Almost periodic solutions of a discrete Lotka–Volterra competition system with delays

Abstract In this paper, we consider a discrete almost periodic Lotka–Volterra competition system with delays. Sufficient conditions are obtained for the permanence and global attractivity of the system. Further, by means of an almost periodic functional hull theory, we show that the almost periodic system has a unique strictly positive almost periodic solution, which is globally attractive. Some examples are presented to verify our main results.

[1]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[2]  A. M. Fink,et al.  Liapunov functions and almost periodic solutions for almost periodic systems , 1969 .

[3]  Zhidong Teng,et al.  Nonautonomous Lotka–Volterra Systems with Delays , 2002 .

[4]  Yoshiaki Muroya.  Persistence and global stability for discrete models of nonautonomous Lotka–Volterra type , 2002 .

[5]  Jialin Hong,et al.  The existence of almost periodic solutions for a class of differential equations with piecewise constant argument , 1997 .

[6]  Zhan Zhou,et al.  Stable periodic solution of a discrete periodic Lotka–Volterra competition system , 2003 .

[7]  Zhong Li,et al.  Almost periodic solutions of a discrete almost periodic logistic equation , 2009, Math. Comput. Model..

[8]  Zhong Li,et al.  Permanence and global attractivity of a discrete Schoener's competition model with delays , 2009, Math. Comput. Model..

[9]  Yoshiaki Muroya.  Persistence and global stability in discrete models of pure-delay nonautonomous Lotka–Volterra type☆ , 2004 .

[10]  Yongkun Li,et al.  Positive periodic solutions of discrete n-species food-chain systems , 2005, Appl. Math. Comput..

[11]  Xiaoxing Chen,et al.  Almost periodic sequence solutions of a discrete Lotka–Volterra competitive system with feedback control , 2009 .

[12]  Xinzhu Meng,et al.  Almost periodic solution of non-autonomous Lotka-Volterra predator-prey dispersal system with delays. , 2006, Journal of theoretical biology.

[13]  Yoshiaki Muroya.  Persistence and global stability in discrete models of Lotka-Volterra type , 2007 .

[14]  Zhan Zhou,et al.  Stable periodic solutions in a discrete periodic logistic equation , 2003, Appl. Math. Lett..

[15]  Zhong Li,et al.  Permanence and global attractivity of the discrete Gilpin-Ayala type population model , 2007, Comput. Math. Appl..

[16]  Guang Zheng,et al.  Almost periodic solutions of delay difference systems , 2002, Appl. Math. Comput..

[17]  A. Fink.  Almost Periodic Differential Equations , 1974 .

[18]  K. Gopalsamy,et al.  Canonical solutions and almost periodicity in a discrete logistic equation , 2000, Appl. Math. Comput..

[19]  Yongkun Li,et al.  Permanence and almost periodic sequence solution for a discrete delay logistic equation with feedback control , 2011 .

[20]  Yongkun Li,et al.  Persistence and almost periodic solutions for a discrete fishing model with feedback control , 2011 .

[21]  Giuseppe Mulone,et al.  Global stability of discrete population models with time delays and fluctuating environment , 2001 .

[22]  Yoshihiro Hamaya.  Existence of an almost periodic solution in a difference equation by Liapunov functions , 2001 .

[23]  Xitao Yang,et al.  Uniform persistence and periodic solutions for a discrete predator–prey system with delays☆ , 2006 .

[24]  Yu Zhang,et al.  Permanence criteria for general delayed discrete nonautonomous n-species Kolmogorov systems and its applications , 2010, Comput. Math. Appl..