Global asymptotic dynamics of a class of nonlinearly coupled neural networks with delays
Jui-Pin Tseng · Discrete and Continuous Dynamical Systems · 2013
This work presents an effectiveapproach to the study of the global asymptotic dynamics of general coupled systems.Under the developed framework, the problem of establishing global synchronizationor global convergencereduces to solving a corresponding system of linear equations. We illustrate this approach with a class of neural networks that consist of a pair ofsub-networks under various types of nonlinear and delayed couplings. We study both the synchronization and theasymptotic synchronous phases of the dynamics, including global convergence to zero, global convergence to multiple synchronous equilibria, and global synchronization with nontrivial synchronous periodic solutions. Our investigationalso provides theoretical support to some numerical findings, and improves or extend some results inthe literature.