title: Dynamic stability conditions for Lotka-Volterra recurrent neural networks with delays.
abstract: The Lotka-Volterra model of neural networks, derived from the membrane dynamics of competing neurons, have found successful applications in many "winner-take-all" types of problems. This paper studies the dynamic stability properties of general Lotka-Volterra recurrent neural networks with delays. Conditions for nondivergence of the neural networks are derived. These conditions are based on local inhibition of networks, thereby allowing these networks to possess a multistability property. Multistability is a necessary property of a network that will enable important neural computations such as those governing the decision making process. Under these nondivergence conditions, a compact set that globally attracts all the trajectories of a network can be computed explicitly. If the connection weight matrix of a network is symmetric in some sense, and the delays of the network are in L2 space, we can prove that the network will have the property of complete stability.
authors.affiliation: College of Computer Science and Engineering, University of Electrical Science and Technology of China, Chengdu 610054, People's Republic of China.
authors.forename: Zhang
authors.initials: Z
authors.lastname: Yi
authors.forename: K K
authors.initials: KK
authors.lastname: Tan