On Fractional Discrete Memristive Model with Incommensurate Orders: Symmetry, Asymmetry, Hidden Chaos and Control Approaches.

Memristives provide a high degree of non-linearity to the model. This property has led to many studies focusing on developing memristive models to provide more non-linearity. This article studies a novel fractional discrete memristive system with incommensurate orders using ϑ i -th Caputo-like operator. Bifurcation, phase portraits and the computation of the maximum Lyapunov Exponent (L E m a x) are used to demonstrate their impact on the system's dynamics. Furthermore, we employ the sample entropy approach (SampEn), C 0 complexity and the 0-1 test to quantify complexity and validate chaos in the incommensurate system. Studies indicate that the discrete memristive system with incommensurate fractional orders manifests diverse dynamical behaviors, including hidden chaos, symmetry, and asymmetry attractors, which are influenced by the incommensurate derivative values. Moreover, a 2D non-linear controller is presented to stabilize and synchronize the novel system. The work results are provided by numerical simulation obtained using MATLAB R2024a codes. [ABSTRACT FROM AUTHOR]