Data‐Driven Dynamics and Chaos Control in a Memristor‐Based Chua Circuit With ψ‐Caputo Fractional Derivatives

Source abstract

ABSTRACT In this paper, the dynamics and regulation of a generalized fractional‐order memristive Chua circuit are investigated from practical, mathematical, and data‐oriented perspectives. The proposed system involves the ‐Caputo fractional derivative, including a general kernel function , which allows it to describe heterogeneous memory effects and non‐uniform time scaling. The paper proves the existence and uniqueness of solutions for the ‐fractional system via Volterra‐type integral equations and the Banach fixed‐point theorem. Additionally, an explicit Lyapunov estimate is derived, ensuring trajectory boundedness on every finite time interval and identifying the nonlinear memristive term's non‐positive contribution to the energy balance. Moreover, we show that after a full equilibrium analysis, a memristive element generates a line of equilibria along the internal state variable (‐axis). Furthermore, Matignon's stability criterion defines the stability region in the complex plane and determines the local asymptotic stability of equilibrium points. In addition, a predictor–corrector quadrature scheme is used to solve the nonlinear fractional differential equations involved and to provide reliable state‐trajectory data for identifying regime transitions. We analyze the convergence and stability of the proposed method and prove that it has a global truncation error of , where is the time step size, and denotes the fractional order. The numerical implementation is further validated using an exact‐solution benchmark and compared with an independent L1 predictor‐corrector method. Numerical simulations for memristive circuits based on physical parameters also indicate that the fractional order is an important bifurcation parameter: lower values (e.g., ) lead to steady periodic oscillations, while higher values (e.g., ) lead to a double‐scroll‐like irregular response, numerically indicative of chaotic dynamics. The instability of the chaotic regime is then discussed using linear state‐feedback control that suppresses unstable chaotic trajectories with a single scalar control input based on observed state data. The present work, therefore, contributes to the study of data‐driven fractional‐order nonlinear dynamics and serves as a basis for secure communication, neuromorphic engineering, and memristor‐based signal‐processing applications.