Global Dynamics of Delayed Sigmoid Beverton–Holt Equation
In this paper, certain dynamic scenarios for general competitive maps in the plane are presented and applied to some cases of second-order difference equation xn+1=fxn,xn−1, n=0,1,…, where f is decreasing in the variable xn and increasing in the variable xn−1. As a case study, we use the difference...
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| Format: | Article |
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Wiley
2020-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/1364282 |
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| author | Toufik Khyat M. R. S. Kulenović |
| author_facet | Toufik Khyat M. R. S. Kulenović |
| author_sort | Toufik Khyat |
| collection | DOAJ |
| description | In this paper, certain dynamic scenarios for general competitive maps in the plane are presented and applied to some cases of second-order difference equation xn+1=fxn,xn−1, n=0,1,…, where f is decreasing in the variable xn and increasing in the variable xn−1. As a case study, we use the difference equation xn+1=xn−12/cxn−12+dxn+f, n=0,1,…, where the initial conditions x−1,x0≥0 and the parameters satisfy c,d,f>0. In this special case, we characterize completely the global dynamics of this equation by finding the basins of attraction of its equilibria and periodic solutions. We describe the global dynamics as a sequence of global transcritical or period-doubling bifurcations. |
| format | Article |
| id | doaj-art-52992bbd3f064416991b103d2cd77fb4 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-52992bbd3f064416991b103d2cd77fb42025-08-20T03:36:30ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/13642821364282Global Dynamics of Delayed Sigmoid Beverton–Holt EquationToufik Khyat0M. R. S. Kulenović1Department of Mathematics, University of Rhode Island, Kingston, Rhode Island 02881-0816, USADepartment of Mathematics, University of Rhode Island, Kingston, Rhode Island 02881-0816, USAIn this paper, certain dynamic scenarios for general competitive maps in the plane are presented and applied to some cases of second-order difference equation xn+1=fxn,xn−1, n=0,1,…, where f is decreasing in the variable xn and increasing in the variable xn−1. As a case study, we use the difference equation xn+1=xn−12/cxn−12+dxn+f, n=0,1,…, where the initial conditions x−1,x0≥0 and the parameters satisfy c,d,f>0. In this special case, we characterize completely the global dynamics of this equation by finding the basins of attraction of its equilibria and periodic solutions. We describe the global dynamics as a sequence of global transcritical or period-doubling bifurcations.http://dx.doi.org/10.1155/2020/1364282 |
| spellingShingle | Toufik Khyat M. R. S. Kulenović Global Dynamics of Delayed Sigmoid Beverton–Holt Equation Discrete Dynamics in Nature and Society |
| title | Global Dynamics of Delayed Sigmoid Beverton–Holt Equation |
| title_full | Global Dynamics of Delayed Sigmoid Beverton–Holt Equation |
| title_fullStr | Global Dynamics of Delayed Sigmoid Beverton–Holt Equation |
| title_full_unstemmed | Global Dynamics of Delayed Sigmoid Beverton–Holt Equation |
| title_short | Global Dynamics of Delayed Sigmoid Beverton–Holt Equation |
| title_sort | global dynamics of delayed sigmoid beverton holt equation |
| url | http://dx.doi.org/10.1155/2020/1364282 |
| work_keys_str_mv | AT toufikkhyat globaldynamicsofdelayedsigmoidbevertonholtequation AT mrskulenovic globaldynamicsofdelayedsigmoidbevertonholtequation |