Synchronization of coupled equations of Hodgkin-Huxley type

• Type: Article in International Scientific Journal
• Date: 2003

Authors

Labouriau, IS (Author) FCUP; Rodrigues, HM (Author) Other

Journal

Title: Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis

Vol. 10

Pages: 463-476

ISSN: 1201-3390

Publisher: Watam Press

Indexing

ISI Web of Knowledge - 12 Citations

Scopus - 15 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-000-HV2

Abstract (EN): We study a class of differential equations modelling the. electrical activity in biological systems. This class includes the Hodgkin-Huxley equations for the nerve impulse, as well as models for other excitable tissue, like muscle fibers, pacemakers and pancreatic cells. We show that when two of these equations are coupled their solutions always synchronize. Synchronization takes place regardless of the initial condition if the coupling is strong enough, and even for two equations with different parameter values, coupled asymetrically. We find a bounded region in phase space that attracts the flow globally and thus contains all points with recurrent behaviour. The size of the region can be calculated from the parameters in the equations. Thus we show that the system is uniformly dissipative. We obtain explicit bounds for this region in terms of the parameters as a tool for establishing synchronization. These estimates are also obtained for the uncoupled equations.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 14