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Mathematical Sciences Letters
An International Journal


Volumes > Vol. 4 > No. 2


Function of Reachability for Autonomous Systems of Differential Equations

PP: 91-99
Katya Dishlieva, Angel Dishliev, Andrey Antonov, Rumyana Chukleva,
The initial value problems for autonomous systems of differential equations are the subject of this paper. In the phase space of such system is defined the so-called reachable set and a function of reachability is introduced. For each starting point x0, there is a corresponding function value which is equal to the time necessary to pass from x0 to the reachable set. Some properties of the function of reachability: continuity, boundedness and more are studied. A generalized model of interaction (competition) of two species, located in the same nutrient medium is considered.

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