Existence and global attractivity of an almost periodic ecological model

The almost periodic Lotka-Volterra model with m-predators and n-preys is considered in this paper. By constructing suitable Lyapunov function, some sufficient conditions are obtained for the existence and global attractivity of a unique positive almost periodic solution of this model. Examples show that our criteria are new, general, and easily verifiable.

[1]  K. Gopalsamy Global asymptotic stability in an almost-periodic Lotka-Volterra system , 1986, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[2]  Lu Zhonghua,et al.  Global asymptotic stability of the periodic Lotka-Volterra System with two-predators and one-prey , 1995 .

[3]  Jinde Cao,et al.  Existence and stability of almost periodic solution for BAM neural networks with delays , 2003, Appl. Math. Comput..

[4]  Alan C. Lazer,et al.  An application of topological degree to the periodic competing species problem , 1986, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[5]  Jinde Cao,et al.  Periodic solutions of the higher-dimensional non-autonomous systems , 2002, Appl. Math. Comput..

[6]  J. Cushing Periodic Lotka-Volterra competition equations , 1986, Journal of mathematical biology.

[7]  P. de Mottoni,et al.  Competition systems with periodic coefficients: A geometric approach , 1981 .

[8]  K. Gopalsamy,et al.  Global asymptotic stability in a periodic Lotka-Volterra system , 1985, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[9]  Jim M Cushing,et al.  Two species competition in a periodic environment , 1980 .

[10]  Wang Wendi,et al.  Asymptotic behavior of predator–prey system with time dependent coefficients , 1989 .

[11]  Jiandong Zhao,et al.  Global asymptotic stability of a periodic ecological model , 2004, Appl. Math. Comput..

[12]  Shair Ahmad On almost periodic solutions of the competing species problems , 1988 .

[13]  F Chen PERIODIC SOLUTIONS OF NONLINEAR INTEGRODIFFERENTIAL EQUATIONS WITH INFINITE DELAY , 2003 .

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

[15]  J. Craggs Applied Mathematical Sciences , 1973 .

[16]  Antonio Tineo,et al.  A, Different Consideraton about the Globally Asymptotically Stable Solution of the Periodic n-Competing Species Problem* , 1991 .

[17]  Jinde Cao,et al.  Existence and attractivity of almost periodic solutions for cellular neural networks with distributed delays and variable coefficients , 2003, Appl. Math. Comput..

[18]  Yang Pinghua,et al.  Global Attractivity of the Periodic Lotka–Volterra System☆ , 1999 .

[19]  Shair Ahmad Convergence and ultimate bounds of solutions of the nonautonomous Volterra-Lotka competition equations , 1987 .

[20]  Jinde Cao,et al.  Discussion of periodic solutions for pth order delayed NDEs , 2002, Appl. Math. Comput..

[21]  K. Gopalsamy,et al.  Exchange of equilibria in two species Lotka-Volterra competition models , 1982, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.