This paper presents an improved dual-memristor-based FitzHugh–Nagumo (DM-FHN) system, which is a non-autonomous circuit derived from FitzHugh–Nagumo (FHN) neuron circuit by substituting the tunnel diode with hyperbolic tangent memductance and connecting an active charge-controlled memristor in series with an inductor. The analysis model of the system is established first, and the rich dynamic behaviors of the system, varying with the circuit component parameters, are studied via the phase diagram, bifurcation diagram and Lyapunov exponential spectrum. Some interesting phenomena, such as bifurcation, periodic-chaotic state transition, periodic-chaotic bubbles, multistability phenomenon, and symmetrical behaviors, are observed. The finite-time synchronization of two coupled DM-FHN neurons for different behaviors due to different initial conditions is also studied. The cubic flux-controlled memristor is used as a synapse between the coupling circuits. The sufficient synchronization conditions for the unidirectional and bidirectional coupling DM-FHN circuits are derived respectively and the influence of the system initial values on the coupling synchronization is also investigated. The rich synchronous dynamics of the coupled DM-FHN systems are illustrated by the numerical simulations, the result of which also validates the presented analysis model.

本文提出了一种改进的基于双忆阻器的 FitzHugh-Nagumo (DM-FHN) 系统，它是一种非自治电路，它是从 FitzHugh-Nagumo (FHN) 神经元电路通过用双曲正切电感代替隧道二极管并连接一个有源电路与电感器串联的电荷控制忆阻器。首先建立了系统的分析模型，通过相图、分岔图和李雅普诺夫指数谱研究了系统随电路元件参数变化的丰富动态行为。观察到了一些有趣的现象，例如分叉、周期混沌状态转变、周期混沌气泡、多稳态现象和对称行为。还研究了两个耦合的 DM-FHN 神经元在不同初始条件下的不同行为的有限时间同步。三次磁通控制忆阻器用作耦合电路之间的突触。分别推导出单向和双向耦合DM-FHN电路的充分同步条件，并研究了系统初始值对耦合同步的影响。数值模拟说明了耦合 DM-FHN 系统的丰富同步动力学，其结果也验证了所提出的分析模型。分别推导出单向和双向耦合DM-FHN电路的充分同步条件，并研究了系统初始值对耦合同步的影响。数值模拟说明了耦合 DM-FHN 系统的丰富同步动力学，其结果也验证了所提出的分析模型。分别推导出单向和双向耦合DM-FHN电路的充分同步条件，并研究了系统初始值对耦合同步的影响。数值模拟说明了耦合 DM-FHN 系统的丰富同步动力学，其结果也验证了所提出的分析模型。