Fitzhugh-nagumo revisited: Types of bifurcations, periodical forcing and stability regions by a lyapunov functional

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 14, Issue 3, 2004, Pages 913-925

  Kostova, Tanya ^a   Ravindran, Renuka ^b   Schonbek, Maria ^c  

^a LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

^b INDIAN INSTITUTE OF SCIENCE   (India)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

FitzHugh Nagumo; Homoclinic bifurcation; Periodic forcing; Subcritical and supercritical Hopf bifurcation

Indexed keywords

ASYMPTOTIC STABILITY; BIFURCATION (MATHEMATICS); CONVERGENCE OF NUMERICAL METHODS; EQUATIONS OF MOTION; NONLINEAR EQUATIONS; OSCILLATORS (MECHANICAL); PHASE LOCKED LOOPS; POLYNOMIAL APPROXIMATION;

FITZHUGH-NAGUMO; HOMOCLINIC BIFURCATION; PERIODIC FORCING; SUBCRITICAL AND SUPERCRITICAL HOPF BIFURCATION;

LYAPUNOV METHODS;

EID: 13844255214     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127404009685     Document Type: Article

References (12)

1. Armbruster, D. [1997] "The (almost) complete dynamics of the FitzHugh Nagumo equations," Nonlinear Dynamics, ed. Guran, A. (World Scientific, Singapore), pp. 89-102.
2. Brown, P. N., Byrne, G. D. & Hindmarsh, A. C. [1989] "VODE, a variable-coefficient ODE solver," SIAM J. Sci. Stat. Comput. 10, 1038-1051.
3. Brown, D. & Rothery, P. [1993] Models in Biology: Mathematics, Statistics and Computing (J. Wiley).
4. Dangelmayr, G. & Guckenheimer, J. [1987] "On a four parameter family of planar vector fields," Arch. Rat. Mech. Anal. 97, 321-352.
5. Farkas, M. [1994] Periodic Motions (Springer-Verlag, Berlin).
6. Guckenheimer, J. & Holmes, P. [1997] Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (Springer-Verlag, Berlin).
7. Kuznetsov, Yu. [1995] Elements of Applied Bifurcation Theory (Springer-Verlag, Berlin).
8. Murray, J. D. [1989] Mathematical Biology (Springer-Verlag, Berlin).
9. Rajasekar, S. & Lakshmanan, M. [1988a] "Period doubling route to chaos for a BVP oscillator with periodic external force," J. Theor. Biol. 133, 473-477.
10. Rajasekar, S. & Lakshmanan, M. [1988b] "Period doubling bifurcations, chaos, phase locking and Devil's staircase in a BVP oscillator," Physica D32, 146-152.
11. Sato, S. & Doi, S. [1992] "Response characteristics of the BVP neuron model to periodic pulse input," Math. Biosci. 112, 243-259.
12. Strogatz, S. H. [1994] Nonlinear Dynamics and Chaos (Perseus Books, Reeding, MA).