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International Journal of Mathematics and Mathematical Sciences
Volume 16, Issue 1, Pages 139-148
http://dx.doi.org/10.1155/S016117129300016X

On point dissipative N-dimensional systems of differential equations with quadratic nonlinearity

Department of Mathematical Sciences, Clemson University, Clemson 29634-1907, SC, USA

Received 17 October 1991

Copyright © 1993 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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 (n1)-dimensional hyperplane.