Deterministic characteristics of spontaneous activity detected by multi-fractal analysis in a spiking neural network with long-tailed distributions of synaptic weights

Stability analysis of fractional order memristor synapse-coupled hopfield neural network with ring structure

A memristor is a nonlinear two-terminal electrical element that incorporates memory features and nanoscale properties, enabling us to design very high-density artificial neural networks. To enhance the 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, increasing the synchronization in the network. 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.

Complex spiking neural networks with synaptic time-delay based on anti-interference function

The research on a brain-like model with bio-interpretability is conductive to promoting its information processing ability in the field of artificial intelligence. Biological results show that the synaptic time-delay can improve the information processing abilities of the nervous system, which are an important factor related to the formation of brain cognitive functions. However, the synaptic plasticity with time-delay of a brain-like model still lacks bio-interpretability. In this study, combining excitatory and inhibitory synapses, we construct the complex spiking neural networks (CSNNs) with synaptic time-delay that more conforms biological characteristics, in which the topology has scale-free property and small-world property, and the nodes are represented by an Izhikevich neuron model. Then, the information processing abilities of CSNNs with different types of synaptic time-delay are comparatively evaluated based on the anti-interference function, and the mechanism of this function is discussed. Using two indicators of the anti-interference function and three kinds of noise, our simulation results consistently verify that: (i) From the perspective of anti-interference function, an CSNN with synaptic random time-delay outperforms an CSNN with synaptic fixed time-delay, which in turn outperforms an CSNN with synaptic none time-delay. The results imply that brain-like networks with more bio-interpretable synaptic time-delay have stronger information processing abilities. (ii) The synaptic plasticity is the intrinsic factor of the anti-interference function of CSNNs with different types of synaptic time-delay. (iii) The synaptic random time-delay makes an CSNN present better topological characteristics, which can improve the information processing ability of a brain-like network. It implies that synaptic time-delay is a factor that affects the anti-interference function at the level of performance.