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Fast–slow dynamics in first-order initial value problems with slowly varying parameters and application to a harvested Logistic model

Authors
Journal
Communications in Nonlinear Science and Numerical Simulation
1007-5704
Publisher
Elsevier
Volume
19
Issue
8
Identifiers
DOI: 10.1016/j.cnsns.2013.12.035
Keywords
  • Slowly Varying Parameters
  • Fast–Slow Dynamics
  • Fast–Slow Decomposition
  • Matching
  • Upper And Lower Solutions

Abstract

Abstract In this paper, by using fast–slow decomposition and matching in singular perturbation theory, we separate the fast–slow dynamics in first-order initial value problems with slowly varying parameters and construct the asymptotic approximations to the solutions. Also we prove that the asymptotic solutions are uniformly valid on O(1/∊) large time interval with O(∊) accuracy by using the method of upper and lower solutions. As an application of the general theory, we consider a Logistic model with slowly varying parameters and linear density dependent harvest, in which, we illustrate the theoretical results through several numerical examples.

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