On point dissipative N-dimensional systems of differential equations with quadratic nonlinearity
Known sufficient conditions for quadratic dynamical system x′=Ax+f(x) to be point dissipative given in terms of A and f for dimensions 2 and 3 are extended to allow for more general forms for the nonlinear term f(x). Furthermore, the conditions extend to n dimensions when f is quadratic with zero se...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1993-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S016117129300016X |
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| _version_ | 1849308571308654592 |
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| author | Anil K. Bose Alan S. Cover James A. Reneke |
| author_facet | Anil K. Bose Alan S. Cover James A. Reneke |
| author_sort | Anil K. Bose |
| collection | DOAJ |
| description | Known sufficient conditions for quadratic dynamical system x′=Ax+f(x) to be
point dissipative given in terms of A and f for dimensions 2 and 3 are extended to allow for
more general forms for the nonlinear term f(x). Furthermore, the conditions extend to n
dimensions when f is quadratic with zero set an (n−1)-dimensional hyperplane. |
| format | Article |
| id | doaj-art-04f00111e9314507bfa7bd57e37fd06e |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1993-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-04f00111e9314507bfa7bd57e37fd06e2025-08-20T03:54:25ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251993-01-0116113914810.1155/S016117129300016XOn point dissipative N-dimensional systems of differential equations with quadratic nonlinearityAnil K. Bose0Alan S. Cover1James A. Reneke2Department of Mathematical Sciences, Clemson University, Clemson 29634-1907, SC, USADepartment of Mathematical Sciences, Clemson University, Clemson 29634-1907, SC, USADepartment of Mathematical Sciences, Clemson University, Clemson 29634-1907, SC, USAKnown sufficient conditions for quadratic dynamical system x′=Ax+f(x) to be point dissipative given in terms of A and f for dimensions 2 and 3 are extended to allow for more general forms for the nonlinear term f(x). Furthermore, the conditions extend to n dimensions when f is quadratic with zero set an (n−1)-dimensional hyperplane.http://dx.doi.org/10.1155/S016117129300016X |
| spellingShingle | Anil K. Bose Alan S. Cover James A. Reneke On point dissipative N-dimensional systems of differential equations with quadratic nonlinearity International Journal of Mathematics and Mathematical Sciences |
| title | On point dissipative N-dimensional systems of differential equations with quadratic nonlinearity |
| title_full | On point dissipative N-dimensional systems of differential equations with quadratic nonlinearity |
| title_fullStr | On point dissipative N-dimensional systems of differential equations with quadratic nonlinearity |
| title_full_unstemmed | On point dissipative N-dimensional systems of differential equations with quadratic nonlinearity |
| title_short | On point dissipative N-dimensional systems of differential equations with quadratic nonlinearity |
| title_sort | on point dissipative n dimensional systems of differential equations with quadratic nonlinearity |
| url | http://dx.doi.org/10.1155/S016117129300016X |
| work_keys_str_mv | AT anilkbose onpointdissipativendimensionalsystemsofdifferentialequationswithquadraticnonlinearity AT alanscover onpointdissipativendimensionalsystemsofdifferentialequationswithquadraticnonlinearity AT jamesareneke onpointdissipativendimensionalsystemsofdifferentialequationswithquadraticnonlinearity |