Permanence of a Lotka-Volterra Ratio-Dependent Predator-Prey Model with Feedback Controls and Prey Diffusion

  • Shuang Pan
  • Yonghong Li
  • Changyou Wang
Keywords: Predator-Prey Model, Feedback Control, Time-Delay, Permanence

Abstract

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.

Author Biographies

Shuang Pan

College of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065 P. R. China

Yonghong Li

Institute of Applied Mathematics, Chongqing University of Posts and Telecommunications, Chongqing 400065 P.R. China

Changyou Wang

Institute of Applied Mathematics, Chongqing University of Posts and Telecommunications, Chongqing 400065 P.R. Chin

References

[1] HASTINGS A. Global Stability of Two Species Systems[J]. Journal of Mathematical Biology, 1978,5(4):399-403. [2] LU Z, WANG W. Permanence and Global Attractivity for Lotka–Volterra Difference Systems[J]. Journal of Mathematical Biology, 1999,39(3):269-282. [3] 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. [4] HADŽIABDIĆ V, MEHULJIĆ M, BEKTEŠEVIĆ J. Lotka-Volterra Model with Two Predators and Their Prey[J]. TEM Journal, 2017,6(1):132-136. [5] 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. [6] 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. [8] 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. [9] 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. [10] 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.
Published
2018-01-31
How to Cite
Pan, S., Li, Y., & Wang, C. (2018, January 31). Permanence of a Lotka-Volterra Ratio-Dependent Predator-Prey Model with Feedback Controls and Prey Diffusion. EPH - International Journal of Mathematics and Statistics (ISSN: 2208-2212), 4(1), 07-21. Retrieved from https://ephjournal.com/index.php/ms/article/view/544