Fractional and non-fractional chaotic amphibian attractors with self-excited and hidden properties: numerical dynamics, circuit realization and FPGA-based application

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In this paper we announce a novel chaotic system which can have self-excited or hidden attractor depending on the parameters. The system shows same Lyapunov exponents for both self-excited and hidden attractors. Fractional order model of the proposed novel chaotic system is derived and investigated. Bifurcation diagrams of the fractional order chaotic system with respect to change in the fractional orders are investigated and it is proved that the system possess its largest Lyapunov exponent in the fractional order. Using the Adomian decomposition method, the proposed fractional order chaotic systems are implemented in FPGA and power efficiency analysis for various fractional orders is done.