Dynamics of a Family of Nonlinear Delay Difference Equations
We study the global asymptotic stability of the following difference equation: xn+1=f(xn-k1,xn-k2,…,xn-ks;xn-m1,xn-m2,…,xn-mt),n=0,1,…, where 0≤k1<k2<⋯<ks and 0≤m1<m2<⋯<mt with {k1,k2,…,ks}⋂{m1,m2,…,mt}=∅, the initial values are positive, and f∈C(Es+t,(0,+∞)) with E∈{(0,+∞),[0,+∞)...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/456530 |
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| author | Qiuli He Taixiang Sun Hongjian Xi |
| author_facet | Qiuli He Taixiang Sun Hongjian Xi |
| author_sort | Qiuli He |
| collection | DOAJ |
| description | We study the global asymptotic stability of the following difference equation: xn+1=f(xn-k1,xn-k2,…,xn-ks;xn-m1,xn-m2,…,xn-mt),n=0,1,…, where 0≤k1<k2<⋯<ks and 0≤m1<m2<⋯<mt with {k1,k2,…,ks}⋂{m1,m2,…,mt}=∅, the initial values are positive, and f∈C(Es+t,(0,+∞)) with E∈{(0,+∞),[0,+∞)}. We give sufficient conditions under which the unique positive equilibrium x- of that equation is globally asymptotically stable. |
| format | Article |
| id | doaj-art-3216379e28cf41d19613649328e2682b |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-3216379e28cf41d19613649328e2682b2025-02-03T06:07:55ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/456530456530Dynamics of a Family of Nonlinear Delay Difference EquationsQiuli He0Taixiang Sun1Hongjian Xi2College of Electrical Engineering, Guangxi University, Nanning, Guangxi 530004, ChinaCollege of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, ChinaDepartment of Mathematics, Guangxi College of Finance and Economics, Nanning, Guangxi 530003, ChinaWe study the global asymptotic stability of the following difference equation: xn+1=f(xn-k1,xn-k2,…,xn-ks;xn-m1,xn-m2,…,xn-mt),n=0,1,…, where 0≤k1<k2<⋯<ks and 0≤m1<m2<⋯<mt with {k1,k2,…,ks}⋂{m1,m2,…,mt}=∅, the initial values are positive, and f∈C(Es+t,(0,+∞)) with E∈{(0,+∞),[0,+∞)}. We give sufficient conditions under which the unique positive equilibrium x- of that equation is globally asymptotically stable.http://dx.doi.org/10.1155/2013/456530 |
| spellingShingle | Qiuli He Taixiang Sun Hongjian Xi Dynamics of a Family of Nonlinear Delay Difference Equations Abstract and Applied Analysis |
| title | Dynamics of a Family of Nonlinear Delay Difference Equations |
| title_full | Dynamics of a Family of Nonlinear Delay Difference Equations |
| title_fullStr | Dynamics of a Family of Nonlinear Delay Difference Equations |
| title_full_unstemmed | Dynamics of a Family of Nonlinear Delay Difference Equations |
| title_short | Dynamics of a Family of Nonlinear Delay Difference Equations |
| title_sort | dynamics of a family of nonlinear delay difference equations |
| url | http://dx.doi.org/10.1155/2013/456530 |
| work_keys_str_mv | AT qiulihe dynamicsofafamilyofnonlineardelaydifferenceequations AT taixiangsun dynamicsofafamilyofnonlineardelaydifferenceequations AT hongjianxi dynamicsofafamilyofnonlineardelaydifferenceequations |