Lipschitz stability criteria for a generalized delayed Kolmogorov model. (Q1847589)

This paper is devoted to the study of the stability of the functional-differential equation \[ x'=B(x)f(t,x,x_t), \quad x_{t_0}= 0 \tag{1} \] where the prime in (1) denotes the derivative with respect to \(t\). By using a new notion, namely Lipschitz stability, the author discusses the so-called \(f_0\)-stability using a cone Lyapunov function. He derives a sufficient condition under which the solutions of (1) are uniformly Lipschitz stable.