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We study the peculiarities of spiral attractors in the Rosenzweig-MacArthurmodel, that describes dynamics in a food chain "prey-predator-superpredator".It is well-known that spiral attractors having a "teacup" geometry are typicalfor this model at certain values of parameters for which the system can beconsidered as slow-fast system. We show that these attractors appear due to theShilnikov scenario, the first step in which is associated with a supercriticalAndronov-Hopf bifurcation and the last step leads to the appearance of ahomoclinic attractor containing a homoclinic loop to a saddle-focus equilibriumwith two-dimension unstable manifold. It is shown that the homoclinic spiralattractors together with the slow-fast behavior give rise to a new type ofbursting activity in this system. Intervals of fast oscillations for such typeof bursting alternate with slow motions of two types: small amplitudeoscillations near a saddle-focus equilibrium and motions near a stable slowmanifold of a fast subsystem. We demonstrate that such type of burstingactivity can be either chaotic or regular.

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