A family of conservative chaotic systems with cyclic symmetry

Abstract

In this paper, we propose a family of circulant systems with conservative property. Various dynamical properties of the circulant systems are derived and investigated. Bifurcation plots are derived and presented for a system and the Lyapunov exponents are derived to show the existence of chaotic oscillations, and their sum being zero confirms the conservativeness for certain values of parameters. One of the proposed systems is then implemented in field programmable gate array (FPGA) to show the hardware reliability. We used the hardware–software co-simulation to see the phase portraits of the FPGA implemented system. The discrete integrators required for solving the initial value problem are implemented using the Euler's method. The register transfer level schematics of the FPGA implemented system and the resources used for the implementations are presented.

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