International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 1, Pages 139-148
doi:10.1155/S016117129300016X
On point dissipative N-dimensional systems of differential equations with quadratic nonlinearity
Anil K. Bose
, Alan S. Cover
and James A. Reneke
Department of Mathematical Sciences, Clemson University, Clemson 29634-1907, SC, USA
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 (n−1)-dimensional hyperplane.