Hidden multistability of fractional discrete non-equilibrium point memristor based map

Abstract

At present, the multistability analysis in discrete nonlinear fractional-order systems is a subject that is receiving a lot of attention. In this article, a new discrete non-equilibrium point memristor-based map with $\gamma-th$ Caputo fractional difference is introduced. In addition, in the context of the commensurate and non-commensurate instances, the non-linear dynamics of the suggested discrete fractional map, such as its multistability, hidden chaotic attractor, and hidden hyperchaotic attractor, are investigated through several numerical techniques, including Lyapunov exponents, phase attractors, bifurcation diagrams, and the $0–1$ test. This dynamic behaviors suggests that the fractional discrete memristive map has a hidden multistability. Finally, to validate the presence of chaos, a complexity analysis is carried out using approximation entropy ($ApEn$) and the $C_0$ measure. The findings show that the model has a high degree of complexity, which is affected by the system parameters and the fractional values.

Generating rotationally hidden attractive sea via a new chaotic system with two mixed memristors

“…It greatly improved the anti-crack capability of the image. The correlation of two adjacent pixels on the horizontal, vertical, and diagonal direction can be calculated by using equation (27).…”

“…Recently, the research for the dynamic behavior of memristive chaotic system has become a hot issue [22]. In particular, several studies show that it can improve chaotic performance by introducing the memristive model to some chaotic systems [23][24][25][26][27][28]. Otherwise, the introduction of memristor can effectively improve the memory performance of neural network.…”

An adaptive energy regulation in a memristive map linearized from a circuit with two memristive channels

“…The discrete memristive Rulkov neuron map [32,33] was developed by introducing a DM into a Rulkov neuron model. A fractional memristive map is proposed in [34]. In addition, DM chaotic maps are hardware implemented by applying DSP platform [35][36][37] and an analog circuit [38].…”

On two-parameter bifurcation and analog circuit implementation of a Chameleon chaotic system

“…With this condition, it is difficult to trigger such attractor via configuring an initial point from the small neighborhood of the system equilibrium. In various cases, the one with no equilibrium is a natural hidden oscillating system since the existence of the attractor is not related to the system equilibrium [25], which makes it have advantages in resisting the prediction of chaotic trajectories in chaos-based security applications [26].…”