The main purpose of this paper is to study the dynamic behavior of the rational difference equation of the fourth order Where α, β and γ are positive constants and the initial conditions y<sub>-3</sub>,...The main purpose of this paper is to study the dynamic behavior of the rational difference equation of the fourth order Where α, β and γ are positive constants and the initial conditions y<sub>-3</sub>, y<sub>-2</sub>, y<sub>-1</sub>, y<sub>0</sub> are arbitrary positive real numbers. Also, we obtain the solution of some special cases of this equation and investigate the existence of a periodic solutions of these equations. Finally, some numerical examples will be given to explicate our results. .展开更多
The dynamics of a single population with non-overlapping generations can be described deterministically by a scalar difference equation in this study. A discrete-time Beverton- Holt stock recruitment model with Allee ...The dynamics of a single population with non-overlapping generations can be described deterministically by a scalar difference equation in this study. A discrete-time Beverton- Holt stock recruitment model with Allee effect, harvesting and hydra effect is proposed and studied. Model with strong Allee effect results from incorporating mate limitation in the Beverton-Holt model. We show that these simple models exhibit some interesting （and sometimes unexpected） phenomena such as the hydra effect, sudden collapses and essential extinction. Along with this, harvesting is a socio-economie issue to continue any system generation after generation. Different dynamical behaviors for these situations have been illustrated numerically also. The biological implications of our analytical and numerical findings are discussed critically.展开更多
The authors investigate the global behavior of the solutions of the difference equation xn＋1=axn-1xn-k/bxn-p＋cxn-q,n=0,1,…where the initial conditions x-r, x-r＋1, x-r＋2,… , x0 are arbitrary positive real numbers...The authors investigate the global behavior of the solutions of the difference equation xn＋1=axn-1xn-k/bxn-p＋cxn-q,n=0,1,…where the initial conditions x-r, x-r＋1, x-r＋2,… , x0 are arbitrary positive real numbers, r = max{l, k,p, q） is a nonnegative integer and a, b, c are positive constants. Some special cases of this equation are also studied in this paper.展开更多
文摘The main purpose of this paper is to study the dynamic behavior of the rational difference equation of the fourth order Where α, β and γ are positive constants and the initial conditions y<sub>-3</sub>, y<sub>-2</sub>, y<sub>-1</sub>, y<sub>0</sub> are arbitrary positive real numbers. Also, we obtain the solution of some special cases of this equation and investigate the existence of a periodic solutions of these equations. Finally, some numerical examples will be given to explicate our results. .
文摘The dynamics of a single population with non-overlapping generations can be described deterministically by a scalar difference equation in this study. A discrete-time Beverton- Holt stock recruitment model with Allee effect, harvesting and hydra effect is proposed and studied. Model with strong Allee effect results from incorporating mate limitation in the Beverton-Holt model. We show that these simple models exhibit some interesting （and sometimes unexpected） phenomena such as the hydra effect, sudden collapses and essential extinction. Along with this, harvesting is a socio-economie issue to continue any system generation after generation. Different dynamical behaviors for these situations have been illustrated numerically also. The biological implications of our analytical and numerical findings are discussed critically.
文摘The authors investigate the global behavior of the solutions of the difference equation xn＋1=axn-1xn-k/bxn-p＋cxn-q,n=0,1,…where the initial conditions x-r, x-r＋1, x-r＋2,… , x0 are arbitrary positive real numbers, r = max{l, k,p, q） is a nonnegative integer and a, b, c are positive constants. Some special cases of this equation are also studied in this paper.
