Loss of synchronization in partially coupled Hodgkin-Huxley equations

• Type: Article in International Scientific Journal
• Date: 2004

Authors

Labouriau, IS (Author) FCUP; Alves Pinto, C (Author) Other

Journal

Title: Bulletin of Mathematical Biology

Vol. 66

Pages: 539-557

ISSN: 0092-8240

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 8 Citations

Scopus - 10 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-000-AFG

DOI: 10.1016/j.bulm.2003.09.006

Abstract (EN): We study the loss of synchronization of two partially coupled space-clamped Hodgkin-Huxley equations, with symmetric coupling. This models the coupling of two cells through an electrical synapse. For strong enough coupling it is known that all solutions of the equations approach a state where the two cells are perfectly synchronized, having the same behaviour at each moment. We describe the local bifurcations that arise when the coupling strength is reduced, using a mixture of analytical and numerical methods. We find that perfect synchrony is retained for very small positive values of the coupling strength, for almost all initial conditions. Although perfect synchrony is lost for negative values of the coupling constant, the system always retains some degree of synchronization until it becomes totally unstable. This happens in two ways: in many cases for almost all initial conditions the solutions still approach a perfectly synchronized state. Even when this is not true, the attracting solutions are still synchronized, with a half-period phase shift.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 19