Geodesic
From Bistability to Coupling-Induced Oscillations in a Two-Habitat Model for the Rotifer Population Dynamics
A. B. Medvinsky1 ; M. M. Gonik1 ; A. V. Rusakov1 ; H. Malchow2
1 Institute of Theoretical and Experimental Biophysics, Pushchino, Moscow Region, 142290, Russia
2 Institute of Environmental Systems Research, University of Osnabrück, D-49069 Osnabrück, Germany
Mathematical modelling of natural phenomena, Tome 3 (2008) no. 3, pp. 103-114.

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We study the role of interactions between habitats in rotifer dynamics. For this purpose we use a modified version of the Consensus model. The Consensus model has been shown to be realistic enough to reproduce distinguishing features of the rotifer species dynamics. Being uncoupled, intrinsically bistable rotifer populations, which inhabit the regions under different environmental conditions, do not impact each other. We show that migration of the rotifers between the habitats leads to the transformation of bistability to oscillatory dynamics. The coupling-induced oscillations of the rotifer biomass are shown to be either regular or irregular depending on the value of the model parameters, which describe environmental conditions and the biomass exchange between the habitats. We show that the irregular oscillations are characterized by positive values of the Lyapunov exponent, which means that they are chaotic.
DOI : 10.1051/mmnp:2008059

A. B. Medvinsky 1 ; M. M. Gonik 1 ; A. V. Rusakov 1 ; H. Malchow 2

1 Institute of Theoretical and Experimental Biophysics, Pushchino, Moscow Region, 142290, Russia
2 Institute of Environmental Systems Research, University of Osnabrück, D-49069 Osnabrück, Germany 
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     author = {A. B. Medvinsky and M. M. Gonik and A. V. Rusakov and H. Malchow},
     title = {From {Bistability} to {Coupling-Induced} {Oscillations} in a {Two-Habitat} {Model} for the {Rotifer} {Population} {Dynamics}},
     journal = {Mathematical modelling of natural phenomena},
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A. B. Medvinsky; M. M. Gonik; A. V. Rusakov; H. Malchow. From Bistability to Coupling-Induced Oscillations in a Two-Habitat Model for the Rotifer Population Dynamics. Mathematical modelling of natural phenomena, Tome 3 (2008) no. 3, pp. 103-114. doi : 10.1051/mmnp:2008059. http://geodesic.mathdoc.fr/articles/10.1051/mmnp:2008059/

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