Almost periodic solutions for a discrete fishing model with feedback control and time delays

Abstract In this paper, we discuss an almost periodic discrete fishing model with feedback control and time delays of the form x ( n + 1 ) = x ( n ) exp a ( n ) 1 + x ( n - σ ) K ( n ) r - b ( n ) - c ( n ) u ( n - τ ) , Δ u ( n ) = - α ( n ) u ( n ) + β ( n ) x ( n - μ ) , where σ, τ and μ are nonnegative integers. By means of an almost periodic functional hull theory, sufficient conditions are established for the existence and uniqueness of globally attractive almost periodic solution to the above system. Three examples and numerical simulations are given to illustrate the effectiveness of our main results.

[1]  Xiaoxing Chen,et al.  Stable periodic solution of a discrete periodic Lotka-Volterra competition system with a feedback control , 2006, Appl. Math. Comput..

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

[3]  Gian Italo Bischi,et al.  Three-dimensional discrete-time Lotka-Volterra models with an application to industrial clusters , 2010 .

[4]  Stability and existence of periodic solutions for a time-varying fishing model with delay , 2010 .

[5]  Robert M. May,et al.  Theoretical Ecology: Principles and Applications , 1981 .

[6]  Junjie Wei,et al.  Bifurcation analysis of discrete survival red blood cells model , 2009 .

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

[8]  Jae-Hun Jung,et al.  A study on the numerical convergence of the discrete logistic map , 2009 .

[9]  Ping Liu,et al.  Positive periodic solutions of a class of functional differential systems with feedback controls , 2004 .

[10]  Hai-Feng Huo,et al.  Positive periodic solutions of delay difference equations and applications in population dynamics , 2005 .

[11]  N. Macdonald.  Biological Delay Systems: Linear Stability Theory , 1989 .

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

[13]  Yang Kuang,et al.  Global qualitative analysis of a ratio-dependent predator–prey system , 1998 .

[14]  Yongkun Li,et al.  Positive periodic solutions of higher-dimensional functional difference equations with a parameter , 2004 .

[15]  Ping Liu,et al.  Multiple positive periodic solutions of nonlinear functional differential system with feedback control , 2003 .

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

[17]  Wan-Tong Li,et al.  Positive periodic solutions of a class of delay differential system with feedback control , 2004, Appl. Math. Comput..

[18]  Ting-Zhu Huang,et al.  Global exponential stability of static neural networks with delay and impulses: Discrete-time case , 2012 .

[19]  Leonid Berezansky,et al.  Stability of a time-varying fishing model with delay , 2008, Appl. Math. Lett..