ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Zagrebneva A. D., Govorukhin V. N., Surkov F. A. Bifurcations in active predator – passive prey model. Izvestiya VUZ. Applied Nonlinear Dynamics, 2014, vol. 22, iss. 3, pp. 94-106. DOI: 10.18500/0869-6632-2014-22-3-94-106

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Bifurcations in active predator – passive prey model

Zagrebneva Anna Dmitrievna, Southern Federal University
Govorukhin V. N., Southern Federal University
Surkov Fedor Alekseevich, Southern Federal University

Bifurcations were studied numerically in the system of partial differential equations, which is  a one variant of predator-prey models. The mathematical model takes into account spatial  distribution in habitat, active directed predator movements, birth and death process in prey  population. The analysis of possible population dynamics development was performed by two  qualitatively different discrete sampling techniques (Bubnov–Galerkin’s method and grid method).  As a bifurcation parameters the predator quantity and predator reaction rate to spatial non- uniformity of prey population were used. As a result of numerical investigation was found that  population under these assumptions can demonstrates a complex bifurcation transitions which leads  to various spatio-temporal dynamics: periodic, quasi-periodic and chaotic regimes.

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