Simulation and dynamical analysis of a chaotic chameleon system designed for an electronic circuit

Abstract

The moment when stability moves to instability and order moves to disorder constitutes a chaotic systems; such phenomena are characterized sensitively on the basis of initial conditions. In this manuscript, a fractal–fractionalized chaotic chameleon system is developed to portray random chaos and strange attractors. The mathematical modeling of the chaotic chameleon system is established through the Caputo–Fabrizio fractal–fractional differential operator versus the Atangana–Baleanu fractal–fractional differential operator. The fractal–fractional differential operators suggest random chaos and strange attractors with hidden oscillations and self-excitation. The limiting cases of fractal–fractional differential operators are invoked on the chaotic chameleon system, including variation of the fractal domain by fixing the fractional domain, variation of the fractional domain by fixing the fractal domain, and variation of the fractal domain as well as the fractional domain. Finally, a comparative analysis of chaotic chameleon systems based on singularity versus non-singularity and locality versus non-locality is depicted in terms of chaotic illustrations.