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Article

Spiral attractors as the root of a new type of "bursting activity" in the Rosenzweig-MacArthur model

European Physical Journal: Special Topics. 2018. No. 227. P. 959-970.
Bakhanova Y., Kazakov A., Korotkov A. G., Levanova T. A., Osipov G. V.

We study the peculiarities of spiral attractors in the Rosenzweig-MacArthur model, that relates to the life-science systems and describes dynamics in a food chain prey-predator-superpredator. It is well-known that spiral attractors having a \teacup" geometry are typical for this model at certain values of parameters for which the system can be considered as slow-fast system. We show that these attractors appear due to the Shilnikov scenario, the first step in which is associated with a supercritical Andronov{Hopf bifurcation and the last step leads to the appearance of a homoclinic attractor containing a homoclinic loop to a saddle-focus equilibrium with two-dimension unstable manifold. It is shown that the homoclinic spiral attractors together with the slow{fast behavior give rise to a new type of bursting activity in this system. Intervals of fast oscillations for such type of bursting alternate with slow motions of two types: small amplitude oscillations near a saddle-focus equilibrium and motions near a stable slow manifold of a fast subsystem. We demonstrate that such type of bursting activity can be either chaotic or regular.