Controlling double-scroll chaotic Lü attractor to difformity

Abstract

By adding a linear control circuit into a chaotic Lu system, a double-scroll chaotic Lu attractor can be controlled by adjusting control parameters to obtain several difform attractors, such as four-scroll attractor, novel double-scroll attractor and spiral attractor, etc., which implies that the new circuit can generate different chaos signal under different control parameters. The proposed control circuit is very simple, with integration and addition function implemented by two operational amplifiers. These difform chaotic attractors along with periodic limit cycles are obtained from simulation of the new circuit and mathematics calculation of the corresponding system equations. The detailed dynamical behaviors of this four-dimensional continuous autonomous dissipative chaotic system, including Lyapunov exponent spectrum, bifurcation diagram, Poincare mapping and phase portrait, etc., are investigated.