Dynamical behavior of a stochastic ratio-dependent predator-prey system with holling type IV functional response

Jing Fu; Daqing Jiang; Ningzhong Shi; Tasawar Hayat; Baslur Abmad

doi:10.2298/FIL1819549F

Dynamical behavior of a stochastic ratio-dependent predator-prey system with holling type IV functional response

Jing Fu
, Daqing Jiang
, Ningzhong Shi
, Tasawar Hayat
, Baslur Abmad

Northeast Normal University
Changchun Normal University
Faculty of Sciences, King Abdulaziz University
China University of Petroleum (East China)
Qudid-I-Ajdm University

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we investigate the dynamical properties of a stochastic ratio-dependent predator-prey system with Holling type IV functional response. The existence of the globally positive solutions to the system with positive initial value is shown employing comparison theorem of stochastic equation and Itô’s formula. We derived some sufficient conditions for the persistence in mean and extinction. This system has a stable stationary distribution which is ergodic. Numerical simulations are carried out for further support of present research.

Original language	English
Pages (from-to)	6549-6562
Number of pages	14
Journal	Filomat
Volume	32
Issue number	19
DOIs	https://doi.org/10.2298/FIL1819549F
State	Published - 2018
Externally published	Yes

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 15 Life on Land

Keywords

Ergodic
Itô’s formula
Persistent in mean
White noise

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10.2298/FIL1819549F

Cite this

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title = "Dynamical behavior of a stochastic ratio-dependent predator-prey system with holling type IV functional response",

abstract = "In this paper, we investigate the dynamical properties of a stochastic ratio-dependent predator-prey system with Holling type IV functional response. The existence of the globally positive solutions to the system with positive initial value is shown employing comparison theorem of stochastic equation and It{\^o}{\textquoteright}s formula. We derived some sufficient conditions for the persistence in mean and extinction. This system has a stable stationary distribution which is ergodic. Numerical simulations are carried out for further support of present research.",

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author = "Jing Fu and Daqing Jiang and Ningzhong Shi and Tasawar Hayat and Baslur Abmad",

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AU - Fu, Jing

AU - Jiang, Daqing

AU - Shi, Ningzhong

AU - Hayat, Tasawar

AU - Abmad, Baslur

PY - 2018

Y1 - 2018

N2 - In this paper, we investigate the dynamical properties of a stochastic ratio-dependent predator-prey system with Holling type IV functional response. The existence of the globally positive solutions to the system with positive initial value is shown employing comparison theorem of stochastic equation and Itô’s formula. We derived some sufficient conditions for the persistence in mean and extinction. This system has a stable stationary distribution which is ergodic. Numerical simulations are carried out for further support of present research.

AB - In this paper, we investigate the dynamical properties of a stochastic ratio-dependent predator-prey system with Holling type IV functional response. The existence of the globally positive solutions to the system with positive initial value is shown employing comparison theorem of stochastic equation and Itô’s formula. We derived some sufficient conditions for the persistence in mean and extinction. This system has a stable stationary distribution which is ergodic. Numerical simulations are carried out for further support of present research.

KW - Ergodic

KW - Itô’s formula

KW - Persistent in mean

KW - White noise

UR - https://www.scopus.com/pages/publications/85061397917

U2 - 10.2298/FIL1819549F

DO - 10.2298/FIL1819549F

M3 - Article

AN - SCOPUS:85061397917

SN - 0354-5180

VL - 32

SP - 6549

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JO - Filomat

JF - Filomat

IS - 19

ER -

Dynamical behavior of a stochastic ratio-dependent predator-prey system with holling type IV functional response

Abstract

UN SDGs

Keywords

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