = {https://s3-eu-west-1.amazonaws.com/pfigshare-u-files/1134364/ExtendedSystems.pdf},
note = {\url{https://s3-eu-west-1.amazonaws.com/pfigshare-u-files/1134364/ExtendedSystems.pdf}}
}
@Manual{extensionsddebiftool_extra_psol,
Title = {Description of extensions ddebiftool\_extra\_psol and ddebiftool\_extra\_rotsym},
Author = {Jan Sieber},
Month = {08},
Year = {2015},
URL = {http://ddebiftool.sourceforge.net/Extra_psol_extension.pdf},
note = {\url{http://ddebiftool.sourceforge.net/Extra_psol_extension.pdf}}
}
@Article{Sieber2014,
Title = {{DDE}-{B}IF{T}OOL {M}anual-{B}ifurcation analysis of delay differential equations},
Author = {Sieber, Jan and Engelborghs, Koen and Luzyanina, Tatyana and Samaey, Giovanni and Roose, Dirk},
Journal = {arXiv preprint arXiv:1406.7144},
Year = {2014},
howpublished = {{\tt arXiv:1406.7144~[math.DS]}}
}
@article{Sprott2007,
AUTHOR = {Sprott, J. C.},
TITLE = {A simple chaotic delay differential equation},
JOURNAL = {Phys. Lett. A},
FJOURNAL = {Physics Letters. A},
VOLUME = {366},
YEAR = {2007},
NUMBER = {4-5},
PAGES = {397--402},
ISSN = {0375-9601},
CODEN = {PYLAAG},
MRCLASS = {34C28 (37D45)},
MRNUMBER = {2570698},
DOI = {10.1016/j.physleta.2007.01.083},
URL = {http://dx.doi.org/10.1016/j.physleta.2007.01.083},
}
@article{Stirzaker1975,
Title = {On a population model},
Author = {Stirzaker, D},
Journal = {Mathematical Biosciences},
Year = {1975},
Number = {3},
Pages = {329--336},
Volume = {23},
Publisher = {Elsevier}
}
@Misc{Szalai2013,
Title = {Knut: A continuation and bifurcation software for delay-differential equations (version 8)},
Author = {Szalai, R},
Year = {2013},
Publisher = {Department of Engineering Mathematics, University of Bristol, UK},
Url = {http://rs1909.github.io/knut/},
note = {\url{http://rs1909.github.io/knut/}}
}
@PhdThesis{Visser2013,
Title = {From spiking neurons to brain waves},
Author = {Sid {Visser}},
School = {University of Twente},
Year = {2013},
Address = {Enschede},
Month = {March},
Eprintid = {23164},
Funding = {NWO 635.100.019, From spiking neurons to brain waves},
HowPublished = {http://eprints.eemcs.utwente.nl/23164/},
Id_number = {10.3990/1.9789036535083},
Isbn_13 = {978-90-365-3508-3},
Keywords = {Mathematical modeling, Neural networks, Dynamical system's theory},
Num_pages = {153},
Official_url = {http://dx.doi.org/10.3990/1.9789036535083},
Phd_type = {A},
Research_groups = {EWI-AA: Applied Analysis, TNW-CNPH: Clinical Neurophysiology},
Research_programs = {MIRA-Neural and Motor Systems},
Research_projects = {Spiking Neurons: From spiking neurons to brain waves},
Supervisors = {S. A. {van Gils} and M. J. A. M. {van Putten}},
note = {\url{http://eprints.eemcs.utwente.nl/23164/}}
}
@Article{Visser2012,
AUTHOR = {Visser, Sid and Meijer, Hil G. E. and van Putten, Michel J. A.
M. and van Gils, Stephan A.},
TITLE = {Analysis of stability and bifurcations of fixed points and
periodic solutions of a lumped model of neocortex with two
delays},
JOURNAL = {J. Math. Neurosci.},
FJOURNAL = {Journal of Mathematical Neuroscience},
VOLUME = {2},
YEAR = {2012},
PAGES = {Art. 8, 24},
ISSN = {2190-8567},
MRCLASS = {34K18 (92C20)},
MRNUMBER = {2990961},
MRREVIEWER = {Shangjiang Guo},
DOI = {10.1186/2190-8567-2-8},
URL = {http://dx.doi.org/10.1186/2190-8567-2-8},
}
@misc{FLU09a,
title = {pydelay -- a python tool for solving delay differential equations},
author = {Flunkert, V. and Sch{\"o}ll, E. },
year = {2009},
howpublished = {{\tt arXiv:0911.1633~[nlin.CD]}},
}
@unpublished{Humphries2016,
Author = {Tony Humphries},
Year = {2016},
Title = {Lecture 3: {C}ontinuation of {DDE}s with {S}tate-{D}ependent {D}elays},
note = {\url{https://www.math.auckland.ac.nz/~hinke/meetings/NZMRI/materials/NZMRI16-Tony3.pdf}}
}
@Article{kouznetsov2014improved,
Title = {{Improved homoclinic predictor for Bogdanov-Takens bifurcation}},
Author = {Kuznetsov, {\mbox {Yu.A}} and Meijer, H. G. E. and {Al Hdaibat}, B and Govaerts, W},
Journal = {International journal of bifurcation and chaos in applied sciences and engineering},
Year = {2014},
Number = {4},
Pages = {1450057},
Volume = {24},
Publisher = {World Scientific}
}
@article {gray-scott2015,
AUTHOR = {Kuznetsov, {\mbox {Yu.A}}. and Meijer, H. G. E. and Al-Hdaibat, B. and
Govaerts, W.},
TITLE = {Accurate approximation of homoclinic solutions in
{G}ray-{S}cott kinetic model},
JOURNAL = {Internat. J. Bifur. Chaos Appl. Sci. Engrg.},
FJOURNAL = {International Journal of Bifurcation and Chaos in Applied
Sciences and Engineering},
VOLUME = {25},
YEAR = {2015},
NUMBER = {9},
PAGES = {1550125, 10},
ISSN = {0218-1274},
MRCLASS = {92C45 (37G15)},
MRNUMBER = {3393913},
DOI = {10.1142/S0218127415501254},
URL = {http://dx.doi.org/10.1142/S0218127415501254},
}
@Article{Al-Hdaibat2016,
Title = {{Initialization of homoclinic solutions near Bogdanov--Takens points: Lindstedt--Poincar\'e compared with regular perturbation method}},
Author = {Al-Hdaibat, B and Govaerts, W and Kuznetsov, {\mbox {Yu.A}} and Meijer, H. G. E.},
Journal = {SIAM Journal on Applied Dynamical Systems},
Year = {2016},
Number = {2},
Pages = {952--980},
Volume = {15},
__markedentry = {[maikel:]},
Owner = {maikel},
Publisher = {SIAM},
Timestamp = {2016.06.19}
}
@Article{Kuznetsov2008,
Title = {{Switching to nonhyperbolic cycles from codim 2 bifurcations of equilibria in ODEs}},
Author = {Kuznetsov, {\mbox {Yu.A}} and Meijer, H. G. E. and Govaerts, Willy and Sautois, B},
Journal = {Physica D: Nonlinear Phenomena},
Year = {2008},
Number = {23},
Pages = {3061--3068},
Volume = {237},
Owner = {maikel},
Publisher = {Elsevier},
Timestamp = {2016.03.30}
}
@Book{Broer1991,
Title = {Structures in Dynamics: Finite Dimensional Deterministic Studies},
Author = {Broer, Hendrik Walter and Dumortier, F and Van Strien, SJ and Takens, F},
Publisher = {Elsevier},
Year = {1991},
Volume = {2},
__markedentry = {[maikel:6]},
Owner = {maikel},
Timestamp = {2016.06.20}
}
@Article{Huang@2008Homoclinic,
Title = {{Homoclinic orbits and Hopf bifurcations in delay differential systems with T-B singularity}},
Author = {{Xu}, Yingxiang and {Huang}, M.},
Journal = {Journal of Differential Equations},
Year = {2008},
Pages = {582-598},
Volume = {244},
Adsnote = {Provided by the SAO/NASA Astrophysics Data System},
Adsurl = {http://adsabs.harvard.edu/abs/2008JDE...244..582X},
Doi = {10.1016/j.jde.2007.09.003}
}
@article {Zhang@2009BogdanovTakensraey,
AUTHOR = {Zhang, Cun-Hua and Yan, Xiang-Ping},
TITLE = {Bogdanov-{T}akens singularity in a network of two coupled
neurons with delayed feedbacks},
JOURNAL = {J. Appl. Math. Comput.},
FJOURNAL = {Journal of Applied Mathematics and Computing},
VOLUME = {29},
YEAR = {2009},
NUMBER = {1-2},
PAGES = {469--479},
ISSN = {1598-5865},
MRCLASS = {34K18 (34K17 37N25 92C20)},
MRNUMBER = {2472127},
MRREVIEWER = {Bernhard Lani-Wayda},
DOI = {10.1007/s12190-008-0150-4},
URL = {http://dx.doi.org/10.1007/s12190-008-0150-4},
}
@Article{wang2013bogdanov,
Title = {Bogdanov-{T}akens singularity in the comprehensive national power model with time delays},
Author = {Wang, Jingnan and Jiang, Weihua},
Journal = {Journal of Applied Analysis and Computation},
Year = {2013},
Number = {1},
Pages = {81--94},
Volume = {3}
}
@Article{he2012bogdanov,
Title = {Bogdanov--{T}akens bifurcation in a single inertial neuron model with delay},
Author = {He, Xing and Li, Chuandong and Shu, Yonglu},
Journal = {Neurocomputing},
Year = {2012},
Pages = {193--201},
Volume = {89},
Publisher = {Elsevier}
}
@article {li2011hopf,
AUTHOR = {Li, Yanqiu and Jiang, Weihua},
TITLE = {Hopf and {B}ogdanov-{T}akens bifurcations in a coupled
{F}itz{H}ugh-{N}agumo neural system with delay},
JOURNAL = {Nonlinear Dynam.},
FJOURNAL = {Nonlinear Dynamics. An International Journal of Nonlinear
Dynamics and Chaos in Engineering Systems},
VOLUME = {65},
YEAR = {2011},
NUMBER = {1-2},
PAGES = {161--173},
ISSN = {0924-090X},
MRCLASS = {37G10 (34K18 37N25 92C20)},
MRNUMBER = {2812016},
MRREVIEWER = {Weinian Zhang},
DOI = {10.1007/s11071-010-9881-5},
URL = {http://dx.doi.org/10.1007/s11071-010-9881-5},
}
@article {dong2013bogdanov,
AUTHOR = {Dong, Tao and Liao, Xiaofeng},
TITLE = {Bogdanov-{T}akens bifurcation in a tri-neuron {BAM} neural
network model with multiple delays},
JOURNAL = {Nonlinear Dynam.},
FJOURNAL = {Nonlinear Dynamics. An International Journal of Nonlinear
Dynamics and Chaos in Engineering Systems},
VOLUME = {71},
YEAR = {2013},
NUMBER = {3},
PAGES = {583--595},
ISSN = {0924-090X},
MRCLASS = {34K18},
MRNUMBER = {3015263},
MRREVIEWER = {Changjin Xu},
DOI = {10.1007/s11071-012-0683-9},
URL = {http://dx.doi.org/10.1007/s11071-012-0683-9},
}
@Article{jiang2007bogdanov,
Title = {{Bogdanov--Takens singularity in van der Pol's oscillator with delayed feedback}},
Author = {Jiang, Weihua and Yuan, Yuan},
Journal = {Physica D: Nonlinear Phenomena},
Year = {2007},
Number = {2},
Pages = {149--161},
Volume = {227},
Publisher = {Elsevier}
}
@Article{qesmi2007symbolic,
Title = {Symbolic computation for center manifolds and normal forms of {B}ogdanov bifurcation in retarded functional differential equations},
Author = {Qesmi, R and Babram, M Ait and Hbid, ML},
Journal = {Nonlinear Analysis: Theory, Methods \& Applications},
Year = {2007},
Number = {12},
Pages = {2833--2851},
Volume = {66},
Publisher = {Elsevier}
}
@incollection {Beyn@2002continuation,
AUTHOR = {Beyn, Wolf-J{\"u}rgen and Champneys, Alan and Doedel, Eusebius
and Govaerts, Willy and Kuznetsov, {\mbox {Yu.A}}. and Sandstede,
Bj{\"o}rn},
TITLE = {Numerical continuation, and computation of normal forms},
BOOKTITLE = {Handbook of dynamical systems, {V}ol. 2},
PAGES = {149--219},
PUBLISHER = {North-Holland, Amsterdam},
YEAR = {2002},
MRCLASS = {37M20 (34C20 34C23 37Gxx 65P30)},
MRNUMBER = {1900655},
MRREVIEWER = {Gerd P{\"o}nisch},
DOI = {10.1016/S1874-575X(02)80025-X},
URL = {http://dx.doi.org/10.1016/S1874-575X(02)80025-X},
}
@Article{Ma2011,
Title = {Fold--{H}opf bifurcations of the {R}ose--{H}indmarsh model with time delay},
Author = {Ma, Suqi and Feng, Zhaosheng},
Journal = {International Journal of Bifurcation and Chaos},
Year = {2011},
Number = {02},
Pages = {437--452},
Volume = {21},
Owner = {maikel},
Publisher = {World Scientific},
Timestamp = {2016.04.15}
}
@Article{Hindmarsh1984,
Title = {A model of neuronal bursting using three coupled first order differential equations},
Author = {Hindmarsh, JL and Rose, RM},
Journal = {Proceedings of the Royal Society of London B: Biological Sciences},
Year = {1984},
Number = {1222},
Pages = {87--102},
Volume = {221},
Owner = {maikel},
Publisher = {The Royal Society},
Timestamp = {2016.04.15}
}
@Article{Hindmarsh1982,
Title = {A model of the nerve impulse using two first-order differential equations},
Author = {Hindmarsh, JL and Rose, RM},
Journal = {Nature},
Year = {1982},
Number = {5853},
Pages = {162--164},
Volume = {296},
Owner = {maikel},
Timestamp = {2016.04.15}
}
@article {Peng2013,
AUTHOR = {Peng, Jian and Wang, Lianhua and Zhao, Yueyu and Zhao,
Yaobing},
TITLE = {Bifurcation analysis in active control system with time delay
feedback},
JOURNAL = {Appl. Math. Comput.},
FJOURNAL = {Applied Mathematics and Computation},
VOLUME = {219},
YEAR = {2013},
NUMBER = {19},
PAGES = {10073--10081},
ISSN = {0096-3003},
CODEN = {AMHCBQ},
MRCLASS = {34K18 (34K20 93B52)},
MRNUMBER = {3055724},
DOI = {10.1016/j.amc.2013.04.014},
URL = {http://dx.doi.org/10.1016/j.amc.2013.04.014},
}
@article {Ding@2016,
AUTHOR = {Ding, Yuting and Cao, Jun and Jiang, Weihua},
TITLE = {Double {H}opf bifurcation in active control system with
delayed feedback: application to glue dosing processes for
particleboard},
JOURNAL = {Nonlinear Dynam.},
FJOURNAL = {Nonlinear Dynamics. An International Journal of Nonlinear
Dynamics and Chaos in Engineering Systems},
VOLUME = {83},
YEAR = {2016},
NUMBER = {3},
PAGES = {1567--1576},
ISSN = {0924-090X},
MRCLASS = {34K18 (37G15 93B52)},
MRNUMBER = {3449494},
DOI = {10.1007/s11071-015-2431-4},
URL = {http://dx.doi.org/10.1007/s11071-015-2431-4},
}
@InCollection{Meijer2009,
Title = {Numerical bifurcation analysis},
Author = {Meijer, H. G. E. and Dercole, Fabio and Oldeman, Bart},
Booktitle = {Encyclopedia of Complexity and Systems Science},
Publisher = {Springer},
Year = {2009},
Pages = {6329--6352},
Owner = {maikel},
Timestamp = {2016.03.30}
}
@article {Bramburger2014,
AUTHOR = {Bramburger, Jason and Dionne, Benoit and LeBlanc, Victor G.},
TITLE = {Zero-{H}opf bifurcation in the {V}an der {P}ol oscillator with
delayed position and velocity feedback},
JOURNAL = {Nonlinear Dynam.},
FJOURNAL = {Nonlinear Dynamics. An International Journal of Nonlinear
Dynamics and Chaos in Engineering Systems},
VOLUME = {78},
YEAR = {2014},
NUMBER = {4},
PAGES = {2959--2973},
ISSN = {0924-090X},
MRCLASS = {34K18 (34K28 37G05)},
MRNUMBER = {3276936},
MRREVIEWER = {Shangjiang Guo},
DOI = {10.1007/s11071-014-1638-0},
URL = {http://dx.doi.org/10.1007/s11071-014-1638-0},
}
@article {Jiang2008,
AUTHOR = {Jiang, Weihua and Wei, Junjie},
TITLE = {Bifurcation analysis in van der {P}ol's oscillator with
delayed feedback},
JOURNAL = {J. Comput. Appl. Math.},
FJOURNAL = {Journal of Computational and Applied Mathematics},
VOLUME = {213},
YEAR = {2008},
NUMBER = {2},
PAGES = {604--615},
ISSN = {0377-0427},
CODEN = {JCAMDI},
MRCLASS = {34K20 (34C20 34K18 37G05 37G10 93B52)},
MRNUMBER = {2392579},
DOI = {10.1016/j.cam.2007.01.041},
URL = {http://dx.doi.org/10.1016/j.cam.2007.01.041},
}
@article {Jiang2010,
AUTHOR = {Jiang, Weihua and Wang, Hongbin},
TITLE = {Hopf-transcritical bifurcation in retarded functional
differential equations},
JOURNAL = {Nonlinear Anal.},
FJOURNAL = {Nonlinear Analysis. Theory, Methods \& Applications. An
International Multidisciplinary Journal. Series A: Theory and
Methods},
VOLUME = {73},
YEAR = {2010},
NUMBER = {11},
PAGES = {3626--3640},
ISSN = {0362-546X},
CODEN = {NOANDD},
MRCLASS = {34K18 (37G15)},
MRNUMBER = {2718165},
MRREVIEWER = {Wei Nian Zhang},
DOI = {10.1016/j.na.2010.07.043},
URL = {http://dx.doi.org/10.1016/j.na.2010.07.043},
}
@Article{Guo2008,
Title = {Two-parameter bifurcations in a network of two neurons with multiple delays},
Author = {Guo, Shangjiang and Chen, Yuming and Wu, Jianhong},
Journal = {Journal of differential equations},
Year = {2008},
Number = {2},
Pages = {444--486},
Volume = {244},
Owner = {maikel},
Publisher = {Elsevier},
Timestamp = {2016.04.12}
}
@article {Wu2012,
AUTHOR = {Wu, Xiaoqin P.},
TITLE = {Zero-{H}opf bifurcation analysis of a {K}aldor-{K}alecki model
of business cycle with delay},
JOURNAL = {Nonlinear Anal. Real World Appl.},
FJOURNAL = {Nonlinear Analysis. Real World Applications. An International
Multidisciplinary Journal},
VOLUME = {13},
YEAR = {2012},
NUMBER = {2},
PAGES = {736--754},
ISSN = {1468-1218},
MRCLASS = {91B64 (34K18 91B55)},
MRNUMBER = {2846877},
MRREVIEWER = {Lorenzo Peccati},
DOI = {10.1016/j.nonrwa.2011.08.013},
URL = {http://dx.doi.org/10.1016/j.nonrwa.2011.08.013},
}
@article {Xu2010,
AUTHOR = {Zhen, Bin and Xu, Jian},
TITLE = {Bautin bifurcation analysis for synchronous solution of a
coupled {FHN} neural system with delay},
JOURNAL = {Commun. Nonlinear Sci. Numer. Simul.},
FJOURNAL = {Communications in Nonlinear Science and Numerical Simulation},
VOLUME = {15},
YEAR = {2010},
NUMBER = {2},
PAGES = {442--458},
ISSN = {1007-5704},
MRCLASS = {34K18 (34K20 37N25 92B20)},
MRNUMBER = {2572575},
MRREVIEWER = {Wendi Wang},
DOI = {10.1016/j.cnsns.2009.04.006},
URL = {http://dx.doi.org/10.1016/j.cnsns.2009.04.006},
}
@book {Hale@1977,
AUTHOR = {Hale, Jack},
TITLE = {Theory of functional differential equations},
EDITION = {Second},
NOTE = {Applied Mathematical Sciences, Vol. 3},
PUBLISHER = {Springer-Verlag, New York-Heidelberg},
YEAR = {1977},
PAGES = {x+365},
MRCLASS = {34KXX},
MRNUMBER = {0508721},
MRREVIEWER = {R. R. Ahmerov},
}