Singular Perturbation Analysis of Competitive Neural Networks with Different Time Scales

Abstract

The dynamics of complex neural networks must include the aspects of long- and short-term memory. The behavior of the network is characterized by an equation of neural activity as a fast phenomenon and an equation of synaptic modification as a slow part of the neural system. The main idea of this paper is to apply a stability analysis method of fixed points of the combined activity and weight dynamics for a special class of competitive neural networks. We present a quadratic-type Lyapunov function for the flow of a competitive neural system with fast and slow dynamic variables as a global stability method and a modality of detecting the local stability behavior around individual equilibrium points.

Existence and global exponential stability of equilibrium of competitive neural networks with different time scales and multiple delays

“…A laterally inhibited neural network with a deterministic signal Hebbian learning law, which can model the dynamics of cortical cognitive maps with unsupervised synaptic modifications, was recently proposed and its global asymptotic stability was investigated in [1][2][3]. In this model, there are two types of state variables, the short-term memory variables (STM) describing the fast neural activity and the long-term memory (LTM) variables describing the slow unsupervised synaptic modifications.…”

Adaptive Exponential Synchronization for Stochastic Competitive Neural Networks with Time-Varying Leakage Delays and Reaction-Diffusion Terms

“…Meyer-Baese et al [1] proposed competitive neural networks with different timescales, which describe the dynamics of cortical cognitive maps with unsupervised synaptic modifications. In the competitive neural networks model, there are two types of state variables: the short-termmemory (STM) variables describing the fast neural activity and the long-term-memory (LTM) variables describing the slow unsupervised synaptic modifications.…”

Passivity Analysis of Dynamic Neural Networks with Different Time-scales

“…Dynamic neural networks with different time-scales can model the dynamics of the short-term memory (neural activity levels) and the long-term memory (dynamics of unsupervised synaptic modifications) [18]. The dynamics of neural networks with different time-scales are extremely complex, exhibiting convergence point attractors and periodic attractors [1].…”