Eur. Phys. J. B 66, 97-106 (2008)
https://doi.org/10.1140/epjb/e2008-00373-8

Dissipative oscillations in spatially restricted ecosystems due to long range migration

¹ Institute of Physical Chemistry, National Center for Scientific Research “Demokritos”, 15310 Athens, Greece
² Department of Mathematical, Physical and Computational Science, Faculty of Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece

Corresponding author: ^a aprovata@limnos.chem.demokritos.gr

Received: 21 April 2008
Revised: 1 August 2008
Published online: 27 September 2008

Abstract

An ecosystem containing three interacting species is studied using both Mean Field approach and Kinetic Monte Carlo simulations on a lattice substrate. The so called 3rd order LLV model involves birth, death and reaction processes with 3rd order nonlinearities and feedbacks. At the mean field level this system exhibits conservative oscillations; the analytic form of the constant of motion is presented. The stochastic simulations show that the density oscillations disappear for sufficiently large lattices, while they are present locally, on small lattice windows. Introduction of mixing via long range migration in the two reacting species changes this picture. For small migration rates p, the behavior remains as with p = 0 and the system is divided into local asynchronous oscillators. As p increases the system passes through a phase transition and exhibits a weak disorder limit cycle through a supercritical Hopf-like bifurcation. The amplitude of the limit cycle depends on the rate p, on the range of migration r and on the system kinetic rates k₁, k₂ and k₃.