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Asymptotic solution for a class of nonlinear slow-fast system with small time delay
Author(s): 
Pages: 146-155
Year: Issue:  2
Journal: Pure and Applied Mathematics

Keyword:  slow-fast systemnonlinearsmall time delaysingular perturbationasymptotic solution;
Abstract: In this paper, the initial value problem for a class of nonlinear slow-fast systems with small time delay is considered. Under suitable assumptions and by using singular perturbation theory and the correction function method, the formal asymptotic solution of the problem is constructed. Then, by means of the differential inequalities theory, the uniformly validity of the asymptotic solution is proved. Finally, a numerical example is done, whose results reveal that time delay may have a significant impact on the slow-fast system, and show that the perturbation method is an effective approximate analytical method. Consequently, the behavior of the dynamic system can be better analyzed and studied by using the asymptotic solution.
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