Nonlinear Phenomena in Complex Systems, 1999, Vol.2, No.2, pp.25--30

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

1999, Volume 2, Number 2, pp.25--30

Global Attractors, Attracting Regions and Regions of Visiting for Dynamical Systems.
A.V. Kartynnick, A.D. Linkevich

The phase space of an autonomous dissipative nonlinear dynamical system is investigated. It is proved that under certain conditions such a system has an attracting region A with a basin of attraction around it, i.e. any trajectory starting somewhere inside this basin reaches the region A after a finite time interval and never leaves A. In certain cases, the region A turns into a global attractor of the system when the basin of attraction coincides with the whole remaining part of the phase space and all attractors of the system lie inside the region A. Another theorem yields sufficient conditions under which a system has a region of visiting G in the phase space, i.e. any trajectory starting outside G reaches this region after a finite time interval (and further can leave G in contrast to the case of an attracting region). Several examples are considered.

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