Attractors of Strongly Dissipative Systems
Volume 57 / 2009
Bulletin Polish Acad. Sci. Math. 57 (2009), 25-31
MSC: 37L99, 47H05, 47H20, 47J35, 78A40, 80A30.
DOI: 10.4064/ba57-1-3
Abstract
A class of infinite-dimensional dissipative dynamical systems is defined 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 $t\to +\infty$, 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)).
