Lyapunov Exponents of Convergent Cohen-Grossberg-Type BAM Networks with Delays and Large Impulses
Sannay Mohamad, Brunei Darussalam · 2008
The article is concerned with the exponential convergence of a CohenGrossberg-type BAM network, with time-varying and distributed transmission delays and large impulses, towards a unique equilibrium point. Without assuming the symmetry of the connection weight matrices and the smoothness and boundedness of amplification and activation functions, the analysis exploits a homeomorphic mapping, a Lyapunov function and a differential inequality to derive an M -matrix condition for the convergence of the network. The result consists of a relation involving the Lyapunov exponent of the corresponding non-impulsive network and the magnitude and frequency of the impulses. As special cases, one can obtain from the main result the exponential stability of a network that is subject to linear impulses of the contraction-type, and also for a network that is free from impulsive state displacements.