Hyperchaotic Oscillation and Multistability in a Fourth Order Smooth Chua System with Implementation Using No Analog Multipliers

Abstract

Abundant dynamical behaviors and succinct realization forms are of great significance for nonlinear circuits and systems. Hyperchaos represents more complex oscillation mode compared with chaos, while multistability means more complex essential features compared with robustness. And the coexistence of the two is rare but interesting. Based on the classic Chua model, a fourth order smooth Chua system is constructed through utilizing linear feedback control method in this article. The introduction of hyperbolic sine nonlinearity remarkably simplifies the physical realization form for the new system. The two interesting nonlinear phenomena of hyperchaotic oscillation and multistability are discovered by adjusting system parameters. Dynamic analyses including bifurcation diagrams and Lyapunov exponent spectra comprehensively reveal the evolution of oscillatory behaviors brought by the variation of system parameters, whereupon more attractors such as periodic attractors, chaotic attractors in different oscillation scales, coexisting quasi-periodic attractors, coexisting multiple attractors and coexisting periodic attractors are found. And the attractor morphologies of this system are rare and significantly different from those in the reported Chua circuits and systems. Hardware circuit experiments without using analog multipliers are performed from a four-layer printed circuit board, which efficiently verify the simulated dynamical behaviors within the acceptable deviation.