Dynamic analysis of wild and sterile mosquito release model with Poincaré map
| Autor: | Hui Dong Cheng, Yu Fei Wang, Qing Jian Li |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Male
Mosquito Control Population Dynamics Boundary (topology) Monotonic function 02 engineering and technology Mosquito Vectors Fixed point Stability (probability) Sexual Behavior Animal 0502 economics and business 0202 electrical engineering electronic engineering information engineering Applied mathematics Animals Computer Simulation Differentiable function Pest Control Biological Mathematics Poincaré map Population Density Applied Mathematics 05 social sciences General Medicine Models Theoretical Computational Mathematics Complex dynamics Mosquito control Culicidae Modeling and Simulation 020201 artificial intelligence & image processing Female General Agricultural and Biological Sciences 050203 business & management |
| Zdroj: | Mathematical biosciences and engineering : MBE. 16(6) |
| ISSN: | 1551-0018 |
| Popis: | In recent years, the application of impulsive semi-dynamic system in state-dependent feed-back control has attracted extensive attention, but most models only discuss their special cases without delving into their complex dynamics. Therefore, we establish the wild and sterile mosquito system with integrated mosquito control, and use the Poincare map method to conduct a comprehensive analysis of the model dynamics. First, the main properties of Poincare map such as monotonicity, continuous differentiability, extremum and fixed point are discussed. Second, we prove the existence and stability of boundary periodic solution and study the influence of its parameters on the system. Then the ex-istence and global stability of the order-1 periodic solution and the existence condition of the order-k (k > 1) periodic solution are analyzed. Finally, our conclusion is verified by numerical analysis. The results show that the population density of wild mosquitoes can be controlled below the threshold by integrated mosquito control. |
| Databáze: | OpenAIRE |
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