Bifurcation and Periodic Solutions in Memristive Hyperchaotic System

Abstract

This paper is devoted to a memristive hyperchaotic system. Different from some the existing literature, we derive analytically, under appropriate conditions, the stability and the analytic expression of the Hopf bifurcation by employing center manifold theorem. The system shows dynamics including equilibrium set with one or three elements, Lyapunov exponents with different signs, such as (0, 0, 0, -), (+, 0, -, -), (+, 0, 0, -), and (+, +, 0, -), by varying only one parameter. Moreover, the coexistence of multiple hyperchaotic attractors is observed. Some simulation examples are presented to illustrate our theoretical results.

Keywords

• Memristor
• hyperchaotic circuit
• Lyapunov exponents
• periodic solutions
• center manifold