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

• Published in: Journal of computational and applied mathematics 2008-06, Vol.216 (1), p.279-296
• Main Authors: Wang, Fengyan, Pang, Guoping, Chen, Lansun
• Format: Article
• Language: English
• Subjects: Asymptotically stable; Calculus of variations and optimal control; Exact sciences and technology; Global analysis, analysis on manifolds; Impulsive semi-dynamical system; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in mathematical programming, optimization and calculus of variations; Order- [formula omitted] periodic solution; Ordinary differential equations; Population models; Sciences and techniques of general use; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2007.05.005

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.