Modeling and complexity analysis of a fractional-order memristor conservative chaotic system

Abstract

Memristors are often utilized in circuit model analysis as one of the fundamental circuit components. In this paper, a five-dimensional conservative memristor chaotic system is built after the introduction of the memristor into a four-dimensional conservative chaotic system. The dynamic changes of the system are examined using phase diagram, bifurcation diagram, and the Lyapunov exponent spectrum. A line equilibrium point, symmetry and multi-stability are characteristics of the system, the phase trajectory can also produce shrinking and structure transformation behavior with the change of parameters. Furthermore, the system has initial offset boosting behaviors, conservative flows of it can be altered in position by changing two initial values, respectively. Most notably, we discover that the complexity of the system rises with the inclusion of memristor and again with the addition of fractional differential operators. It is shown that the complexity of chaotic systems may increase with the addition of memristors and fractional-order differential operators. At last, the NIST is used to test the randomness of the sequence, and the system’s physical realizability is confirmed by the DSP platform.

Cross-channel image encryption algorithm on the basis of a conservative hyperchaotic system

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Mittag-Leffler function based security control for fractional-order complex network system subject to deception attacks via Observer-based AETS and its applications

“…This is mostly because it gives very accurate models of systems and processes that have memory and are passed down from generation to generation. Fractional-order calculus, which is the generalization of integer-order calculus, has recently gotten a lot of attention because it has many possible uses in biology, earthquake dynamics, chaotic dynamics, electrical circuits, finance, and other fields [3,4]. Recently, some researchers have suggested incorporating fractional calculus into complex networks (CNs) to generate fractional-order complex networks (FOCNs), and they have also discussed the dynamics of FOCNs, including state estimation, synchronization, stability, Mittag-Leffler stability, asymptotic stability, exponential stability, and more [5,6].…”

A novel 5D memristor conservative chaotic system with multiple forms of hidden flows

“…However, in this paper, we find a new transient transition behavior. In 2023, Leng et al [28] proposed a four-dimensional memristor conservative chaotic system, which has the initial value offset enhancement behavior, and the complexity of chaotic sequence is improved by introducing memristor. In the same year, Li et al [29] proposed a four-dimensional conservative chaotic system, which has many characteristics such as hidden coexistence attractor, initial value shift boosting and so on.…”