Existence and Uniqueness of Asymptotic Periodic Solution in the Cyclic Four Species Predator-Prey Model

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Rahmani Doust Mohammad Hossein; Motahari Nasab Farzaneh

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Journal: ADVANCES IN MATHEMATICAL MODELING Year:2019 | Volume:9 | Issue:1 Page(s): 143-160

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Title

Existence and Uniqueness of Asymptotic Periodic Solution in the Cyclic Four Species Predator-Prey Model

Author(s)

Rahmani Doust Mohammad Hossein | Motahari Nasab Farzaneh | Issue Writer Certificate

Keywords

PredatorQ1

prey Functional response Sigmoidal Lyapanov function StabilityQ1

Abstract

In the past decades, in the area of mathematical ecology, the dynamical properties occurring in the Predator-prey models have been studied. Moreover, the stability and boundedness of the solution for population model such as cyclic, delayed and etc. have been studied. In the present paper, a nonlinear cyclic Predator-prey system with sigmoidal type functional response is analyzed. Indeed, a model of four species Predator-prey system has been investigated and the sufficient conditions for stability and boundedness of the solutions of Predator-prey system have been presented. For this purpose, the differential inequality theory is employed and finally, by constructing a suitable Lyapanov function the existence and uniqueness of asymptotically periodic solution which is globally asymptotically stable are proved.

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APA: Copy

Rahmani Doust, Mohammad Hossein, & Motahari Nasab, Farzaneh. (2019). Existence and Uniqueness of Asymptotic Periodic Solution in the Cyclic Four Species Predator-Prey Model. ADVANCES IN MATHEMATICAL MODELING, 9(1 ), 143-160. SID. https://sid.ir/paper/243903/en

Vancouver: Copy

Rahmani Doust Mohammad Hossein, Motahari Nasab Farzaneh. Existence and Uniqueness of Asymptotic Periodic Solution in the Cyclic Four Species Predator-Prey Model. ADVANCES IN MATHEMATICAL MODELING[Internet]. 2019;9(1 ):143-160. Available from: https://sid.ir/paper/243903/en

IEEE: Copy

Mohammad Hossein Rahmani Doust, and Farzaneh Motahari Nasab, “Existence and Uniqueness of Asymptotic Periodic Solution in the Cyclic Four Species Predator-Prey Model,” ADVANCES IN MATHEMATICAL MODELING, vol. 9, no. 1 , pp. 143–160, 2019, [Online]. Available: https://sid.ir/paper/243903/en

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