Global convergence of Lotka-Volterra recurrent neural networks with delays

Recurrent neural networks of the Lotka-Volterra model have been proven to possess characteristics which are desirable in some neural computations. A clear understanding of the dynamical properties of a recurrent neural network is necessary for efficient applications of the network. This paper studies the global convergence of general Lotka-Volterra recurrent neural networks with variable delays. The contributions of this paper are: 1) sufficient conditions are established for lower positive boundedness of the networks; 2) global exponential stability conditions are obtained for the networks. These conditions are totally independent of the variable delays which are therefore allowed to be uncertain; 3) novel Lyapunov functionals are constructed to establish delays dependent conditions for global asymptotic stability, and 4) simulation results and examples are provided to supplement and illustrate the theoretical contributions presented.

I. Introduction

Global convergence of recurrent neural networks is an important dynamic property of neural networks for certain applications, including those relating to optimization. The global convergence of neural networks has been widely studied in recent years. One main goal of global convergence analysis is to establish weak and simple conditions which can be verified to guarantee the global convergence of networks. Since many neural networks are described in terms of nonlinear differential systems, necessary and sufficient conditions are difficult to derive. Recently, many sufficient conditions of global convergence for recurrent neural networks have been reported.