System-Size Effects on the Collective Dynamics of Cell Populations with Global Coupling
Abstract
Phase-transition-like behavior is found to occur in globally coupled systems consisting of finite numbers of elements, and a theoretical explanation of this behavior is given. The system studied is a population of globally pulse-coupled integrate-and-fire cells subject to a small additive noise. As the population size is changed, the system exhibits phase-transition-like behavior, that is, there exists a well-defined critical system size above which the system remains in a monostable state with high-frequency activity and below which a new phase characterized by the alternation of high- and low-frequency types of activity appears. The mean field motion obeys a stochastic process with a state-dependent noise, and the above described phenomenon can be interpreted as a noise-induced transition characteristic of such processes. The coexistence of high- and low-frequency activity observed in finite size systems was reported by Cohen, Soen and Braun [Physica A 249 (1998), 600] in experiments on cultivated heart cells. The present report gives the first qualitative interpretation of their experimental results.
- Publication:
-
Progress of Theoretical Physics
- Pub Date:
- January 2003
- DOI:
- 10.1143/PTP.109.51
- arXiv:
- arXiv:nlin/0210048
- Bibcode:
- 2003PThPh.109...51T
- Keywords:
-
- Nonlinear Sciences - Adaptation and Self-Organizing Systems;
- Condensed Matter;
- Quantitative Biology - Cell Behavior
- E-Print:
- doi:10.1143/PTP.109.51