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Hyperchaotic spiking oscillators with periodic pulse-train input

This paper studies simple spiking oscillators with periodic pulse-train input. The circuits are piecewise linear and a normal form circuit equation is derived in order to extract essential parameters. The return map and its Jacobian matrix can be described precisely. If the input is not present, the circuits can exhibit hyperchaotic and periodic attractors. As the input is applied, the attractors can be changed into various periodic, chaotic and hyperchaotic attractors. The phenomena are characterized by Lyapunov exponents of the return map. Typical phenomena can be confirmed experimentally. These results provide basic information for analysis of bifurcation phenomena and application to pulse-coupled networks.