TAILIEUCHUNG - Indentical synchronization in complete network of reaction diffusion equations of Fizhugh - Nagumo

In this paper, we study about the synchronization in complete network consisting of n nodes. Each node is connected to all other nodes by linear coupling and it is represented by a system of reaction-diffusion of FitzHugh-Nagumo type which is obtained by simplifying the famous Hodgkin-Huxley model. | An Giang University Journal of Science – 2017, Vol. 5 (2), 51 – 58 INDENTICAL SYNCHRONIZATION IN COMPLETE NETWORK OF REACTION-DIFFUSION EQUATIONS OF FIZHUGH-NAGUMO Phan Van Long Em1 1 An Giang University Information: Received: 09/05/2016 Accepted: 10/06/2016 Published: 06/2017 Keywords: FitzHugh-Nagumo model, synchronization, coupling strength, complete network ABSTRACT Synchronization is a ubiquitous feature in many natural systems and nonlinear science. In this paper, we study about the synchronization in complete network consisting of n nodes. Each node is connected to all other nodes by linear coupling and it is represented by a system of reaction-diffusion of FitzHughNagumo type which is obtained by simplifying the famous Hodgkin-Huxley model. From this complete network, we seek a sufficient condition under the coupling strength such that we have the synchronization phenomenon. The result shows that the networks with bigger in-degrees of the nodes synchronize more easily. When we have a such consequence, we test this theoretical result numerically and see that there is a compromise. 1. INTRODUCTION The FitzHugh-Nagumo model was introduced as a dimensional reduction of the well-known Hodgkin-Huxley model (see, . Ermentrout, 2009 ; Hodgkin, 1952 ; Izhikevich, 2007 ; Keener, 2009 ; Murray, 2010 ; Nagumo, 1962). It is more analytically tractable and it maintains a certain biophysical meaning. The model is constituted by two equations in two variables u and v . The first one is the fast variable called excitatory: it represents the transmembrane voltage. The second variable is the slow recovery variable: it describes the time dependence of several physical quantities, such as the electrical conductance of the ion currents across the membrane. The FitzHughNagumo equations (FHN), using the notation in (Ambrosio & Aziz-Alaoui, 2012 ; Ambrosio, 2009 ; Ambrosio & Aziz-Alaoui, 2012 ; Ambrosio & Aziz-Alaoui, 2013), are given by, du dt f (u ) v dv au

• Vật lý
• Indentical synchronization
• FitzHugh Nagumo model
• Coupling strength
• Complete network
• Reaction diffusion equations
• Hodgkin Huxley model