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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自然界中的异宿循环

摘要 异宿循环是由稳态（或更一般的不变子集）和异宿轨迹组成的动力系统的不变量。具有异宿循环的动力系统的行为是间歇性的：一个典型的轨迹在接近稳态时停留很长时间，而状态之间的转换发生得更快。间歇性存在于各种物理现象中，例如地球大气环流、长时间间隔考虑的气候变化、物种进化、疾病分布、地球磁场的行为等。在本文中，我们考虑了这个自然系统的例子和各自具有异环环的数学模型。