IJPAM: Volume 83, No. 2 (2013)

EXISTENCE OF AN OSCILLATING BEHAVIOR IN
THE DYNAMICS OF POPULATIONS MODELED BY
DELAY DIFFERENTIAL EQUATIONS WITH IMPULSES

V.I. Donev
Department of Mathematics
Technical University of Sliven
8800, Sliven, BULGARIA


Abstract. This paper is dealing with the investigation of oscillating properties of delay differential equations with impulses, which model the dynamics of populations. A technique based on a special function called ``impulsive exponent" is developed for construction of their characteristic equations. The resulting characteristic equations are examined for conditions under which the constructed solutions of the studied differential equations are found to be oscillating. The proposed method can be applied to solve practical problems in the field of the population dynamics, econometrics (dynamics of Goodwin's business cycles) etc.

Received: December 11, 2012

AMS Subject Classification:

Key Words and Phrases: delay differential equation, impulse, oscillating solution, characteristic equation, impulsive exponent

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DOI: 10.12732/ijpam.v83i2.15 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 83
Issue: 2