Connective stability of competitive equilibrium

The purpose of this paper is to derive necessary and sufficient conditions for connective stability of non-linear matrix systems described by the equation $\text{x}\text{?}\text{= A(t, x) x}$, where the matrix A(t, x) has time-varying nonlinear elements. The obtained results can be used to study stability of competitive equilibrium in as diverse fields as economics and engineering, model ecosystems and arms races.