Leveraging the ability of locally active memristors to generate and flexibly modulate neuronal firing patterns with simple topologies, this paper proposes a dual-channel memristive neural circuit for scalable neuromorphic implementation. The proposed design employs two structurally identical branches, each incorporating a locally active memristor, enabling on-demand control of firing dynamics within a unified hardware framework. We systematically analyze the stability distribution of equilibrium points and investigate the underlying firing patterns under various stimulus conditions through numerical bifurcation analysis. The results demonstrate that the proposed neural circuit topology supports controllable transitions among resting, spiking, bursting, and chaotic states under undriven, DC-driven, and pulse-triggered conditions. These transitions are achieved through electrical modulation of key circuit parameters, namely the memristor bias voltages, external stimulation, and coupling resistance. PCB-level experimental measurements validate the feasibility of the theoretical and simulation analyses. Overall, this work provides fundamental guidance for designing LAM-based neural circuits and contributes to the development of essential building blocks for neuromorphic engineering.

Designing a universal framework for configuring bionic spiking circuits is an attractive topic for spike-based applications. This paper comprehensively considers the electrophysiological properties of a biological neuron and electrical features of mem-elements, then presents a new universal framework for configuring fully mem-element-based bionic spiking circuits. The universal framework contains a current-controlled locally active memristor (LAM), a charge-controlled memcapacitor, and a flux-controlled meminductor to respectively characterize the electrophysiological properties of ion channels, liquid bilayer membrane, and electromagnetic induction of a biological membrane. The universal framework only involves the three mem-elements and a DC current stimulus. Afterward, a case of a mem-element emulator-based bionic spiking circuit is configured employing the universal framework. Numerical explorations and experimental measurements based on analog hardware circuits are performed to validate the effectiveness of the universal framework in generating abundant bifurcation behaviors and spiking activities. Actually, the universal framework is available for employing different mem-element emulators or physical mem-elements to construct bionic spiking circuits. The universal framework is extensible and sheds new light on the configuration of fully mem-element-based bionic spiking circuits.

Neuromorphic circuits with diverse neuronal firing features are the foundation for implementing neuron-based intelligent tasks. The locally active memristor (LAM) is a good candidate for constructing such kind of artificial circuits. However, it is attractive and challenging to explore synchronicity of firing patterns between LAM-based neuromorphic circuits, especially on hardware level. To this end, a neuromorphic circuit is constructed with a newly designed LAM emulator, a capacitor, a DC voltage, and an external current stimulus. Abundant stimulus-relating firing patterns are numerically revealed, whose bifurcation mechanism are theoretically discussed. Besides, using a LAM emulator as the coupling synapse, the interactions between two firing neuromorphic circuits are explored under identical and nonidentical stimulus conditions. The results manifest that the amplitude and phase of the stimulus current, as well as the static potential of the LAM branch, all exert significant influences on the synchronization behaviors. Furthermore, PCB-based analog circuits are implemented to demonstrate the firing patterns of single and coupled neuromorphic circuits from the perspective of physical experiments. This research could provide a viable paradigm to theoretical research and engineering application of memristive neuromorphic circuits.

Because of the special nonlinearity with inner states, memristors can induce the initial-condition-dependent extreme multistability in their constituent systems. However, when the memristor is taken as a coupler to synchronize two identical memristive systems, what synchronous behaviors could be achieved? So far, it has not been comprehensively concerned in literature. To this end, this paper presents a 9-D memristor-coupled system consisting of two homogenous memristive systems and studies its initial-boosted dynamics and synchronous behaviors. Dynamics evolutions related to the coupling memristor and two subsystem memristors are elaborated. Using Lyapunov’s stability theorem, the synchronicities of the initial-condition-sensitive dynamics are demonstrated theoretically. Furthermore, based on the integral transformation model, the synchronization parameter regions are estimated quantitatively using a newly proposed variable-parameter conversion method. Thereafter, various coexisting synchronous behaviors are discovered by tuning the memristor initial conditions and verified via the microcontroller-based hardware measurements. It is demonstrated that the memristor coupler provides a flexible control scheme for the synchronization of memristive systems.

Extreme multistability has seized scientists’ attention due to its rich diversity of dynamical behaviors and great flexibility in engineering applications. In this paper, a four-dimensional (4D) memcapacitive oscillator is built using four linear circuit elements and one nonlinear charge-controlled memcapacitor with a cosine inverse memcapacitance. The 4D memcapacitive oscillator possesses a line equilibrium set, and its stability periodically evolves with the initial condition of the memcapacitor. The 4D memcapacitive oscillator exhibits initial-condition-switched boosting extreme multistability due to the periodically evolving stability. Complex dynamical behaviors of period doubling/halving bifurcations, chaos crisis, and initial-condition-switched coexisting attractors are revealed by bifurcation diagrams, Lyapunov exponents, and phase portraits. Thereafter, a reconstructed system is derived via integral transformation to reveal the forming mechanism of the initial-condition-switched boosting extreme multistability in the memcapacitive oscillator. Finally, an implementation circuit is designed for the reconstructed system, and Power SIMulation (PSIM) simulations are executed to confirm the validity of the numerical analysis.

A four-dimensional memristive system is constructed using a novel ideal memristor with cosine memductance. Due to the special memductance nonlinearity, this memristive system has a line equilibrium set (0, 0, 0, δ ) located along the coordinate of the inner state variable of the memristor, whose stability is periodically varied with a change of δ. Nonlinear and one-dimensional initial offset boosting behaviors, which are triggered by not only the initial condition of the memristor but also other two initial conditions, are numerically uncovered. Specifically, a wide variety of coexisting attractors with different positions and topological structures are revealed along the boosting route. Finally, circuit simulations are performed by Power SIMulation (PSIM) to confirm the unique dynamical features.