Dissipative system
D-system, limit-bounded system
A system of ordinary differential equations
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with continuous right-hand side, whose solutions satisfy the properties of uniqueness and infinite extendability to the right, and for which there exists a number
such that for any solution
it is possible to find a moment in time
such that
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In other words, each solution is immersed, sooner or later, in a fixed sphere . An important particular case of a dissipative system are the so-called systems with convergence, for which all solutions
are defined for
and, in addition, there exists a unique bounded solution on the entire axis which is asymptotically stable in the large. Such systems have been thoroughly studied (see, for example, [1]).
References
[1] | V.A. Pliss, "Nonlocal problems of the theory of oscillations" , Acad. Press (1966) (Translated from Russian) |
[2] | B.P. Demidovich, "Lectures on the mathematical theory of stability" , Moscow (1967) (In Russian) |
Comments
References
[a1] | J.K. Hale, "Ordinary differential equations" , Wiley (1980) |
Dissipative system. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Dissipative_system&oldid=46751