On the Review of Some Stability Properties of Fixed Points for Linear Differential Systems
Eziokwu, C. Emmanuel *
Department of Mathematics, Michael Okpara University of Agricuture Umudike, Abia State, Nigeria.
Aboaja Onyinyechi
Department of Mathematics, Michael Okpara University of Agricuture Umudike, Abia State, Nigeria.
Ekwoma Hannah
Department of Mathematics, Michael Okpara University of Agricuture Umudike, Abia State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This paper reviews the stability of coupled system of first order ordinary differential equations such that if F : R + xR2 \(\to\) Rn is continous, a fixed point \(\bar{x}\)(t), t\(\epsilon\)R+, of the system (1) is said to be stable provided it starts with \(\bar{x}\)0(t) at the origin and remains near \(\bar{x}\)0(t) for all t \(\epsilon\) R+ in a certain sense. This of course implies that small interferences in the system that effects small perturbations to the initial conditions of fixed points near to \(\bar{x}\) (0) do not intact cause a considerable change to these fixed points over the interval R+ . Though there exist numerous types of fixed point stability, but we in this work discuss basically the types that are most important in the applications of ordinary differential equations.
Keywords: Chromosome structure and function, Differential system, Fragile sites, fixed point for differential systems, stability of fixed points, eigen values of systems, perturbed differential equation