On point-dissipative systems of differential equations with quadratic nonlinearity

Abstract

The system x′=Ax+f(x) of nonlinear vector differential equations, where the nonlinear term f(x) is quadratic with orthogonality property xTf(x)=0 for all x, is point-dissipative if uTAu<0 for all nontrivial zeros u of f(x).

Keywords

• point-dissipative
• quadratic nonlinearity
• symmetric matrices
• commutative but generally non-associative algebra.