Chaos and multi-layer attractors in asymmetric neural networks coupled with discrete fractional memristor

Dynamics of heterogeneous Hopfield neural network with adaptive activation function based on memristor

Memristor and activation function are two important nonlinear factors of the memristive Hopfield neural network. The effects of different memristors on the dynamics of Hopfield neural networks have been studied by many researchers. However, less attention has been paid to the activation function. In this paper, we present a heterogeneous memristive Hopfield neural network with neurons using different activation functions. The activation functions include fixed activation functions and an adaptive activation function, where the adaptive activation function is based on a memristor. The theoretical and experimental study of the neural network's dynamics has been conducted using phase portraits, bifurcation diagrams, and Lyapunov exponents spectras. Numerical results show that complex dynamical behaviors such as multi-scroll chaos, transient chaos, state jumps and multi-type coexisting attractors can be observed in the heterogeneous memristive Hopfield neural network. In addition, the hardware implementation of memristive Hopfield neural network with adaptive activation function is designed and verified. The experimental results are in good agreement with those obtained using numerical simulations.

Offset boosting in a discrete system

Offset boosting plays an important role in chaos application in electronic engineering. A direct variable substitution typically will destroy the dynamics of a discrete map even though the initial condition is well considered. The internal fundamental reason is that the left-hand side of a discrete system does not have the dimension of variable differentiation (DVD) like the one of a continuous system. When the key property of DVD is completely preserved, the offset boosting based on a parameter or the initial condition can be reasonably achieved like in a differential system. Consequently, by the initial condition-oriented offset boosting, flexible multistability like attractor self-reproducing or attractor doubling can be further realized. A circuit experiment is completed for the verification of reliable offset boosting. The systematic exploration of offset boosting in a map will cast a new light on chaos regulation and attractor transportation in a discrete map. As a simple case, a two-dimensional Hénon map is taken as the example demonstrating the achievement of offset boosting via the parameter or initial condition.

Coexisting Firing Patterns in an Improved Memristive Hindmarsh-Rose Neuron Model with Multi-Frequency Alternating Current Injection

With the development of memristor theory, the application of memristor in the field of the nervous system has achieved remarkable results and has bright development prospects. Flux-controlled memristor can be used to describe the magnetic induction effect of the neuron. Based on the Hindmarsh-Rose (HR) neuron model, a new HR neuron model is proposed by introducing a flux-controlled memristor and a multi-frequency excitation with high-low frequency current superimposed. Various firing patterns under single and multiple stimuli are investigated. The model can exhibit different coexisting firing patterns. In addition, when the memristor coupling strength changes, the multiple stability of the model is eliminated, which is a rare phenomenon. Moreover, an analog circuit is built to verify the numerical simulation results.