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

Ze Wang,Guoyuan Qi

doi:10.3390/e23010071

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.

Highlights

Since the HP laboratory [1] confirmed memristors’ physical existence in 2008, the memristors [2] have received extensive attention from the academic community
Two-terminal memristors have proved the basic principle of neurons, the synapses of one neuron are far more than one, so it is necessary to study multi-terminal memristors
Mouttet proposed the basic definition of the three-terminal memristor [11] based on the two-terminal memristor passive nonlinear system [12] by Chua

Summary

Introduction

Since the HP laboratory [1] confirmed memristors’ physical existence in 2008, the memristors [2] have received extensive attention from the academic community. The conservative chaos has a full dimension in phase volume, and encryption based on conservative systems is better than dissipative systems in anti-attack [17,18,19]. There are two research routes of two-terminal memristor chaotic systems based on dissipative system: (1) The memristor is used to replace nonlinear components such as the Chua circuits [14,21], oscillator circuits [22], etc. We consider designing a conservative three-terminal memristor chaotic system based on the 4D Euler equation given in [18]. By coupling the Euler equation with a three-terminal memristor, the energy conservation is broken, but the phase-volume conservation (divergence being zero) is still kept. This paper constructs a three-terminal-memristor-based conservative chaotic system, and gives its energy function, pointing out the cause of its chaos.

Modeling of Three-Terminal Memristor

Dynamical Analysis with Analysis with Different Initial