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.

Details

Title
Dynamic analysis of a prey–predator model with state-dependent control strategy and square root response function
Author
Liu, Hongxia 1 ; Cheng, Huidong 2 

 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 
 College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, China 
Pages
1-13
Publication year
2018
Publication date
Feb 2018
Publisher
Springer Nature B.V.
ISSN
1687-1839
e-ISSN
1687-1847
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
2130789555
Copyright
Advances in Difference Equations is a copyright of Springer, (2018). All Rights Reserved., © 2018. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.