Chaotic Properties of the Hénon Map with a linear filter
Rodrigo T. Fontes1; Marcio Eisencraft1
1 Escola Politécnica, University of São Paulo
Resumo
An interesting way of limiting the bandwidth of the transmitted signal in a chaos-based communication scheme is to use linear discrete-time filters in the feedback loop. It was recently proved that such filters do not disturb chaotic synchronization. However, there is no guarantee that the generated signals remain chaotic. In this paper, we consider the Hénon map plus a linear time-invariant finite impulsive response filter. We numerically access its larger Lyapunov exponent as a function of the filter coefficients, obtaining regions where chaotic, periodic or unbounded orbits are present.
Palavras-chave: Analysis and Control of Nonlinear Dynamical Systems with Practical Applications ; Time Series Analysis ; Discrete Dynamical Systems