Period-adding bifurcations in a one parameter family of interval maps

Mathematical and Computer Modelling

Volumn 24, Issue 4, 1996, Pages 27-41

  LoFaro, T ^a  

^a WASHINGTON STATE UNIVERSITY   (United States)

Author keywords

Bifurcation; Period adding

Indexed keywords

EID: 0030209435     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/0895-7177(96)00105-7     Document Type: Article

References (13)

1. 1. J. Rinzel and W.C. Troy, A one-variable map analysis of bursting in the Belousov-Zhabotinskii reaction, In Nonlinear Partial Differential Equations, Contemporary Mathematics, (Edited by J.A. Smoller), Vol. 17, pp. 1-23, (1982).
2. 2. T. LoFaro, N. Kopell, E. Marder and S. Hooper, Subharmonic coordination in networks of neurons with slow conductances, Neural Computation 6, 69-84, (1994).
3. 3. T. LoFaro, A period adding bifurcation in a pair of coupled neurons, Doctoral Thesis, Boston University, (1994).
4. 4. T. LoFaro and N. Kopell, Reduction of a network of voltage gated conductance equation to a one-dimensional map, (in preparation), (1995).
5. 5. M. Levi, Qualitative analysis of the periodically forced relaxation oscillations, Mem. AMS 214, 1-147, (1981).
6. 6. M. Levi, A period-adding phenomenon, SIAM J. Appl. Math. 50, 943-955, (1990).
7. 7. J.P. Keener, Chaotic behavior in piecewise continuous difference equations, Trans. of the AMS 261, 589-604, (1980).
8. 8. J. Milnor and R. Thurston, On iterated maps of the interval I and II, Unpublished notes, Princeton University Press, Princeton, (1977).
9. 9. A. Devaney, An Introduction to Chaotic Dynamical Systems, 2nd Edition, Addison-Wesley, Redwood City, CA, (1989).
10. 10. J. Guckenheimer and P. Holmes, Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, In Applied Mathematical Sciences, Vol. 42, Springer-Verlag, New York, (1983).
11. 11. B. van der Pol and J. van der Mark, Frequency demultiplication, Nature 120, 363-364, (1927).
12. 12. C. Bonet, Singular perturbation of relaxed periodic orbits, J. Diff. Eqns. 66, 301-339, (1987).
13. 13. E.F. Mischenko and N. Rosov, Differential Equations with Small Parameters and Relaxation Oscillations, Plenum Press, New York, (1980).