PERMANENCE OF A LOTKA-VOLTERRA RATIO-DEPENDENT PREDATOR-PREY MODEL WITH FEEDBACK CONTROLS AND PREY DIFFUSION
DOI:
https://doi.org/10.53555/eijms.v4i1.15Abstract
A three species multi-delay Lotka-Volterra ratio-dependent predator-prey model with feedback controls and prey diffusion is investigated. By developing some new analysis methods, some sufficient conditions are derived for the permanence of the system.
References
. HASTINGS A. Global Stability of Two Species Systems [J]. Journal of Mathematical Biology, 1978, 5(4):399-
. LU Z, WANG W. Permanence and Global Attractivity for Lotka–Volterra Difference Systems [J]. Journal of
Mathematical Biology, 1999, 39(3):269-282.
. LLIBRE J, XIAO D. Global Dynamics of a Lotka--Volterra Model with Two Predators Competing for One Prey
[J]. Siam Journal on Applied Mathematics, 2014, 74(2):434-453.
. HADŽIABDIĆ V, MEHULJIĆ M, BEKTEŠEVIĆ J. Lotka-Volterra Model with Two Predators and Their Prey
[J]. TEM Journal, 2017, 6(1):132-136.
. LANSUN C, ZHENGYI L, WENDI W. The Effect of Delays on the Permanence for Lotka-Volterra Systems [J].
Applied Mathematics Letters, 1995, 8(4):71-73.
. XIA Y. Existence of Positive Periodic Solutions of Mutualism Systems with Several Delays [J]. Advances in
Dynamical Systems and Applications, 2006, 1(2):209-217.[7]. GUICHEN L, ZHENGYI L. Permanence for Two-Species Lotka-Volterra Cooperative Systems with Delays [J].
Mathematical Biosciences and Engineering, 2008, 5(3):477-484.
. LU G, LU Z, ENATSU Y. Permanence for Lotka–Volterra Systems with Multiple Delays [J]. Nonlinear Analysis:
Real World Applications, 2011, 12(5):2552-2560.
. MUHAMMADHAJI A, TENG Z, REHIM M. Dynamical Behavior for a Class of Delayed Competitive–
Mutualism Systems [J]. Differential Equations and Dyanical Systems, 2015, 23(3):281-301.
. SONG X, CHEN L. Persistence and Periodic Orbits for Two-Species PredatorPrey System with Diffusion [J].
Canadian Applied Mathematics Quarterly, 1998, 6(3):233-244.
. SONG X, CHEN L. Persistence and Global Stability for Nonautonomous PredatorPrey System with Diffusion and
Time Delay [J]. Computers and Mathematics with Applications, 1998, 35(6):33-40.
. CUI J. The Effect of Dispersal on Permanence in a Predator-Prey Population Growth Model [J]. Computers and
Mathematics with Applications, 2002, 44(8):1085-1097.
. WEI F, LIN Y, QUE L, et al. Periodic Solution and Global Stability for a Nonautonomous Competitive Lotka–
Volterra Diffusion System [J]. Applied Mathematics and Computation, 2010, 216(10):3097-3104.
. WANG J, WANG K. Dynamics of a Ratio-dependent one Predator-two Competing Prey Model [J]. Mathematica
Applicata, 2004,17(2):172-178.(In Chinese)
. CHEN G, TENG Z, HU Z. Analysis of Stability for a Discrete Ratio-Dependent Predator-Prey System [J]. Indian
Journal of Pure & Applied Mathematics, 2011, 42(1):1-26.
. [16]Alan A. Berryman. The Orgins and Evolution of Predator-Prey Theory [J]. Ecology, 1992, 73(5):1530-1535.
. LUNDBERG P, FRYXELL J M. Expected Population Density versus Productivity in Ratio-Dependent and PreyDependent Models [J]. 1995, 146(1):153-161.
. XU R, CHAPLAIN M A J. Persistence and Global Stability in a Delayed PredatorPrey System with Michaelis--
Menten Type Functional Response [J]. Applied Mathematics and Computation, 2002, 130(1):441-455.
. XU R, CHEN L. Persistence and Global Stability for a Three-Species Ratio Dependent Predator-Prey System with
Time Delays in Two-Patch Environments [J].
. Acta Mathematica Scientia, 2002, 22(4):533-541.
. HUO H, LI W. Periodic Solution of a Delayed Predator-Prey System with Michaelis-Menten Type Functional
Response [J]. Journal of Computational and Applied Mathematics, 2004, 166(2):453-463.
. SUN S, YUAN C. Analysis for Three-Species Mixture Model with Diffusion and Ratio-Dependence [J]. Journal
of Systems Science and Mathematical Sciences, 2005, 25(1):87-95. (In chinese)
. ZHOU X, SHI X, SONG X. Analysis of Nonautonomous Predator-Prey Model with Nonlinear Diffusion and Time
Delay [J]. Applied Mathematics and Computation, 2008, 196(1):129-136.
. XU R, CHAPLAIN M, DAVIDSON F A. Periodic Solution of a Lotka–Volterra Predator–Prey Model with
Dispersion and Time Delays [J]. Applied Mathematics and Computation, 2004, 148(2):537-560.
. DU C, WU Y. Existence of Positive Periodic Solutions for a Generalized PredatorPrey Model with Diffusion
Feedback Controls [J]. Advances in Difference Equations, 2013, 2013(1):1-14.
. GOPALSAMY K, WENG P. Global Attractivity in a Competition System with Feedback Cdntrols [J]. Computers
and Mathematics with Applications, 2003, 45:665-676.
. XIE W, WENG P. Existence of Periodic Solution for a Predator - Prey Model with Patch - Diffusion and Feedback
Control [J]. Journal of South China Normal University (Natural Science Edition), 2012, 44(1):42-47.
. XU J, CHEN F. Permanence of a Lotka-Volterra Cooperative System with Time Delays and Feedback Controls
[J]. Communications in Mathematical Biology & Neuroscience, 2015, 18:1-12.
. JIANXIU L. The Permanence and Global Stability of A Two-species Cooperation System with Time Delays and
Feedback Controls[J]. Journal of Ningxia University(Natural Science Edition), 2016,37(2):161-164.(In Chinese)
. WANG C, LIU H, PAN S, et al. Globally Attractive of a Ratio-Dependent LotkaVolterra Predator-Prey Model
with Feedback Control [J]. Advances in Bioscience and Bioengineering, 2016, 4(5):59.
. CHEN F. On a Nonlinear Nonautonomous Predator-Prey Model with Diffusion and Distributed Delay [J]. Journal
of Computational and Applied Mathematics, 2005, 180:33-49.
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