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Equivalent Construction of Ordinary Differential Equations from Impulsive System

I. M. Esuabana, U. A. Abasiekwere*, J. A. Ugboh and Z. Lipcsey
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I. M. Esuabana: Department of Mathematics, University of Calabar, Calabar, Cross River State, Nigeria
U. A. Abasiekwere*: Department of Mathematics and Statistics, University of Uyo, Uyo, Akwa Ibom State, Nigeria
J. A. Ugboh: Department of Mathematics, University of Calabar, Calabar, Cross River State, Nigeria
Z. Lipcsey: Department of Mathematics, University of Calabar, Calabar, Cross River State, Nigeria

Academic Journal of Applied Mathematical Sciences, 2018, vol. 4, issue 8, 77-89

Abstract: We construct an ordinary differential equation representation of an impulsive system by a bijective transformation that structurally maps the solutions of the initial value problem of the impulsive differential equations to the solutions of the initial value problems of the ordinary differential equations. Established in this work is the relationship between impulsive differential equations and ordinary differential equations which play a fundamental role in qualitative analysis of the former. It is also established that an n-dimensional impulsive differential equation can be represented in terms of a 2n-dimensional ordinary differential equation. Figures are used to demonstrate the practicability of the methodology developed.

Keywords: Stability; Impulsive; Ordinary differential equations; Bijective transformation (search for similar items in EconPapers)
Date: 2018
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