论文信息 - Bifurcations in the Rose-Hindmarch Model and the Chay Model

Bifurcations in the Rose-Hindmarch Model and the Chay Model

We have examined a model of a neuron: the Rose-Hindmarch model and a model of an excitable membrane: the Chay model. Chaos was known to exist in both models. As chaos is (often) reached after a sequence of bifurcations of periodic solutions, we have traced curves of bifurcation points of periodic solutions, and thereby determined the regions within which chaos can be found.

C. Kaas-Petersen

[1] B. Hassard,et al. Theory and applications of Hopf bifurcation , 1981 .

[2] L. Petzold. Automatic Selection of Methods for Solving Stiff and Nonstiff Systems of Ordinary Differential Equations , 1983 .

[3] P. Holmes,et al. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[4] J. Hindmarsh,et al. A model of neuronal bursting using three coupled first order differential equations , 1984, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[5] Teresa Ree Chay,et al. Chaos in a three-variable model of an excitable cell , 1985 .