Modeling and Analysis of a Three-Terminal-Memristor-Based Conservative Chaotic System

Abstract

In this paper, a three-terminal memristor is constructed and studied through changing dual-port output instead of one-port. A new conservative memristor-based chaotic system is built by embedding this three-terminal memristor into a newly proposed four-dimensional (4D) Euler equation. The generalized Hamiltonian energy function has been given, and it is composed of conservative and non-conservative parts of the Hamiltonian. The Hamiltonian of the Euler equation remains constant, while the three-terminal memristor’s Hamiltonian is mutative, causing non-conservation in energy. Through proof, only centers or saddles equilibria exist, which meets the definition of the conservative system. A non-Hamiltonian conservative chaotic system is proposed. The Hamiltonian of the conservative part determines whether the system can produce chaos or not. The non-conservative part affects the dynamic of the system based on the conservative part. The chaotic and quasiperiodic orbits are generated when the system has different Hamiltonian levels. Lyapunov exponent (LE), Poincaré map, bifurcation and Hamiltonian diagrams are used to analyze the dynamical behavior of the non-Hamiltonian conservative chaotic system. The frequency and initial values of the system have an extensive variable range. Through the mechanism adjustment, instead of trial-and-error, the maximum LE of the system can even reach an incredible value of 963. An analog circuit is implemented to verify the existence of the non-Hamiltonian conservative chaotic system, which overcomes the challenge that a little bias will lead to the disappearance of conservative chaos.

A conservative system based on a triangular wave memristor and its application in image encryption

“…The characteristic roots of the characteristic equation have positive and negative real parts, and equilibrium points are saddle or center. At the same time, they proved that the system is non-Hamiltonian conservative [14]. Reference [18] reported the dynamic behavior of homogeneous or heterogeneous multistability of a memristor conservative chaotic system accompanied by initial-dependent offset boosting behavior and gave a digital DSP implementation.…”

“…In chaotic cryptosystems, the system itself is usually used as an important part of the secret key, and the chaotic attractors generated by dissipative systems can be reconstructed using the time-delay method [12], which in turn enables to crack the key and attack the cryptosys-tem [13]. In contrast, the conservative chaotic system is sensitive to the initial conditions and has the characteristics of random motion trajectory, but does not form chaotic attractors [14,15], thus having the excellent quality of resisting the reconstruction of the key. To the authors' knowledge, no conservative chaotic systems composed of memristors have been used for image encryption.…”

A Robust Memristor-Enhanced Polynomial Hyper-Chaotic Map and Its Multi-Channel Image Encryption Application

“…Once the aforementioned research was reported, it immediately garnered significant attention from numerous researchers. Subsequently, an increasing amount of related research has emerged on the utilization of memristors to enhance chaotic map [20][21][22][23][24].…”

A new 5D fractional-order conservative hyperchaos system

“…Systems inheriting different time scales can be successfully reconstructed using non-uniform delays [2,3], which are easy to reconstruct, so algorithms based on dissipative chaos are not yet secure enough. The conservative system has better ergodicity than the dissipative system [4], the initial value sensitivity is higher, and there is no attractor. Therefore, compared with the dissipative system, the conservative system is more suitable for acting on encryption technology.…”