Geodesic
Synchronous oscillations of two populations of different species linked via interspecific interference competition
Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 23 (2015) no. 4, pp. 3-23.

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A model for competition of two different species is considered. It is assumed that each consumer specializes on one resource only. The resource uptake rates are held constant.The basic feature of the model is that the dynamics of the resource is much slower than that of the consumer.The two consumers are coupled through direct reciprocal inhibition. Besides, self-limitation of the consumers due to overcrowding is also taken into account. The resources are noninteractive. When uncoupled, each population is completely nonoscillatory.The application of multiple-scale analysis yields that strong competition leads to bistability and hysteresis in the system, while weak coupling results in synchronous antiphase relaxation oscillations of the populations.
Keywords: Consumer-resource, predator-prey, competition, relaxation oscillations, synchronization. 
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     author = {A. Mustafin},
     title = {Synchronous oscillations of two populations of different species linked via interspecific interference competition},
     journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
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     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVP_2015_23_4_a0/}
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A. Mustafin. Synchronous oscillations of two populations of different species linked via interspecific interference competition. Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 23 (2015) no. 4, pp. 3-23. http://geodesic.mathdoc.fr/item/IVP_2015_23_4_a0/