Abstract
The synchronization in complete network consisting of nodes is studied in this paper. Each node is connected to all other ones by nonlinear coupling and is represented by a reaction-diffusion system of FitzHugh-Nagumo type which can be obtained by simplifying the famous Hodgkin-Huxley model. From this complete network, the sufficient condition on the coupling strength to achieve the synchronization is found. The result shows that the networks with bigger in-degrees of nodes synchronize more easily. The paper also presents the numerical simulations for theoretical result and shows a compromise between the theoretical and numerical results.
Reference13 articles.
1. Synchronization and control of coupled reaction-diffusion systems of the FitzHugh-Nagumo-type;Ambrosio;Computers and Mathematics with Applications 64,2012
2. Synchronization and control of a network of coupled reaction-diffusion systems of generalized FitzHugh-Nagumo type;Ambrosio;ESAIM,2013
3. Synchronization of Chaos;Aziz-Alaoui;Encyclopedia of Mathematical Physics Elsevier 5,2006
4. Synchronization of bursting neurons: What matters in the network topology;Belykh;Phys,2005
5. Corson, N. (2009). Dynamique d'un modèle neuronal, synchronisation et complexité (doctoral dissertation). University of Le Havre, France.