%0 Journal Article %T Global attractivity of a two-species competitive system with nonlinear inter-inhibition terms %A Chen, Baoguo %J Journal of Mathematics and Computer Science %D 2016 %V 16 %N 4 %@ ISSN 2008-949X %F Chen2016 %X Sufficient conditions are obtained for the global attractivity of the positive equilibrium and boundary equilibria of the following two-species competitive system with nonlinear inter-inhibition terms \[\frac{dy_1(t)}{dt}=y_1(t)\left[r_1-a_1y_1-\frac{b_1y_2}{1+y_2}\right],\] \[\frac{dy_2(t)}{dt}=y_2(t)\left[r_2-a_2y_2-\frac{b_2y_1}{1+y_1}\right],\] where \(r_i, a_i, b_i, i = 1, 2\) are all positive constants. Our result shows that conditions which ensure the permanence of the system are almost enough to ensure the global stability of the system. The results not only improve but also complement the main results of Wang et al. [Q. L. Wang, Z. J. Liu, Z. X. Li, R. A. Cheke, Int. J. Biomath., 7 (2014), 18 pages]. %9 journal article %R 10.22436/jmcs.016.04.02 %U http://dx.doi.org/10.22436/jmcs.016.04.02 %P 481-494 %0 Journal Article %T On a nonlinear nonautonomous predator-prey model with diffusion and distributed delay %A F. D. Chen %J J. Comput. Appl. Math. %D 2005 %V 180 %F Chen 2005 %0 Journal Article %T Average conditions for permanence and extinction in nonautonomous Gilpin-Ayala competition model %A F. D. Chen %J Nonlinear Anal. Real World Appl. %D 2006 %V 7 %F Chen 2006 %0 Journal Article %T Some new results on the permanence and extinction of nonautonomous Gilpin-Ayala type competition model with delays %A F. D. Chen %J Nonlinear Anal. Real World Appl. %D 2006 %V 7 %F Chen2006 %0 Journal Article %T Extinction in a Lotka-Volterra competitive system with impulse and the effect of toxic substances %A L. J. Chen %A J. T. Sun %A F. D. Chen %A L. Zhao %J Appl. Math. Model. %D 2016 %V 40 %F Chen2016 %0 Journal Article %T Dynamic behaviors of a Lotka-Volterra competitive system with infinite delays and single feedback control %A F. D. Chen %A H. N. Wang %J J. Nonlinear Funct. Anal. %D 2016 %V 2016 %F Chen2016 %0 Journal Article %T Global stability of a stage-structured predator-prey system %A F. D. Chen %A H. N. Wang %A Y. H. Lin %A W. L. Chen %J Appl. Math. Comput. %D 2013 %V 223 %F Chen2013 %0 Journal Article %T Partial survival and extinction of a delayed predator-prey model with stage structure %A F. D. Chen %A X. D. Xie %A Z. Li %J Appl. Math. Comput. %D 2012 %V 219 %F Chen2012 %0 Journal Article %T Extinction in two species nonautonomous nonlinear competitive system %A F. D. Chen %A X. D. Xie %A Z. S. Miao %A L. Q. Pu %J Appl. Math. Comput. %D 2016 %V 274 %F Chen2016 %0 Journal Article %T Global stability in a competition model of plankton allelopathy with infinite delay %A F. D. Chen %A X. D. Xie %A H. N. Wang %J J. Syst. Sci. Complex. %D 2015 %V 28 %F Chen2015 %0 Journal Article %T Permanence for an integrodifferential model of mutualism %A F. D. Chen %A M. S. You %J Appl. Math. Comput. %D 2007 %V 186 %F Chen2007 %0 Book %T Stability and oscillations in delay differential equations of population dynamics %A K. Gopalsamy %D 1992 %I Mathematics and its Applications, Kluwer Academic Publishers Group %C Dordrecht %F Gopalsamy 1992 %0 Journal Article %T Permanence, extinction and global attractivity of the periodic Gilpin-Ayala competition system with impulses %A M. X. He %A Z. Li %A F. D. Chen %J Nonlinear Anal. Real World Appl. %D 2010 %V 11 %F He2010 %0 Journal Article %T Extinction in periodic competitive stage-structured Lotka-Volterra model with the effects of toxic substances %A Z. Li %A F. D. Chen %J J. Comput. Appl. Math. %D 2009 %V 231 %F Li2009 %0 Journal Article %T Asymptotic behavior of the reaction-diffusion model of plankton allelopathy with nonlocal delays %A Z. Li %A F. D. Chen %A M. X. He %J Nonlinear Anal. Real World Appl. %D 2011 %V 12 %F Li2011 %0 Journal Article %T Global stability of a delay differential equations model of plankton allelopathy %A Z. Li %A F. D. Chen %A M. X. He %J Appl. Math. Comput. %D 2012 %V 218 %F Li2012 %0 Journal Article %T Global stability of a stage-structured predator-prey model with modified Leslie-Gower and Holling-type II schemes %A Z. Li %A M. Han %A F. D. Chen %J Int. J. Biomath. %D 2012 %V 5 %F Li2012 %0 Journal Article %T Convergences of a stage-structured predator-prey model with modified Leslie-Gower and Holling-type II schemes %A Y. H. Lin %A X. D. Xie %A F. D. Chen %A T. T. Li %J Adv. Difference Equ. %D 2016 %V 2016 %F Lin2016 %0 Journal Article %T Extinction in two-species nonlinear discrete competitive system %A L. Q. Pu %A X. D. Xie %A F. D. Chen %A Z. S. Miao %J Discrete Dyn. Nat. Soc. %D 2016 %V 2016 %F Pu2016 %0 Journal Article %T Permanence and global stability of positive periodic solutions of a discrete competitive system %A W. J. Qin %A Z. J. Liu %A Y. P. Chen %J Discrete Dyn. Nat. Soc. %D 2009 %V 2009 %F Qin2009 %0 Journal Article %T Extinction in a nonautonomous Lotka-Volterra competitive system with infinite delay and feedback controls %A C. L. Shi %A Z. Li %A F. D. Chen %J Nonlinear Anal. Real World Appl. %D 2012 %V 13 %F Shi2012 %0 Journal Article %T Uniformly asymptotic stability of positive almost periodic solutions for a discrete competitive system %A Q. L. Wang %A Z. J. Liu %J J. Appl. Math. %D 2013 %V 2013 %F Wang2013 %0 Journal Article %T Positive almost periodic solutions for a discrete competitive system subject to feedback controls %A Q. L. Wang %A Z. J. Liu %A Z. X. Li %J J. Appl. Math. %D 2013 %V 2013 %F Wang2013 %0 Journal Article %T Existence and global asymptotic stability of positive almost periodic solutions of a two-species competitive system %A Q. L. Wang %A Z. J. Liu %A Z. X. Li %A R. A. Cheke %J Int. J. Biomath. %D 2014 %V 7 %F Wang2014 %0 Journal Article %T Note on the stability property of a cooperative system incorporating harvesting %A X. D. Xie %A F. D. Chen %A Y. L. Xue %J Discrete Dyn. Nat. Soc. %D 2014 %V 2014 %F Xie2014 %0 Journal Article %T Global attractivity of an integrodifferential model of mutualism %A X. D. Xie %A F. D. Chen %A K. Yang %A Y. L. Xue %J Abstr. Appl. Anal. %D 2014 %V 2014 %F Xie2014 %0 Journal Article %T Global stability of a discrete mutualism model %A K. Yang %A X. D. Xie %A F. D. Chen %J Abstr. Appl. Anal. %D 2014 %V 2014 %F Yang2014 %0 Journal Article %T Global asymptotic stability of a predator-prey model with modified Leslie-Gower and Holling- type II schemes %A S. B. Yu %J Discrete Dyn. Nat. Soc. %D 2012 %V 2012 %F Yu 2012 %0 Journal Article %T Permanence for a discrete competitive system with feedback controls %A S. B. Yu %J Commun. Math. Biol. Neurosci. %D 2015 %V 2015 %F Yu2015 %0 Journal Article %T Dynamics of a modified LeslieGower predatorprey model with Holling-type II schemes and a prey refuge %A Q. Yue %J SpringerPlus %D 2016 %V 5 %F Yue 2016