Abstract
Heteroclinic cycle is an invariant of a dynamical system comprised of steady states (or more general invariant subsets) and heteroclinic trajectories. The behavior of a dynamical system with a heteroclinic cycle is intermittent: a typical trajectory stays for a long time close to a steady state while the transitions between the states occur much faster. Intermittency is present in various physical phenomena, e.g., Earth’s atmospheric circulation, climate variations considered on long time intervals, evolution of species, distribution of diseases, behavior of the Earth’s magnetic field and many others. In this paper, we consider the examples of this natural system and the respective mathematical models possessing heterocliic cycles.
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