Least fractional order memristor nonlinearity to exhibits chaos in a hidden hyperchaotic system

Abstract

In this article, we present least fractional nonlinearity for exhibiting chaos in a memristor-based hyper-chaotic multi-stable hidden system. When implementing memristor-based systems, distinct dimensions/order define the memristor nonlinearity. In this work, the memristor dimension has been changed fractionally to identify the lowest order of nonlinearity required to induce chaos in a proposed system. The two-parameter frequency scanning helps in understanding both oscillation and non-oscillation regimes. The system fractional nonlinearity strength will help in deeper understanding of mathematical modelling and control. In addition, multistability and hidden oscillations were thoroughly investigated in the proposed system. The current work combines analytical, numerical, and experimental methods to demonstrate the system dynamics.