An alternative bifurcation analysis of the Rose-Hindmarsh model

Chaos, Solitons and Fractals

Volumn 23, Issue 5, 2005, Pages 1643-1649

  Nikolov, Svetoslav ^a  

^a INSTITUTE OF MECHANICS   (Bulgaria)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; COMPUTER SIMULATION; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; NUMERICAL ANALYSIS; POLYNOMIALS;

BIFURCATION ANALYSIS; MEMBRANE POTENTIAL; ROSE-HINDMARSH MODEL (RHM);

BIFURCATION (MATHEMATICS);

EID: 9544252187     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(04)00427-8     Document Type: Article

References (24)

1. Keener J, Sneyd J. Mathematical physiology. Springer-Verlag; 1998.
2. Fall C, Marland E, Wagner J, Tyson J. Computational cell biology. NY: Springer-Verlag; 2002.
3. Hindmarsh JL, Rose RM. A model of neuronal bursting using three coupled first order differential equations. Proc R Soc London Ser B 1984;221:87-102.
4. Panchev S, Spassova T. Reaction of two simple nonlinear dynamical systems to constant forcing. Atmosfera 1999;12:161-71.
5. Guckenheimer J, Worfolk P. Dynamical systems: some computational problems. In: Schlomiuk D, editor. Bifurcations and periodic orbits of vector fields. Kluwer Academic Publishers; 1992. p. 241-79.
6. Holden A, Fan Y. From simple to simple bursting oscillatory behavior via chaos in the Rose-Hindmarsh model for neuronal activity. Chaos, Solitons & Fractals 1992;2(3):221-36.
7. Holden A, Fan Y. From simple to complex oscillatory behavior via intermittent chaos in the Rose-Hindmarsh model for neuronal activity. Chaos, Solitons & Fractals 1992;2(4):349-69.
8. Fan Y, Holden A. Bifurcations burstings, chaos, and crises in the Rose-Hindmarsh model for neuronal activity. Chaos, Solitons & Fractals 1993;3(4):439-49.
9. Fan Y, Chay T. Crisis transitions in excitable cell models. Chaos, Solitons & Fractals 1993;3(6):603-15.
10. Holden A. Nonlinear phenomena in excitable physiological systems. Chaos, Solitons & Fractals 1995;5(3-4):317-8.
11. Fan Y, Chay T. Crisis and topological entropy. Phys Rev E 1995;51(2):1012-9.
12. Fan Y, Holden A. An asymmetrical phase locking structure for a non-excitable cell model. Chaos, Solitons & Fractals 1998;9(10):1637-50.
13. Sabbagh H. Control of chaotic solutions of the Hindmarsh-Rose equations. Chaos, Solitons & Fractals 2000;11(8):1213-8.
14. Longtin A. Autonomous stochastic in bursting neurons. Phys Rev E 1997;55(1):868-76.
15. Raghavachari S, Glazier J. Waves in diffusively coupled bursting cells. Phys Rev Lett 1999;82(14):2991-4.
16. de Souza S, Caldas I, Viana R, Balthazar J. Sudden changes in chaotic attractors and transient basins in a model for rattling in gear boxes. Chaos, Solitons & Fractals 2004;21(3):763-72.
17. Alligood K, Sauer T, Yorke J. Chaos, an introduction to dynamical system. Springer-Verlag; 1996.
18. Bautin N. Behavior of dynamical systems near the boundary of stability. Moscow: Nauka; 1984.
19. Andronov A, Vitt A, Khaikin S. Theory of oscillations. Reading, MA: Addison-Wesley; 1966.
20. Nikolov S, Petrov V. New results about route to chaos in Rossler system. Int J Bifurcat Chaos 2004;14(1):293-308.
21. Neimark Yu, Landa P. Stochastic and chaotic oscillations. Kluwer Academic Publishers; 1992.
22. Arnold V. Theory of crises. Moscow University; 1983.
23. Panchev S. Theory of chaos. Bulgarian Academic Press; 2001.
24. Hegger R, Kantz H, Schreiber T. Practical implementation of nonlinear time series methods: the TISEAN package. Chaos 1999;9:413-35.