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Mathematical Model of Dynamics and Synchronization of Coupled Neurons Using Hindmarsh-Rose Model
| Content Provider | Semantic Scholar |
|---|---|
| Author | Mamat, Mustafa Kurniawan, Putra Wira Kartono, Agus Salleh, Zabidin |
| Copyright Year | 2012 |
| Abstract | This paper presents mathematical model of the dynamics and synchronization of coupled neurons. The aim is first the understanding of the biological meaning of existing mathematical systems concerning neurons such as Hindmarsh-Rose models. Synchronization is an interesting phenomenon that can occur in such large topologies consisting of connected systems, i.e. after a certain time period either some or all systems do show identical behavior. First of all the dynamical behavior of the Hindmarsh-Rose model is investigated. By using a fast-slow analysis the occurrence of the typical spiking and bursting modes are explained. The fast subsystem is responsible for the generation of periodic orbits, i.e. the spiking behavior, whereas the slow subsystem acts as a perturbation on them. Furthermore, by means of a bifurcation diagram it is shown that the outputs of the model can be chaotic. The analysis of these networks uses the synchronization theory via connections between neurons and can give rise to emergent properties and self-organization. In this paper, simulation results have showed two coupled neurons until ten coupled neurons. The values of strength coupled will small if the number of coupled neurons is many. It will show that many nerve cells in our body become synchronize with a smallest value of strength coupled. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.m-hikari.com/ams/ams-2012/ams-49-52-2012/mamatAMS49-52-2012-1.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
