Local exponential stability of competitive neural networks with different time scales

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.…”

“…In [4], the theory of flow invariance was used to prove the boundedness of solutions of the neural network, and a sufficient condition was derived based on Lyapunov method. Meyer-B¨ase et al [2] presented a condition for the uniqueness and global exponential stability of neurosynaptic system also based on the theory of flow invariance. A special case of these neural networks was given in [8].…”

“…Cohen and Grossberg [7] found a Lyapunov functional for such a neural network, and derived some sufficient conditions ensuring absolute stability. For the competitive neural network with two time scales, the stability was studied in [1,2,4]. In [1], the theory of singular perturbations was employed to derive a condition for global asymptotic stability of the neural networks (1) and (2).…”

“…For the competitive neural network with two time scales, the stability was studied in [1,2,4]. In [1], the theory of singular perturbations was employed to derive a condition for global asymptotic stability of the neural networks (1) and (2). In [4], the theory of flow invariance was used to prove the boundedness of solutions of the neural network, and a sufficient condition was derived based on Lyapunov method.…”

Synchronization of unknown chaotic delayed competitive neural networks with different time scales based on adaptive control and parameter identification

“…Recently, Meyer-Bäse et al [13][14][15] proposed the so-called competitive neural networks with different time scales. In the competitive neural networks model, there are two types of state variables: the short-term memory (STM) variable describing the fast neural activity, and the long-term memory (LTM) variable describing the slow unsupervised synaptic modifications.…”