Quasi-periodic states in coupled rings of cells

• Type: Article in International Scientific Journal
• Date: 2010

Authors

antoneli, f (Author) Other; dias, aps (Author) FCUP; pinto, cma (Author) Other

Journal

Title: Communications in Nonlinear Science and Numerical Simulation

Vol. 15 No. 4

Pages: 1048-1062

ISSN: 1007-5704

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 8 Citations

Scopus - 11 Citations

Scientific classification

FOS: Humanities > Languages and Literature

Other information

Authenticus ID: P-003-7PS

DOI: 10.1016/j.cnsns.2009.05.035

Abstract (EN): We study some dynamical features of certain coupled cell networks that consist of two (unidirectional or bidirectional) rings of cells coupled through a 'buffer' cell. Depending on how the rings and the buffer cell are coupled. the full network may have a non-trivial group of symmetries or a non-trivial group of 'interior' symmetries. This group is Z(p) x Z(q) in the unidirectional case and D-p x D-q in the bidirectional case. We are interested in finding quasi-periodic motion in these networks, motivated by an example presented by Golubitsky, Nicol and Stewart (Some curious phenomena in coupled cell systems, J Nonlinear Sci 2004; 14(2):207-36). In the examples considered here, we obtain quasi-periodic states through a sequence of Hopf bifurcations. Interestingly, we observe relaxation oscillation phenomena appearing further away from the last Hopf bifurcation point. We use XPPAUT and MATLAB to compute numerically the relevant states.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 15