Dissipative oscillations in spatially restricted ecosystems due to long range migration |
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Authors: | N Kouvaris A Provata |
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Institution: | (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 |
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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. |
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Keywords: | PACS" target="_blank">PACS 82 40 Bj Oscillations chaos and bifurcations 05 45 Xt Synchronization coupled oscillators 92 20 jp 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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