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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Dynamical Behavior of Cooperative Supportive System Involving Intra-Network Delays in Information Propagation

Journal of Applied Nonlinear Dynamics 11(3) (2022) 719--739 | DOI:10.5890/JAND.2022.09.012

Shirisha G., Venkata Ratnam K.

Department of Mathematics, Birla Institute of Technology and Science-Pilani-Hyderabad Campus, Jawahar

Nagar, Hyderabad-500078, Telangana State, India

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Abstract

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.

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