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

For citation:

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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Russian
Heading: 
Bifurcations in Dynamical Systems
Article type: 
Article
UDC: 
51-76:519.63
DOI: 
10.18500/0869-6632-2014-22-3-94-106

Bifurcations in active predator – passive prey model

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

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.

Key words: 
Population dynamics
bifurcations
numerical analysis
taxis
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Received: 
18.04.2014
Accepted: 
16.07.2014
Published: 
31.10.2014
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