The qualitative analysis of a dynamical system of differential equations arising from the study of multilayer scales on pure metals II期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

The qualitative analysis of a dynamical system of differential equations arising from the study of multilayer scales on pure metals II

Authors:	R. L. Baker

Affiliation:	Department of Mathematics, University of Iowa, Iowa City, Iowa 52242

Abstract:	We provide a qualitative analysis of the -dimensional dynamical system: $begin{displaymath}dot q_i=-sum _{j=1}^n frac{a_{ij}}{q_j^k},quad q_i(t)>0,qquad i=1,dots, n, end{displaymath}$ where is an arbitrary positive integer. Under mild algebraic conditions on the constant matrix $A=(a_{ij})$ , we show that every solution , , extends to a solution on , such that $lim _{tto+infty} q_i(t)=+infty$ , for . Moreover, the difference between any two solutions approaches as . We then use this result to give a complete qualitative analysis of a 3-dimensional dynamical system introduced by F. Gesmundo and F. Viani in modeling parabolic growth of three-oxide scales on pure metals.

Keywords:	Differential equations dynamical systems nonlinear dynamical systems cooperative dynamical systems

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