System-Size Effects on the Collective Dynamics of Cell Populations with Global Coupling

Phase-transitionlike behavior is found to occur in globally coupled systems of finite number of elements, and its theoretical explanation is provided. The system studied is a population of globally pulse-coupled integrate-and-fire cells subject to small additive noise. As the population size is changed, the system shows a phase-transitionlike behavior. That is, there exits a well-defined critical system size above which the system stays in a monostable state with high-frequency activity while below which a new phase characterized by alternation of high- and low frequency activities appears. The mean field motion obeys a stochastic process with state-dependent noise, and the above phenomenon can be interpreted as a noise-induced transition characteristic to such processes. Coexistence of high- and low frequency activities observed in finite size systems is reported by N. Cohen, Y. Soen and E. Braun[Physica A249, 600 (1998)] in the experiments of cultivated heart cells. The present report gives the first qualitative interpretation of their experimental results.