Dynamical investigation and chaotic associated behaviors of memristor Chua’s circuit with a non-ideal voltage-controlled memristor and its application to voice encryption

Abstract

In this paper we modified the conventional Chua’s circuit with a non-ideal voltage-controlled memristor with a quadratic internal state. Dynamical behaviors of Modified Memristor based Chua’s Circuit (MMCC) are investigated and Stability of equilibrium points are discussed we have computed the volume contraction rate and proved the system is dissipative. The existence of positive Lyapunov exponent showed the chaotic attractor present in the system. We found many Literatures on dynamic analysis on memristor based Chua’s circuit but most of them are restricted to only Poincare maps and Lyapunov spectrum. We carried out bifurcation analysis, bifurcations attained by varying the circuit parameters when evolving on a fixed manifold, bifurcations attained by changing the initial conditions, and hence changing between different manifolds, for a fixed set of parameters, and bifurcations due to changing circuit parameters as well as manifolds. The circuit hold multistability, to check the existence of coexisting attractors and the interesting phenomena of antimonotonicity is identified in the circuit. These special properties shows the intricacy of the circuit, which is vital for secure communication. We successfully implemented MMCC for voice encryption and proved the effective usability of the system in engineering application.