ON PERIOD-K SOLUTION FOR A POPULATION SYSTEM WITH STATE-DEPENDENT IMPULSIVE EFFECT | Zendy

Xiaowei Tang | Zendy; Xilin Fu | Zendy

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ON PERIOD-<i>K</i> SOLUTION FOR A POPULATION SYSTEM WITH STATE-DEPENDENT IMPULSIVE EFFECT

Author(s) -

Xiaowei Tang,

Xilin Fu

Publication year - 2017

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/2017028

Subject(s) - eigenvalues and eigenvectors , mathematics , period (music) , population , trajectory , differential equation , mathematical analysis , control theory (sociology) , physics , computer science , quantum mechanics , demography , control (management) , artificial intelligence , sociology , acoustics

The period-k solutions of population differential system with statedependent impulsive effect are investigated by the theory of discontinuous dynamical system. Through G-function theory, the necessary and sufficient conditions are obtained for trajectory direction of a population differential system, and the results are better than the previous work. Also, the local stability of period-k solutions is studied by the mapping structure and the theory of eigenvalue analysis. Furthermore, the existence of period-1 solution is investigated for a special impulsive population differential system, and the analytical condition is established. Finally, the trajectory of period-1 solution and the relationship between different parameters and the module of eigenvalues are illustrated.

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