IJPAM: Volume 70, No. 2 (2011)

ORBITAL HAUSDORFF CONTINUOUS DEPENDENCE
OF THE SOLUTIONS OF IMPULSIVE DIFFERENTIAL
EQUATIONS WITH RESPECT TO IMPULSIVE
PERTURBATIONS

A.B. Dishliev$^1$, K.G. Dishlieva$^2$
$^1$Department of Mathematics
University of Chemical Technology and Metallurgy
8, Kliment Ohridsky, Sofia 1756, BULGARIA
e-mail: [email protected]
$^2$Faculty of Applied Mathematics and Informatics
Technical University of Sofia
Sofia, BULGARIA
email: [email protected]


Abstract. The impulsive nonlinear autonomous systems of differential equations with non fixed moments of impulsive perturbation are the fundamental objects of investigation in the present paper. The impulses are realized when the trajectory of the solution falls over the so called ``impulsive set'', situated in the phase space of the system. For such type of problems are introduced the concepts orbital Hausdorff continuous dependence with respect to the initial point and the impulsive perturbations. Sufficient conditions are found out under which the solutions possess this property. The results are applied to the generalized mathematical model of the evolution dynamics of a prey-predator type co association, which is subjected to short term external influences.

Received: February 22, 2011

AMS Subject Classification: 34A37, 92D50

Key Words and Phrases: autonomous differential equations, impulses, variable impulsive moments, orbital Hausdorff continuous dependence, impulsive perturbations, Lotka-Volterra model

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 70
Issue: 2