References¶
- AHGKM16
B. Al-Hdaibat, W. Govaerts, Yu. A. Kuznetsov, and H. G. E. Meijer. Initialization of homoclinic solutions near bogdanov–takens points: lindstedt–poincaré compared with regular perturbation method. SIAM Journal on Applied Dynamical Systems, 15(2):952–980, 2016. arXiv:https://doi.org/10.1137/15M1017491, doi:10.1137/15M1017491.
- BAH15
Willy Govaerts Bashir Al-Hdaibat. Continuation of homoclinic orbits starting from a generic bogdanov-takens point with matcont. SourceForge, 2015. URL: https://sourceforge.net/projects/matcont/files/NewestDocumentation/MatContODE/AdvancedTutorials/labinithom2.pdf.
- BR00
A.S. Bazanella and R. Reginatto. Robustness margins for indirect field-oriented control of induction motors. IEEE Trans. Automat. Contr., 45(6):1226–1231, June 2000. doi:10.1109/9.863613.
- Baz85
A. D. Bazykin. \cyr Matematicheskaya biofizika vzaimodeĭ \cyr stvuyushchikh populyatsiĭ. “Nauka”, Moscow, 1985.
- Bey94
W.-J. Beyn. Numerical analysis of homoclinic orbits emanating from a takens-bogdanov point. IMA J Numer Anal, 14(3):381–410, 1994. doi:10.1093/imanum/14.3.381.
- BS79
F. Brauer and A.C. Soudack. Stability regions and transition phenomena for harvested predator-prey systems. J. Math. Biol., 7(4):319–337, 1979. doi:10.1007/bf00275152.
- BIK78
V.I. Bykov, G.S. Iablonskii, and V.F. Kim. Simple-model of kinetic auto-oscillation model in catalytic reaction of co-oxidation. Doklady Akademii Nauk SSSR, 242:637–639, 1978.
- DGK+08
A. Dhooge, W. Govaerts, Yu.A. Kuznetsov, H.G.E. Meijer, and B. Sautois. New features of the software matcontfor bifurcation analysis of dynamical systems. Mathematical and Computer Modelling of Dynamical Systems, 14(2):147–175, April 2008. doi:10.1080/13873950701742754.
- HH52a
A. L. Hodgkin and A. F. Huxley. A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology, 117(4):500–544, 1952. arXiv:https://physoc.onlinelibrary.wiley.com/doi/pdf/10.1113/jphysiol.1952.sp004764, doi:https://doi.org/10.1113/jphysiol.1952.sp004764.
- HH52b
A. L. Hodgkin and A. F. Huxley. Currents carried by sodium and potassium ions through the membrane of the giant axon of loligo. The Journal of Physiology, 116(4):449–472, 1952. arXiv:https://physoc.onlinelibrary.wiley.com/doi/pdf/10.1113/jphysiol.1952.sp004717, doi:https://doi.org/10.1113/jphysiol.1952.sp004717.
- JP21
C. B. Jepsen and F. K. Popov. Homoclinic rg flows, or when relevant operators become irrelevant. arXiv, 2021. URL: arXiv:2105.01625v1.
- Khi90
A. I. Khibnik. LINLBF: A Program for Continuation and Bifurcation Analysis of Equilibria Up to Codimension Three, pages 283–296. Springer Netherlands, Dordrecht, 1990. doi:10.1007/978-94-009-0659-4_19.
- Kuz21
Bosschaert M.M. Kuznetsov, I.A. Interplay between normal forms and center manifold reduction for homoclinic predictors near bogdanov-takens bifurcation. arXiv, 2021.
- KMGS08
Yu.A. Kuznetsov, H.G.E. Meijer, W. Govaerts, and B. Sautois. Switching to nonhyperbolic cycles from codim 2 bifurcations of equilibria in odes. Physica D: Nonlinear Phenomena, 237(23):3061–3068, December 2008. doi:10.1016/j.physd.2008.06.006.
- Kuz04
Yu.A Kuznetsov. Elements of Applied Bifurcation Theory. Volume 112 of Applied Mathematical Sciences. Springer-Verlag, New York, third edition, 2004. ISBN 0-387-21906-4. doi:10.1007/978-1-4757-3978-7.
- ML81
C. Morris and H. Lecar. Voltage oscillations in the barnacle giant muscle fiber. Biophysical Journal, 35(1):193–213, July 1981. doi:10.1016/s0006-3495(81)84782-0.
- SGAR08
F. Salas, F. Gordillo, J. Aracil, and R. Reginatto. Codimension-two bifurcations in indirect field oriented control of induction motor drives. Int. J. Bifurcation Chaos, 18(03):779–792, March 2008. doi:10.1142/s0218127408020641.
- SZ14
Chunhua Shan and Huaiping Zhu. Bifurcations and complex dynamics of an sir model with the impact of the number of hospital beds. Journal of Differential Equations, 257(5):1662–1688, September 2014. doi:10.1016/j.jde.2014.05.030.
- ShilNikovNN95
A. Shil'Nikov, G. Nicolis, and C. Nicolis. Bifurcation and predictability analysis of a low-order atmospheric circulation model. Int. J. Bifurcation Chaos, 05(06):1701–1711, December 1995. doi:10.1142/s0218127495001253.
- SEL+14
Jan Sieber, Koen Engelborghs, Tatyana Luzyanina, Giovanni Samaey, and Dirk Roose. Dde-biftool manual - bifurcation analysis of delay differential equations. 2014. arXiv:arXiv:1406.7144.
- vV03
Lennaert van Veen. Baroclinic flow and the lorenz-84 model. Int. J. Bifurcation Chaos, 13(08):2117–2139, August 2003. doi:10.1142/s0218127403007904.
- XR99
Dongmei Xiao and Shigui Ruan. Bogdanov-Takens bifurcations in predator-prey systems with constant rate harvesting. In Differential equations with applications to biology (Halifax, NS, 1997), volume 21 of Fields Inst. Commun., pages 493–506. Amer. Math. Soc., Providence, RI, 1999.