title: Global asymptotic stability of a class of dynamical neural networks.
abstract: The dynamics of cortical cognitive maps developed by self-organization must include the aspects of long and short-term memory. The behavior of the network is such characterized by an equation of neural activity as a fast phenomenon and an equation of synaptic modification as a slow part of the neural biologically relevant system. We present new stability conditions for analyzing the dynamics of a biological relevant system with different time scales based on the theory of flow invariance. We prove the existence and uniqueness of the equilibrium, and give a quadratic-type Lyapunov function for the flow of a competitive neural system with fast and slow dynamic variables and thus prove the global stability of the equilibrium point.
authors.affiliation: Department of Electrical and Computer Engineering, Florida State University, Tallahassee, FL 32310-6046, USA.
authors.forename: Anke
authors.initials: A
authors.lastname: Meyer-Bäse
authors.forename: Sergei S
authors.initials: SS
authors.lastname: Pilyugin
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D008568:Memory / Q000502:physiology*; D008959:Models, Neurological; D016571:Neural Networks, Computer; D017711:Nonlinear Dynamics