Existence and Global Exponential Stability of Equilibrium Solution to Reaction‐Diffusion Recurrent Neural Networks on Time Scales
Kaihong Zhao, Yongkun Li · Discrete Dynamics in Nature and Society · 2010
The existence of equilibrium solutions to reaction‐diffusion recurrent neural networks with Dirichlet boundary conditions on time scales is proved by the topological degree theory and M‐matrix method. Under some sufficient conditions, we obtain the uniqueness and global exponential stability of equilibrium solution to reaction‐diffusion recurrent neural networks with Dirichlet boundary conditions on time scales by constructing suitable Lyapunov functional and inequality skills. One example is given to illustrate the effectiveness of our results.