Dynamics analysis and fractional-order nonlinearity system via memristor-based Chua oscillator

This article discusses the utilisation of a Chua oscillator with a memristor to produce chaos with minimal nonlinearity. The memristor, a device that changes its flux or charges over time, has its nonlinear strength altered fractionally to determine the lowest-order memristor nonlinearity for generating chaos. An experimental analog circuit in real-time has been constructed. A linear parameter varying (LPV) approach, incorporating a suitable Lyapunov functional (LK) method, has been introduced to find new sufficient conditions for the robust stability of the resulting closed-loop system through linear matrix inequalities (LMIs). By observing the behaviour of the system without control, it is possible to understand the basic characteristics of chaotic oscillations and how they are affected by changes in the fractional order. These results can then be used as a starting point to study the effectiveness of various control techniques, such as feedback control, in reducing chaos and stabilising the system of this article. The efficiency of the cost-function-based control scheme is evaluated using the simulation results and relevant applications are addressed. (author)