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.