In this paper, the concepts and the direct theorems of stability in the sense of Liapunov, within the framework of Birkhoffian dynamical systems on manifolds, are considered. The Liapunov-type functions are constructed for linear and nonlinear LC and RLC electrical networks, to prove stability under certain conditions.

Existence of global weak solutions to a spatially inhomogeneous kinetic model for coalescing particles is proved, each particle being identified by its mass, momentum and position. The large time convergence to zero is also shown. The cornestone of our analysis is that, for any nonnegative and convex function, the associated Orlicz norm is a Liapunov functional. Existence and asymptotic behavio...

where/ : U—>R is continuous on the open set UC.RXR, is frequentlystudied by means of a continuous function V: U—*R. I t is sometimes unnecessary to know the solutions explicitly. If for example V is independent of /, V(xo) = 0 for some #o, V(x)>0 for XT^X^ and if for each solution of (E), V(</)(t)) is a monotonically decreasing function of t for t^Oy then x0 is a stable critical point of (E...

This paper discusses a discrete multispecies Gilpin-Ayala mutualism system. We first study the permanence and global attractivity of the system. Assume that the coefficients in the system are almost periodic sequences, we obtain the sufficient conditions for the existence of a unique almost periodic solution which is globally attractive and uniformly asymptotically stable by constructing a suit...

The dynamic behaviors in a chemostat model with delayed nutrient recycling and periodically pulsed input are studied. By introducing new analysis technique, the sufficient and necessary conditions on the permanence and extinction of the microorganisms are obtained. Furthermore, by using the Liapunov function method, the sufficient condition on the global attractivity of the model is established...

This paper is concerned with systems of functional differential equations with either finite or infinite delay. We give conditions on the system and on a Liapunov function to ensure that the zero solution is asymptotically stable. Section 2 is devoted to finite delay, Section 3 to infinite delay, and Section 4 to examples. The remainder of this section introduces the problem for the finite dela...

This paper investigates the problem of event-based synchronization of linear discrete-time dynamical networks. Leader-following and leaderless synchronizations are achieved by a distributed event-trigger strategy. It is shown that feedback control updating is unnecessary until an event is triggered. The combinational-state variables and the Riccati equation are used to construct a Liapunov func...

global Liapunov function. The absolute stability of systems Mth infinite but totally disconnected sets of equilibrium points can then be studied using the LaSalle invariance principle, the theory of several complex variables, and sam's theorem. The symmetry of matrix C is important since competitive systems of the form (1) exist wherein C is arbitrarily close to a symmetric matrix but almost al...

In this paper a numerical method for the detection and computation of degenerate Hopf bifurcation points is presented. The degeneracies are classi ed and de ning equations characterizing each of the equivalence classes are constructed by means of a generalized Liapunov-Schmidt reduction. The numerical computation of the sign of the rst Liapunov coe cient which determines the stability of the bi...