Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

Permanence for two-species Lotka-Volterra cooperative systems with delays

1. Department of Mathematics, Wenzhou University, Wenzhou, 325035

In this paper, a two-species Lotka-Volterra cooperative delay sys- tem is considered, and the relationships between the delays and the permanence are obtained. Some sufficient conditions for the permanence under the assumption of smallness of the delays are obtained. Two examples are given to illustrate the theorems.
  Figure/Table
  Supplementary
  Article Metrics

Keywords permanence; cooperative; discrete delay; Lotka-Volterra system

Citation: Guichen Lu, Zhengyi Lu. Permanence for two-species Lotka-Volterra cooperative systems with delays. Mathematical Biosciences and Engineering, 2008, 5(3): 477-484. doi: 10.3934/mbe.2008.5.477

 

This article has been cited by

  • 1. Jinglei Tian, Yongguang Yu, Hu Wang, Stability and Bifurcation of Two Kinds of Three-Dimensional Fractional Lotka-Volterra Systems, Mathematical Problems in Engineering, 2014, 2014, 1, 10.1155/2014/695871
  • 2. Yukihiko Nakata, Yoshiaki Muroya, Permanence for nonautonomous Lotka–Volterra cooperative systems with delays, Nonlinear Analysis: Real World Applications, 2010, 11, 1, 528, 10.1016/j.nonrwa.2009.01.002
  • 3. Xiangdong Xie, Fengde Chen, Kun Yang, Yalong Xue, Global Attractivity of an Integrodifferential Model of Mutualism, Abstract and Applied Analysis, 2014, 2014, 1, 10.1155/2014/928726
  • 4. YUKIHIKO NAKATA, PERMANENCE FOR THE LOTKA–VOLTERRA COOPERATIVE SYSTEM WITH SEVERAL DELAYS, International Journal of Biomathematics, 2009, 02, 03, 267, 10.1142/S1793524509000716
  • 5. Ahmadjan Muhammadhaji, Zhidong Teng, Mehbuba Rehim, Dynamical Behavior for a Class of Delayed Competitive–Mutualism Systems, Differential Equations and Dynamical Systems, 2015, 23, 3, 281, 10.1007/s12591-014-0226-6
  • 6. Xinyuan Liao, Xianhua Tang, Shengfan Zhou, Existence of traveling wavefronts in a cooperative systems with discrete delays, Applied Mathematics and Computation, 2009, 215, 5, 1806, 10.1016/j.amc.2009.07.032
  • 7. Guichen Lu, Zhengyi Lu, Yoichi Enatsu, Permanence for Lotka–Volterra systems with multiple delays, Nonlinear Analysis: Real World Applications, 2011, 12, 5, 2552, 10.1016/j.nonrwa.2011.03.004
  • 8. Changyou Wang, Linrui Li, Yuqian Zhou, Rui Li, On a delay ratio-dependent predator–prey system with feedback controls and shelter for the prey, International Journal of Biomathematics, 2018, 1850095, 10.1142/S179352451850095X
  • 9. Changyou Wang, Linrui Li, Qiuyan Zhang, Rui Li, Dynamical behaviour of a Lotka–Volterra competitive-competitive–cooperative model with feedback controls and time delays, Journal of Biological Dynamics, 2019, 13, 1, 43, 10.1080/17513758.2019.1568600
  • 10. Martin P. Arciga-Alejandre, Jorge Sanchez-Ortiz, Francisco J. Ariza-Hernandez, Gabriel Catalan-Angeles, A Multi-Stage Homotopy Perturbation Method for the Fractional Lotka-Volterra Model, Symmetry, 2019, 11, 11, 1330, 10.3390/sym11111330

Reader Comments

your name: *   your email: *  

Copyright Info: 2008, , licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved