Coexistence of a Strongly Coupled Prey-predator Model for Holling’s Type III

Chinese Quarterly Journal of Mathematics ›› 2009, Vol. 24 ›› Issue (3): 389-393.

Coexistence of a Strongly Coupled Prey-predator Model for Holling’s Type III

1. Department of Mathematics, Shaoguan University2. College of Mathe-matics Science, Yangzhou University3. Department of Applied Mathematics, South China Agricultural University

Received:2008-01-05 Online:2009-09-30 Published:2023-06-28
About author: HUANG You-liang(1969- ), male, native of Shixing, Guangdong, M.S.D., a lecturer of Shaoguan University, engages in the dynamical system and the teaching research of mathematics; ZHANG Lai(1982- ), male, native of Xuzhou, Jiangsu, M.S.D., engages in biomathematics and PDE; FANG Shaomei(1964- ), female, native of Yili, Xinjiang, Ph.D., a professor of South China Agricultural University, engages in the dynamical system and biomathematics.
Supported by:
Supported by the National Natural Science Foundation of China(10576013； 10871075)；

Abstract

Abstract: In this paper, the two-species prey-predator Lotka-Volterra model with the Holling’s type Ⅲ is discussed. By the method of coupled upper and lower solutions and its associated monotone iterations, the existence of solutions for a strongly coupled elliptic system with homogeneous of Dirchlet boundary conditions is derived. These results show that this model admits at least one coexistence state if across-diffusions are weak.

Key words: reaction diffusion system, strongly coupled, coexistence

CLC Number:

O175.26

HUANG You-liang, ZHANG Lai, FANG Shao-mei. Coexistence of a Strongly Coupled Prey-predator Model for Holling’s Type III [J]. Chinese Quarterly Journal of Mathematics, 2009, 24(3): 389-393.

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Coexistence of a Strongly Coupled Prey-predator Model for Holling’s Type III

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