Journal
APPLIED MATHEMATICAL MODELLING
Volume 77, Issue -, Pages 1842-1859Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2019.09.033
Keywords
Prey-predator system; Square root functional response; Ratio-dependent state impulsive control; Order-k periodic orbit; Global finite time convergence
Funding
- National Natural Science Foundation of China [11771059]
- China Scholarship Council (CSC) [201806130100]
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This paper studies the global dynamic behavior of a prey-predator model with square root functional response under ratio-dependent state impulsive control strategy. It is shown that the boundary equilibrium point of the controlled system is globally asymptotically stable. An order-k periodic orbit is obtained by employing the Brouwer's fixed point theorem. Furthermore, the critical values are determined for the existence of orbitally asymptotically stable order-1 and order-2 periodic orbits in finite time. These critical values play an important role in determining different kinds of order-k periodic orbits and can also be used for designing the control parameters to obtain the desirable dynamic behavior of the controlled prey-predator system. Moreover, it is found that the local equilibrium point is also globally asymptotically stable under the control strategy. Numerical examples are provided to validate the effectiveness and feasibility of the theoretical results. (C) 2019 Elsevier Inc. All rights reserved.
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