کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4638337 | 1632000 | 2016 | 17 صفحه PDF | دانلود رایگان |

• Novel predator–prey model with state-dependent feedback control is proposed and analyzed.
• The Poincare map is constructed in phase sets according to phase portraits of ODE model.
• The semi-trivial periodic solution is studied and then the transcritical bifurcation is discussed.
• The existence and nonexistence of order- k(k≥1)k(k≥1) periodic solutions are investigated.
• Numerical investigations are performed to verify our results.
We propose a Holling II predator–prey model with nonlinear pulse as state-dependent feedback control strategy and then provide a comprehensively qualitative analysis by using the theories of impulsive semi-dynamical systems. First, the Poincaré map is constructed based on the domains of impulsive and phase sets which are defined according to the phase portraits of the model. Second, the threshold conditions for the existence and stability of the semi-trivial periodic solution are given, and subsequently an order-1 periodic solution is generated through the transcritical bifurcation. Furthermore, the different parameter spaces for the existence and stability of an order-1 periodic solution are investigated. In addition, the existence and nonexistence of order-k(k≥2)k(k≥2) periodic solutions have been studied theoretically. Moreover, the numerical investigations are presented in order to substantiate our theoretical results and show the complex dynamics of proposed model. Finally, some biological implications of the mathematical results are discussed in the conclusion section.
Journal: Journal of Computational and Applied Mathematics - Volume 291, 1 January 2016, Pages 225–241