Please use this identifier to cite or link to this item: https://doi.org/10.1103/PhysRevE.66.011910
Title: Dynamic stability conditions for Lotka-Volterra recurrent neural networks with delays
Authors: Yi, Z.
Tan, K.K. 
Issue Date: Jul-2002
Citation: Yi, Z., Tan, K.K. (2002-07). Dynamic stability conditions for Lotka-Volterra recurrent neural networks with delays. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 66 (1) : 011910/1-011910/8. ScholarBank@NUS Repository. https://doi.org/10.1103/PhysRevE.66.011910
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. ©2002 The American Physical Society.
Source Title: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
URI: http://scholarbank.nus.edu.sg/handle/10635/82188
ISSN: 15393755
DOI: 10.1103/PhysRevE.66.011910
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