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Proceeding of International Conference
Kazutoshi Kinoshita, Tetsushi Ueta, Bifurcation Analysis of Coupled Nagumo-Sato Models, Proc. NOLTA2010, 488-491, Cracow, Sep. 2010.
Abstract: The Nagumo-Sato model is one of mathe- matical neuron models described by a piecewise linear dif- ference equation. Since there is a conditional character which is discontinuous at the threshold value, the system can be classified as a hybrid dynamical system. Bifurca- tion phenomena are occurred by changing internal param- eters and chaotic attractors are also given. The dynamical properties were exactly studied analytically. In this paper, we investigate the bifurcations of diffusively-coupled Nagumo-Sato models. By using com- plementarity a shooting algorithm and brute-force method, complete bifurcation diagrams are obtained. In spite of the discontinuities inside the coupled system, our shoot- ing method can solve bifurcation problems. A period- locking regions edged by border-collision bifurcation sets are found, and chaotic regions are distinguished by a tan- gent bifurcation. We discuss on changing bifurcation struc- tures with parameter variations.

Contact address: ueta @