Bifurcations and Phase Differences of Nonlinear Coupled Dictyostelium Systems

Abstract

Nagano proposed a mathematical model of coupled Dictyostelium systems and demonstrated the strong tendency of in-phase synchronization. In this study, we investigate the mechanisms of this phenomenon by obtaining bifurcation sets and analyzing the phase differences of responses. From the analysis results, the model has a wide parameter range giving a stable 1-periodic solution. Thus, the one-to-one synchronization is maintained regardless of changes in the environment parameters. For example, even if the frequency ratio of two oscillators is extremely unbalanced, the model with an appropriate coupling factor shows a 1-periodic solution.