Complex dynamics induced by a sine nonlinearity in a five-term chaotic system: FPGA hardware design and synchronization.

Abstract

This paper presents a new five-term chaotic model derived from the Rössler prototype-4 equations. The proposed system is elegant, variable-boostable, multiplier-free, and exclusively based on a sine nonlinearity. However, its algebraic simplicity hides very complex dynamics demonstrated here using familiar tools such as bifurcation diagrams, Lyapunov exponents spectra, frequency power spectra, and basins of attraction. With an adjustable number of equilibrium, the new model can generate infinitely many identical chaotic attractors and limit cycles of different magnitudes. Its dynamic behavior also reveals up to six nontrivial coexisting attractors. Analog circuit and field programmable gate array-based implementation are discussed to prove its suitability for analog and digital chaos-based applications. Finally, the sliding mode control of the new system is investigated and simulated.