Stability Analysis of Fractional Order Memristor Synapse-coupled Hopfield Neural Network with Ring Structure

A memristor is a non-linear two-terminal electrical element that incorporates memory features and nanoscale properties, enabling us to design very high-density artificial neural networks. To examine the embedded memory property, we should use mathematical frameworks like fractional calculus, which is capable of doing so. Here, we first present a fractional-order memristor synapse-coupling Hopfield neural network on two neurons and then extend the model to a neural network with a ring structure that consists of $n$ sub-network neurons. Necessary and sufficient conditions for the stability of equilibrium points are investigated, highlighting the dependency of the stability on the fractional-order value and the number of neurons. Numerical simulations and bifurcation analysis, along with Lyapunov exponents, are given in the two-neuron case that substantiates the theoretical findings, suggesting possible routes towards chaos when the fractional order of the system increases. In the $n$-neuron case also, it is revealed that the stability depends on the structure and number of sub-networks.

A Novel Refreshment Circuit for 2T1M Neuromorphic Synapse

Neuromorphic systems are the future computing systems to overcome the von Neumann’s power consumption and latency wall between memory and processing units. The two main components of any neuromorphic computing system are neurons and synapses. Synapses carry the weight of the system to be multiplied by the neuromorphic attributes, which represent the features of the task to be solved. Memristor (memoryresistor) is the most suitable circuit element to act as a synapse. Its ability to store, update and do matrix multiplication in nanoscale die area makes it very useful in neuromorphic synapses. One of the most popular memristor synapse configurations is the two-transistor–one-memristor (2T1M) synapse. This configuration is very useful in neuromorphic synapses for its ability to control reading and updating the weight on a chip by signals. The main problem with this synapse is that the reading operation is destructive, which results in changing the stored weight value. In this paper, a novel refreshment circuit is proposed to restore the correct weight in case of any destructive reading operations. The circuit makes a small interrupt time during operation without disconnecting the memristor, which makes the circuit very practical. The circuit has been simulated by using hardware-calibrated CMOS TSMC 130[Formula: see text]nm technology on Cadence Virtuoso and linear ion drift memristor Verilog-A model. The proposed circuit achieves the refreshment task accurately for several error types. It is used to refresh 2T1M synapse with any destructive reading signal shape.

Memristor Initial-Offset Boosting in Memristive HR Neuron Model with Hidden Firing Patterns

A new three-dimensional (3D) memristive HR neuron model is presented, which is improved from an existing memristive HR neuron model using a memristor synapse with sine memductance to substitute the original one. The improved memristive HR neuron model has no equilibrium but hidden firing activities can emerge with discrete memristor initial-offset boosting. Treating the neuron model as a two-dimensional (2D) major subsystem controlled by a magnetic flux variable, fold bifurcations for hidden chaotic and periodic firing patterns are elaborated. The coexistence of hidden firing patterns induced by memristor initial boosting is quantitatively analyzed and numerically simulated by bifurcation plots, phase plots, and basins of attraction. The results demonstrate that the improved memristive HR neuron model can exhibit a discrete memristor initial-offset boosting behavior owning infinitely many disconnected basins of attraction and the generating firing patterns can be boosted to different discrete levels by changing the memristor initial value, differing entirely from various boosting behaviors reported previously. Therefore, infinitely many hidden coexisting offset-boosted firing patterns with the same initial-offsets and attractor types are disclosed along the boosting route, which are homogenous with extreme multistability and are perfectly validated by PSIM circuit simulations based on a physically implementation-oriented analog circuit.

Memristor Synapse-Based Morris–Lecar Model: Bifurcation Analyses and FPGA-Based Validations for Periodic and Chaotic Bursting/Spiking Firings

Electromagnetic induction current sensed by the membrane potential in biological neurons can be characterized with a memristor synapse, which can be employed to demonstrate the real oscillating voltage patterns of Barnacle muscle fibers. This paper presents a 3D autonomous memristor synapse-based Morris–Lecar (abbreviated as m-ML) model, which is implemented through introducing a memristor synapse-based induction current to substitute the externally applied current in an existing 2D nonautonomous Morris–Lecar model. Making use of one- and two-parameter bifurcation plots and time-domain representations, diverse period-adding bifurcations as well as abundant periodic and chaotic burst firings are demonstrated. Through constructing the fold and Hopf bifurcation sets of fast spiking subsystem, bifurcation analyses of these chaotic and periodic burst firings are carried out. Moreover, the periodic and chaotic spiking firings and coexisting firing behaviors are illustrated by using one- and two-parameter bifurcation plots and local attraction basins. Finally, based on a field programmable gate array (FPGA) board, a compact digital electronic neuron is fabricated for the 3D m-ML model, from which periodic and chaotic bursting/spiking firings are experimentally measured to verify the results of the numerical simulations.