Locally active memristor (LAM), which has an ability to amplify fluctuations, is a natural component for constructing artificial neuron circuits. This paper proposes a novel third-order neuron circuit by paralleling two LAMs and a capacitor. Firstly, two parallel LAMs are equivalently modeled as a second-order LAM to facilitate theoretical analysis. Regarding the third-order neuron, the parameter design and operating condition are obtained by calculating its small signal impedance functions poles or Jacobin matrixs eigenvalues. It is demonstrated that the neuron exhibits various neuromorphic behaviors, including periodic spiking, chaos and burst-number adaptation. Due to the two different LAMs, the proposed thirdorder system has multiple equilibrium points, leading to the generation of coexisting attractors. Interestingly, the generated chaotic attractor does not revolve around a single unstable equilibrium point, but is located between two unstable equilibrium points. Furthermore, the emergence of oscillating behaviors is dependent on the distance between the two unstable equilibrium points. Detailed theoretical and simulation analysis are presented to investigate the neuron dynamics and provide an explanation for the observed neuromorphic behaviors. Finally, physical circuit implementation of the neuron is constructed based on the memristor emulator, which also demonstrates the practicability of the proposed neuron model and the correctness of the theoretical analysis.

The symmetry-breaking phenomenon, appearing, under suitable conditions, when identical reaction cells, quiet on their own, are let interact via diffusion processes, is dubbedTuring Instability. Its local form exposes the local destabilization, which allows two multistable cells lose stability at one of its locallyasymptotically-stableoperating points. While the globalTuring Instabilityand its mechanisms have been recently explained in (Ascoli et al., 2022), its local form and an experimental demonstration of these complex effects on a physical memristive medium have not been reported yet. This paper investigates a local form ofTuring Instabilityin a two-cell array, when one of the possiblelocally asymptotically-stableandlocally-activestatic solutions loses stability, when let interact with an identical reaction cell via diffusion processes, resulting in the emergence of two different static solutions after transients fade away. In order to study its mechanisms, this paper first introduces a current-controlled Chua Corsage Memristor (CCM), and demonstrates the operating point destabilization in a single current-controlled CCM-based cell. Adding a dissipative resistor and a capacitor to the current-controlled CCM, preliminarily poised on anedge of chaosoperating point, gives birth to two unstable circuits, inducing a local quiescent bi-stability and a local oscillation, respectively. The mechanisms behind a local form ofTuring Instability, appearing in a current-controlled CCM-based two-cell array, have been elucidated, and the bifurcation, spawning symmetry-breaking effects, locally, across the cellular network, has been identified. Both numerical and experimental results confirm the correctness of the theoretical analysis.

Chua corsage memristor (CCM) is characterized by its local activity and can be used to construct neuron circuits. Edge of chaos is a subset of the locally active domain, which is responsible for the emergence of complexity and neuromorphic behaviors. When two identical resting “dead” CCM neurons poised on the edge of chaos are coupled through a linear passive resistor, these two neurons can be activated and a couple of oscillations appear. This phenomenon is referred to as the Smale paradox, which has not been observed from hardware circuits. The present paper addresses this issue by proposing the stability criterion of the two-port coupled system using the small-signal analysis method and then derives an emergence condition of the Smale paradox based on two coupled “dead” CCM neurons in terms of the parameter value ranges. Simulation results demonstrate the correctness of the theoretical analysis. Interestingly, anti-phase synchronization is observed after two identical neurons are coupled with a linear resistor, which is different from the traditional in-phase synchronization between resistively coupled oscillators. The resistively coupled memristive neurons are implemented by hardware based on the poor man’s circuit. The experimental results confirm the reproduction of the Smale paradox and reveal the effect of the coupling resistance on the dynamics of the system.

Inspired by recent research reported in [1], this paper investigates the bio-inspired bifurcation patterns of a simple memristive neuron on edge of chaos. The adopted memristive neuron, comprising a DC current source, a current-controlled locally active memristor, and a capacitor, successfully reproduces the bifurcation cascade patterns observed in the Hodgkin-Huxley (H-H) neuron model, including fold limit cycle bifurcation (FLCB), subcritical Hopf bifurcation (SUB-HB), and supercritical Hopf bifurcation (SUP-HB). Through attraction basin analysis and pulse-based initial state regulation, we verify the coexistence phenomenon of stable and unstable limit cycles induced by FLCB, as well as the bistable behaviors triggered by SUB-HB. Furthermore, taking resistively coupled memristive neurons as an example, we explore the influence of the dynamics of individual neurons on the bifurcation patterns of coupled networks, where two neurons have identical parameters but different initial states. The results demonstrate that the three bifurcation modes also emerge in memristive coupled networks, and their evolutionary patterns are closely related to the dynamic behaviors of individual neurons. Finally, hardware experiments successfully reproduce the bifurcation cascade phenomenon thereby validating the correctness of theoretical analysis and simulation results.

In this paper, we propose a novel inductor-free chaotic circuit by using two locally active memristors (LAMs), a capacitor, and a DC bias. These two LAMs are the current-controlled and voltage-controlled type, respectively, exhibiting S-type and N-type DC V-I (voltage-current) characteristics. Only when the two LAMs are both operated in the negative differential resistance (NDR) regions, may the periodical and chaotic dynamic behaviors appear in the proposed circuit. This may be because the local activity contributes to the generation of complexity. With different initial conditions, the coexisting attractors are observed in the circuit, which is analyzed through the equilibrium points and phase portraits. Finally, physical circuit realizations of the inductor-free chaotic circuit are presented, including the S-type and N-type memristor emulators. Both simulation and experimental results demonstrate the feasibility of the proposed chaotic circuit.

This article proposes a new compact model and presents a circuit-theoretical analysis for a third-order memristive neuromorphic element fabricated by Kumar et al. The proposed model mainly consists of a box-shaped resistor model and a simplified piecewise-linear memristor model. Since the dynamic behavior of the box-shaped hysteresis in the quasistatic current–voltage curve is mostly unexplored, we first extract the box-shaped resistor model and construct its oscillators. The coordinate system shifting method and dynamic route analysis method are used to reveal the operating mechanism of boxshaped resistor-based oscillators. Both the theoretical analysis and simulation verification indicate that the box-shaped hysteresis characteristic facilitates the generation of neuromorphic action potentials. The proposed new compact model not only captures quasi-static characteristics but also includes dynamic behaviors, such as action potential, periodic spiking, and periodic bursting. The influences of the model parameters are further investigated to reveal the mechanism of the neuromorphic behaviors in the box-shaped hysteresis and positive differential resistance regions. Simulation results manifest the feasibility of the proposed model and the correctness of the presented analysis methods, which pave the way to the optimized design of memristive devices and the research of neuromorphic dynamics.

Locally-active memristor (LAM) is one of the promising candidates of artificial neurons, indicating it has potential applications in neuromorphic computing. Quantitative theoretical analysis on LAMs can provide benefits for designing related oscillator circuits and systems. This study begins with the aim of assessing the importance of DCV-Icharacteristic in the performance of LAMs by using small-signal analysis method. The DCV-Icurve of the LAM is specified by two parameters involving resistance (conductance) and differential resistance (differential conductance). In addition to these two static parameters, we extract a crucial dynamic parameter to describe the behavior of the LAM. Theoretical analysis demonstrates that the performance of generic current-controlled and voltage-controlled LAMs is closely associated with three crucial parameters, i.e., the above two static and one dynamic parameters. Hence, only based on these three parameters, can one derive the small-signal equivalent circuit of LAMs and determine the oscillation frequency range and condition for simple LAM-based oscillators. By applying the presented universal dynamics analysis results, we further propose a modified mathematical model with higher accuracy to mimic the quasi-static and oscillating behaviors of a real Nb2O5device, and provide some fundamental guidance for the design of LAM-based high-frequency oscillators.

Neuromorphic computing can solve computationally hard problems with energy efficiencies unattainable for von Neumann architectures. A locally-active memristor, which possesses the capability to amplify infinitesimal fluctuations in energy and can be used to generate neuromorphic behaviors, is a natural candidate for constructing an electronic equivalent of biological neurons. This paper identifies some unknown neuromorphic dynamics of the Chua corsage memristor (CCM), and shows that the CCM, when biased at the edge of chaos domain, can exhibit rich dynamics of biological neurons. Using Chua’s theories of local activity and edge of chaos, we demonstrate that under the destabilizing of the input voltage and the circuit parameters (inductance or capacitance), two CCM-based circuits can produce thirteen types of neuromorphic behaviors either on, or near the edge of chaos domain via supercritical or subcritical Hopf bifurcation. In addition, we give the conditions to test the edge of chaos of the CCM and the CCM-based circuit only by using the poles and the zero of their admittance functions.