The dynamics of a Lotka–Volterra predator–prey model with state dependent impulsive harvest for predator |
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| Authors: | Linfei Nie Zhidong Teng Lin Hu Jigen Peng |
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| Institution: | aCollege of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China;bDepartment of Applied Mathematics, Xi’an Jiaotong University, Xi’an 710049, China;cInstitute for Information and System Sciences, Research Center for Applied Mathematics, Xi’an Jiaotong University, Xi’an 710049, China |
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| Abstract: | According to the economic and biological aspects of renewable resources management, we propose a Lotka–Volterra predator–prey model with state dependent impulsive harvest. By using the Poincaré map, some conditions for the existence and stability of positive periodic solution are obtained. Moreover, we show that there is no periodic solution with order larger than or equal to three under some conditions. Numerical results are carried out to illustrate the feasibility of our main results. The bifurcation diagrams of periodic solutions are obtained by using the numerical simulations, and it is shown that a chaotic solution is generated via a cascade of period-doubling bifurcations, which implies that the presence of pulses makes the dynamic behavior more complex. |
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| Keywords: | State-dependent impulsive harvesting Predator– prey system Poincaré map Periodic solution Stability Bifurcation |
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