Dynamical Behavior of Cooperative Supportive System Involving Intra-Network Delays in Information Propagation - G., Shirisha; K., Venkata Ratnam (Journal of Applied Nonlinear Dynamics, 2026)
A Cooperative Supportive network system consisting of the main system supported by a subsystem whose dynamics are described in two separate neuronal fields is considered. Time delays are introduced in intra-network propagation (communication) of information in the main system. The qualitative behavior of the solutions of the system is analyzed. The existence and uniqueness of equilibria and their stability is investigated. Several independent criteria on the parameters and the functional relations of the systems are obtained, to establish the global stability of the equilibrium. Estimates on time delay parameter for which the system remains stable are also obtained, using Lyapunov functional. Several numerical examples are provided to illustrate the results. Levenberg-Marquardt Algorithm is utilized for training the network and obtaining simulation results for the examples provided.