Qualitative analysis and applications of a kind of state-dependent impulsive differential equations

Authors:
Fengyan Wang;Guoping Pang;Lansun Chen
Affiliations:
College of Science, Jimei University, Xiamen Fujian 361021, PR China;Department of Mathematics and Computer Science, Yulin Normal University, Yulin Guangxi 537000, PR China;Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

Citing 3
Cited 1

Optimization problems for one-impulsive models from population dynamics

Nonlinear Analysis: Theory, Methods & Applications - Series A: Theory and Methods
An invariance principle for nonlinear hybrid and impulsive dynamical systems

Nonlinear Analysis: Theory, Methods & Applications
Optimal impulsive harvesting policy for single population

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Existence and stability of periodic solution of a Lotka-Volterra predator-prey model with state dependent impulsive effects

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Abstract

This paper analyzes a certain type of impulsive differential equations (IDEs). Several useful theorems for its periodic solutions and their stabilities are given. The key idea is that a periodically time-dependent IDE can be transformed into the state-dependent IDE. As applications of our theory, the optimization problems in population dynamics are studied. That is, the maximum sustainable yields of single population models with periodically impulsive constant harvesting are discussed. Furthermore, we apply these results to the studies of the order-1 periodic solutions and their stability of a single population model with stage structure in which the mature is impulsively proportionally harvested while the immature is impulsively added with the constant.