Global stability in a competition model of plankton allelopathy with infinite delay

A competition model of plankton allelopathy with infinite delay is considered in this paper. By using an iterative method, the global stability of the interior equilibrium point of the system is investigated. The result shows that for this system, delay and toxic substances are harmless for the stability of the interior equilibrium point.

[1]  Fengde Chen,et al.  Permanence for an integrodifferential model of mutualism , 2007, Appl. Math. Comput..

[2]  Fengde Chen,et al.  Permanence in nonautonomous multi-species predator-prey system with feedback controls , 2006, Appl. Math. Comput..

[3]  G. P. Samanta,et al.  A two-species competitive system under the influence of toxic substances , 2010, Appl. Math. Comput..

[4]  Canrong Tian,et al.  Asymptotic behavior of solutions of a periodic diffusion system of plankton allelopathy , 2010 .

[5]  Zhong Li,et al.  Global stability of a delay differential equations model of plankton allelopathy , 2012, Appl. Math. Comput..

[6]  Lansun Chen,et al.  Positive periodic solution of a general discrete non-autonomous difference system of plankton allelopathy with delays , 2006 .

[7]  Fengde Chen,et al.  Permanence of a nonlinear integro-differential prey-competition model with infinite delays , 2008 .

[8]  Fengde Chen On a nonlinear nonautonomous predator-prey model with diffusion and distributed delay , 2005 .

[9]  Canrong Tian,et al.  The stability of a diffusion model of plankton allelopathy with spatio–temporal delays ☆ , 2009 .

[10]  Emilio García-Ladona,et al.  Modelling allelopathy among marine algae , 2005 .

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

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

[13]  Zhong Li,et al.  Extinction in periodic competitive stage-structured Lotka-Volterra model with the effects of toxic substances , 2009, J. Comput. Appl. Math..

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

[15]  Zhien Ma,et al.  Periodic solutions for delay differential equations model of plankton allelopathy , 2002 .

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

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

[18]  Balram Dubey,et al.  A model for the allelopathic effect on two competing species , 2000 .

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

[20]  Norbert Hungerbühler,et al.  Existence, uniqueness and stability analysis of allelopathic stimulatory phytoplankton model☆ , 2010 .

[21]  Fengde Chen,et al.  On a periodic multi-species ecological model , 2005, Appl. Math. Comput..

[22]  Y. Kuang Delay Differential Equations: With Applications in Population Dynamics , 2012 .

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

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

[25]  J. M. Smith Models in Ecology , 1975 .

[26]  Wan-Tong Li,et al.  Permanence and global stability for nonautonomous discrete model of plankton allelopathy , 2004, Appl. Math. Lett..

[27]  Fengde Chen,et al.  Global attractivity in an almost periodic multi-species nonlinear ecological model , 2006, Appl. Math. Comput..