Persistence, attractivity, and delay in facultative mutualism

Xue zhong He; K. Gopalsamy

doi:10.1006/jmaa.1997.5632

Persistence, attractivity, and delay in facultative mutualism

Xue zhong He^*, K. Gopalsamy

^*Corresponding author for this work

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

94 Citations (Scopus)

Abstract

Relations between persistence and ultimate boundedness of the solutions of the Lotka-Volterra systemdx(t)dt=x(t)[r₁-a₁₁x(t-τ)+a₂₂y(t-τ)]dy(t)dt=y(t)[r₂+a₂₁x(t-τ)-a₂₂y(t-τ)]modelling "facultative mutualism" with delayed responses are established and sufficient conditions are obtained for the global attractivity of the positive equilibrium of the delay system.

Original language	English
Pages (from-to)	154-173
Number of pages	20
Journal	Journal of Mathematical Analysis and Applications
Volume	215
Issue number	1
DOIs	https://doi.org/10.1006/jmaa.1997.5632
Publication status	Published - 1 Nov 1997
Externally published	Yes

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title = "Persistence, attractivity, and delay in facultative mutualism",

abstract = "Relations between persistence and ultimate boundedness of the solutions of the Lotka-Volterra systemdx(t)dt=x(t)[r1-a11x(t-τ)+a22y(t-τ)]dy(t)dt=y(t)[r2+a21x(t-τ)-a22y(t-τ)]modelling {"}facultative mutualism{"} with delayed responses are established and sufficient conditions are obtained for the global attractivity of the positive equilibrium of the delay system.",

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year = "1997",

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T1 - Persistence, attractivity, and delay in facultative mutualism

AU - He, Xue zhong

AU - Gopalsamy, K.

PY - 1997/11/1

Y1 - 1997/11/1

N2 - Relations between persistence and ultimate boundedness of the solutions of the Lotka-Volterra systemdx(t)dt=x(t)[r1-a11x(t-τ)+a22y(t-τ)]dy(t)dt=y(t)[r2+a21x(t-τ)-a22y(t-τ)]modelling "facultative mutualism" with delayed responses are established and sufficient conditions are obtained for the global attractivity of the positive equilibrium of the delay system.

AB - Relations between persistence and ultimate boundedness of the solutions of the Lotka-Volterra systemdx(t)dt=x(t)[r1-a11x(t-τ)+a22y(t-τ)]dy(t)dt=y(t)[r2+a21x(t-τ)-a22y(t-τ)]modelling "facultative mutualism" with delayed responses are established and sufficient conditions are obtained for the global attractivity of the positive equilibrium of the delay system.

UR - https://www.scopus.com/pages/publications/0031260789

U2 - 10.1006/jmaa.1997.5632

DO - 10.1006/jmaa.1997.5632

M3 - Article

AN - SCOPUS:0031260789

SN - 0022-247X

VL - 215

SP - 154

EP - 173

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Persistence, attractivity, and delay in facultative mutualism

Abstract

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