A computational approach is presented in this paper to construct local Lyapunov functions for autonomous dynamical systems with multiple isolated locally asymptotically stable (such as point-like, periodic, or strange) attractors. We consider of nonlinear ODEs, where the right-hand-side dynamic equations given form rational (i.e., fraction polynomials). The function searched a parameterized qua...

In this paper we use a class of stochastic functional Kolmogorov-type model with jumps to describe the evolutions of population dynamics. By constructing a special Lyapunov function, we show that the stochastic functional differential equation associated with our model admits a unique global solution in the positive orthant, and, by the exponential martingale inequality with jumps, we dis...

In the paper presents a brief survey of some new developments in Lyapunov’s approach including the generalized perturbation equation and its applications; the use of nonanalytic Lyapunov functions; an extension of the Barbashin-Krasovskii theorem related to asymptotic stability assured by a Lyapunov function with nonpositive derivative; the consistency condition for a time-space mosaic that con...

The Lyapunov stability theorem is used to derive a control law that can be used to control the spacing between vehicles in a platoon. A third order system is adopted to model the vehicle and power-train dynamics. In addition, the concept of "Expected Spacing Error" is introduced and used to form a Lyapunov function. Then a control law that always decreases the Lyapunov function is selected. A p...

The use of Lyapunov conditions for proving functional inequalities was initiated in [5]. It was shown in [4, 30] that there is an equivalence between a Poincaré inequality, the existence of some Lyapunov function and the exponential integrability of hitting times. In the present paper, we close the scheme of the interplay between Lyapunov conditions and functional inequalities by • showing that...