Wang Ze, Qi Guoyuan
Tianjin Key Laboratory of Advanced Technology of Electrical Engineering and Energy, Tiangong University, Tianjin 300387, China.
Entropy (Basel). 2021 Jan 4;23(1):71. doi: 10.3390/e23010071.
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 (), 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 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.
本文通过改变双端口输出而非单端口来构建和研究三端忆阻器。将这种三端忆阻器嵌入新提出的四维（4D）欧拉方程中，构建了一个基于忆阻器的新型保守混沌系统。给出了广义哈密顿能量函数，它由哈密顿量的保守部分和非保守部分组成。欧拉方程的哈密顿量保持不变，而三端忆阻器的哈密顿量是可变的，导致能量不守恒。经证明，该系统仅存在中心或鞍点平衡点，符合保守系统的定义。提出了一个非哈密顿保守混沌系统。保守部分的哈密顿量决定系统是否能产生混沌，非保守部分则在保守部分的基础上影响系统的动力学。当系统具有不同的哈密顿量水平时，会产生混沌和准周期轨道。利用李雅普诺夫指数（）、庞加莱映射、分岔和哈密顿图来分析非哈密顿保守混沌系统的动力学行为。系统的频率和初始值具有广泛的可变范围。通过机制调整而非试错法，系统的最大[具体指标]甚至可以达到令人难以置信的963值。实现了一个模拟电路来验证非哈密顿保守混沌系统的存在，克服了微小偏差会导致保守混沌消失的挑战。
