Synchronization Phenomena in an Array of Population Dynamic Systems

Abstract

The paper applies continuation methods to examine fundFigureamental features of the complex dynamics that can arise in a cascaded system of population dynamic models. The individual model describes a bacterial population interacting with a population of viruses that attack the cells and exploit their reproductive system for their own replication. Coupling between the subsystems is brought about through a unidirectional flow of primary resources. In this way the individual subsystem is modulated by the varying nutrient concentration in the overflow from the upstream habitat. Synchronization of a single subsystem to an external periodic forcing exhibits an unusual bifurcation structure with global bifurcations appearing already at the lowest forcing amplitudes. This peculiarity is also observed for autonomous systems of two and three coupled habitats. Finally, local and global synchronization phenomena are investigated for a chain of 20 coupled population pools.