ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

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Rout to Chaos in Food Chain Dynamics


George Osipenko

Laboratory of Nonlinear Analysis,
St. Petersburg State Polytechnic University


The paper proves that a real discrete system with biological origin possesses a non-oriented invariant manifold - Möbius band. The obtained results demonstrate the existence of multiple attractors in food-chains models. Moreover, the parameter region with three coexisting and closely-spaced attractors was found. It should be noted that such a proximity does not exclude the possibility that a complicated situation may appear, which may lead to more intriguing biological consequences in the system under study or similar systems.
The route to chaos in the food-chain dynamics is investivated. The initial system (as a parameter M0 < 2.9 ) has a single stable fixed point, when the parameter M0 increases the systems passes through non-trivial cascad of the bifurcations which, when M0=3.65, results in the appearance of a minimal chaotic attractor covering a Möbius band.

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