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Abstract
In this work, a prey-predator model with square root response function under a state-dependent impulse is proposed. Firstly, according to the differential equation geometry theory and the method of successor function, the existence, uniqueness and attractiveness of the order-1 periodic solution are analyzed. Then the stability of the order-1 periodic solution is discussed by the Poincaré criterion for impulsive differential equations. Finally, we show a specific example and carry out numerical simulations to verify the theoretical results.
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Details
1 College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, China; State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao, China
2 College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, China