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Attractors of strongly dissipative systems

Ramm A. G.

Bulletin of the Polish Academy of Sciences. Mathematics

2009

Vol. 57, no 1

25-31

A class of infinite-dimensional dissipative dynamical systems is denned for which there exists a unique equilibrium point, and the rate of convergence to this point of the trajectories of a dynamical system from the above class is exponential. All the trajectories of the system converge to this point as t → +∞, no matter what the initial conditions are. This class consists of strongly dissipative systems. An example of such systems is provided by passive systems in network theory (see, e.g., MR0601947 (83m:45002)).