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- W1570971029 abstract "The state of a dynamic system at a given moment t, the vector x(t) is an effect, its cause being a vector function on time, g(τ) defined for τ ⩽ t, representing the history of inputs till the moment t. The relation is x(t) = F[g(τ); τ ⩽ t], where F is the constitutive functional of the system. Generally, the dynamic system S has an infinite, but fading memory. The proposed mathematical model uses: 1) an adequate locally convex topology on the set Ωt of the functions g(τ) that may represent the infinite history of the causes which determine the state x(t) of the system; 2) the continuity of the constitutive functional F on this set Ωt, thus the fading memory being ensured; 3) the differentiability of F on the locally convex space Ωt in the Fréchet — Marinescu’s sense. A conclusion of this study is that a dynamic system is a superposition of a linear system, a synergetic system and a chaotic system." @default.
- W1570971029 created "2016-06-24" @default.
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- W1570971029 date "2004-01-01" @default.
- W1570971029 modified "2023-09-25" @default.
- W1570971029 title "The Synergy and the Chaos Identified in the Constitutive Equation of a Dynamic System" @default.
- W1570971029 cites W1546311093 @default.
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- W1570971029 doi "https://doi.org/10.1063/1.1787336" @default.
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