The European Physical Journal B

, Volume 66, Issue 1, pp 97–106 | Cite as

Dissipative oscillations in spatially restricted ecosystems due to long range migration

Interdisciplinary Physics


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.


82.40.Bj Oscillations, chaos, and bifurcations 05.45.Xt Synchronization; coupled oscillators Ecosysystems, structure, dynamics and modeling 02.70.Uu Applications of Monte Carlo methods 05.65.+b Self-organized systems 05.45.-a Nonlinear dynamics and chaos 


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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  1. 1.Institute of Physical ChemistryAthensGreece
  2. 2.Department of Mathematical, Physical and Computational ScienceFaculty of Engineering, Aristotle University of ThessalonikiThessalonikiGreece

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