Numerical Analysis for Hidden Chaotic Behavior of a Coupled Memristive Dynamical System Via Fractal-Fractional Operator Based on Newton Polynomial Interpolation

Abstract

Dynamical features of a coupled memristive chaotic system have been studied using a fractal-fractional derivative in the sense of Atangana-Baleanu. Dissipation, Poincare section, phase portraits, and time-series behaviors are all examined. The dissipation property shows that the suggested system is dissipative as long as the parameter g > 0. Similarly, from the Poincare section it is observed that, lowering the value of the fractal dimension, an asymmetric attractor emerges in the system. In addition, fixed point notions are used to analyze the existence and uniqueness of the solution from a fractal-fractional perspective. Numerical analysis using the Adams-Bashforth method which is based on Newton's Polynomial Interpolation is performed. Furthermore, multiple projections of the system with different fractional orders and fractal dimensions are quantitatively demonstrated, revealing new characteristics in the proposed model. The coupled memristive system exhibits certain novel, strange attractors and behaviors that are not observable by the local operators.