Asymptotic behavior of periodic Cohen-Grossberg neural networks with delays.
Without assuming the positivity of the amplification functions, we prove some M-matrix criteria for the R(n)(+)-global asymptotic stability of periodic Cohen-Grossberg neural networks with delays. By an extension of the Lyapunov method, we are able to include neural systems with multiple nonnegative periodic solutions and nonexponential convergence rate in our model and also include the Lotka-Volterra system, an important prototype of competitive neural networks, as a special case. The stability criteria for autonomous systems then follow as a corollary. Two numerical examples are provided to show that the limiting equilibrium or periodic solution need not be positive.
Lin
Wei
W
Department of Mathematics, University of Southern California, Los Angeles, CA 90089, USA. linwei@usc.edu
D000818:Animals; D003198:Computer Simulation; D006801:Humans; D009415:Nerve Net / Q000502:physiology*; D016571:Neural Networks, Computer; D017711:Nonlinear Dynamics; D010363:Pattern Recognition, Automated; D010507:Periodicity; D013997:Time Factors