Impulsive control in a stage structure population model with birth pulses

• Published in: Applied mathematics and computation Vol. 217; no. 7; pp. 3453 - 3460
• Main Authors: Ma, Zhongjun, Yang, Jian, Jiang, Guirong
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01.12.2010; Elsevier
• Subjects: Bifurcation theory; Birth; Birth pulse; Exact sciences and technology; Flip bifurcation; Global analysis, analysis on manifolds; Impulsive pest management strategy; Management; Mathematical analysis; Mathematical models; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Ordinary differential equations; Periodic solution; Pests; Sciences and techniques of general use; Stage structure population model; Strategy; Theorems; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; Birth pulse; Stage structure population model; Impulsive pest management strategy; Flip bifurcation; Periodic solution; Existence condition; Existence theorem; Bifurcation; Attractor; Numerical analysis; Applied mathematics; Stage structure; Positive solution; Numerical stability
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2010.09.012

The dynamical behavior of a stage structure population model with birth pulses and impulsive pest management strategy is discussed analytically and numerically. It is assumed that birth pulse and impulsive pest management strategy act with the same period, but not simultaneously. The existence and stability of the positive 2 T-period solution are investigated. By using center manifold theorem and bifurcation theorem, the conditions of existence for flip bifurcation are derived. Moreover, some detailed numerical results for phase portraits, periodic solutions, bifurcation diagram, and chaotic attractors, which are illustrated with two examples, are in good agreement with the theoretical analysis.