Extinction in periodic competitive stage-structured Lotka-Volterra model with the effects of toxic substances

In this paper, we consider a periodic competitive stage-structured Lotka-Volterra model with the effects of toxic substances. It is shown that toxic substances play an important role in the extinction of species. We obtain a set of sufficient conditions which guarantee that one of the components is driven to extinction while the other is globally attractive. The numerical simulation of an example verifies our main results.

[1]  Li Wang,et al.  Global attractivity of a positive periodic solution for a nonautonomous stage structured population dynamics with time delay and diffusion , 2006 .

[2]  Fengde Chen,et al.  Note on the permanence of a competitive system with infinite delay and feedback controls , 2007 .

[3]  Benedetta Lisena Competitive exclusion in a periodic Lotka-Volterra system , 2006, Appl. Math. Comput..

[4]  Lansun Chen,et al.  Effects of diffusion on a stage-structured population in a polluted environment , 2004, Appl. Math. Comput..

[5]  Rui Xu,et al.  Stability and Hopf bifurcation in a predator-prey model with stage structure for the predator , 2008 .

[6]  Zhidong Teng On the non-autonomous Lotka-Volterra N-species competing systems , 2000, Appl. Math. Comput..

[7]  Fengde Chen Permanence of periodic Holling type predator-prey system with stage structure for prey , 2006, Appl. Math. Comput..

[8]  Xinyu Song,et al.  The prey-dependent consumption two-prey one-predator models with stage structure for the predator and impulsive effects. , 2006, Journal of theoretical biology.

[9]  Permanence extinction and global asymptotic stability in a stage structured system with distributed delays , 2005 .

[10]  Zhijun Liu,et al.  Periodic solution of a two-species competitive system with toxicant and birth pulse , 2007 .

[11]  Lansun Chen,et al.  Effects of toxicants on a stage-structured population growth model , 2001, Appl. Math. Comput..

[12]  Malay Bandyopadhyay,et al.  DYNAMICAL ANALYSIS OF A ALLELOPATHIC PHYTOPLANKTON MODEL , 2006 .

[13]  K. S. Chaudhuri,et al.  On non-selective harvesting of two competing fish species in the presence of toxicity , 2003 .

[14]  M. Zeeman,et al.  Extinction in nonautonomous competitive Lotka-Volterra systems , 1996 .

[15]  H. I. Freedman,et al.  A time-delay model of single-species growth with stage structure. , 1990, Mathematical biosciences.

[16]  A. Tineo,et al.  AN ITERATIVE SCHEME FOR THE N-COMPETING SPECIES PROBLEM , 1995 .

[17]  Jifa Jiang,et al.  Average conditions for permanence and extinction in nonautonomous Lotka–Volterra system , 2004 .

[18]  Jitka Laitochová,et al.  Dynamic behaviors of a delay differential equation model of plankton allelopathy , 2007 .

[19]  John Maynard Smith Models in ecology , 1974 .

[20]  Xinyu Song,et al.  A stage-structured predator–prey model with disturbing pulse and time delays , 2009 .

[21]  Fengde Chen Almost periodic solution of the non-autonomous two-species competitive model with stage structure , 2006, Appl. Math. Comput..

[22]  Extinction in a two dimensional Lotka–Volterra system with infinite delay , 2006 .

[23]  Antonio Tineo Asymptotic behaviour of positive solutions of the nonautonomous Lotka-Volterra competition equations , 1993 .

[24]  Shair Ahmad,et al.  On the nonautonomous Volterra-Lotka competition equations , 1993 .

[25]  Jean-Pierre Gabriel,et al.  Differential equation models of some parasitic infections: Methods for the study of asymptotic behavior , 1985 .

[26]  Zhong Li,et al.  Extinction in two dimensional nonautonomous Lotka-Volterra systems with the effect of toxic substances , 2006, Appl. Math. Comput..

[27]  Shengqiang Liu,et al.  Extinction and permanence in nonautonomous competitive system with stage structure , 2002 .

[28]  Zhengqiu Zhang Periodic solutions of a predator–prey system with stage-structures for predator and prey , 2005 .

[29]  W. D. Evans,et al.  PARTIAL DIFFERENTIAL EQUATIONS , 1941 .

[30]  Fengde Chen,et al.  Average conditions for permanence and extinction in nonautonomous Gilpin–Ayala competition model , 2006 .

[31]  Guilie Luo,et al.  Asymptotic behaviors of competitive Lotka–Volterra system with stage structure , 2002 .

[32]  Jianjun Jiao,et al.  A single stage-structured population model with mature individuals in a polluted environment and pulse input of environmental toxin , 2009 .

[33]  Rui Xu,et al.  Periodic solutions of a nonautonomous predator-prey system with stage structure and time delays , 2006 .

[34]  Xinyu Song,et al.  Permanence and stability of a predator-prey system with stage structure for predator , 2007 .

[35]  Joydev Chattopadhyay,et al.  Effect of toxic substances on a two-species competitive system , 1996 .

[36]  Guilie Luo,et al.  Extinction and permanence in competitive stage structured system with time-delays , 2002 .

[37]  Rui Xu,et al.  The effect of dispersal on the permanence of a predator–prey system with time delay , 2008 .

[38]  Fengde Chen,et al.  Some new results on the permanence and extinction of nonautonomous Gilpin–Ayala type competition model with delays , 2006 .

[39]  J. Chattopadhyay,et al.  A delay differential equations model of plankton allelopathy. , 1998, Mathematical biosciences.

[40]  H. I. Freedman,et al.  Analysis of a model representing stage-structured population growth with state-dependent time delay , 1992 .