On a pulse-coupled system of bifurcation neuron with triangular base signal

摘要

This paper studies a pulse-coupled system of two bifurcating neurons with a periodic triangular base signal. The dynamics of single neuron is described by a ID pulse position map and that of the pulse-coupled system is described by the composition of maps of two single neurons. In the case of triangular base signal, the composite map is piecewise linear and we can analyze rich phenomena precisely. We demonstrate two typical phenomena: 1) periodic pulse-train of single neurons is changed into chaotic pulse-train by the pulse-coupling and 2) chaotic pulse-train of single neurons is changed into periodic pulse-train by the pulse-coupling. These results may be developed into novel bifurcation theory of pulse-coupled systems.