CHAOS AND PHASE SYNCHRONIZATION IN ECOLOGICAL SYSTEMS

Abstract

An ecological population model is presented for the purposes of exploring complex synchronization phenomena in biological systems. The model describes a three level predator–prey–resource system which oscillates with Uniform Phase evolution, yet has Chaotic Abundance levels or Amplitudes (UPCA). We investigate the phase synchronization of two nonidentical diffusively coupled phase coherent models (i.e. with UPCA dynamics) and extend the analysis to study the models' "funnel" regimes and response to noise forcing. Similar synchronization effects are reported for a two-dimensional lattice of chaotic population models coupled via nearest neighbors. With weak coupling, a collective phase synchronization emerges yet the peak population abundance levels are chaotic and largely uncorrelated. The synchronization patterns and traveling wave structures found in the spatial model correspond to those observed in natural systems — in particular, Ecology's well-known Canadian hare–lynx cycle. We show that phase synchronization has important applications in the study of ecological communities where the spatial coupling of populations can lead to large scale complex synchronization effects.