The Degasperis-Procesi equation can be derived as a member of a oneparameter family of asymptotic shallow water approximations to the Euler equations with the same asymptotic accuracy as that of the CamassaHolm equation. It is noted that the Degasperis-Procesi equation, unlike the Camassa-Holm equation, has not only peakon solitons but also shock peakons. In this paper, we study the orbital sta...

We show via a Liapunov function that in every model ecosystem governed by generalized Lotka±Volterra equations, a feasible steady state is globally asymptotically stable if the number of interaction branches equals nÿ 1, where n is the number of species. This means that the representative graph for which the theorem holds is a `tree' and not only an alimentary chain. Our result is valid also in...

A class of globally coupled one dimensional maps is studied. For the uncoupled one dimensional map it is possible to compute the spectrum of Liapunov exponents exactly, and there is a natural equilibrium measure (Sinai-Ruelle-Bowen measure), so the corresponding `typical' Liapunov exponent may also be computed. The globally coupled systems thus provide examples of blowout bifurcations in arbitr...

This work is devoted to the stability of random-switching systems of differential equations. After presenting the formulation of random-switching systems, the notion of stability is recalled, and sufficient conditions in terms of the Liapunov function are presented. Then easily verifiable conditions for stability and instability of systems arising in approximation are established. Using a logar...

In this paper, Liapunov-type integral inequalities has been obtained for third order dynamic equations on time scales by using elementary analysis. A criterion for disconjugacy of third order dynamic equation is obtained in an interval [a, σ(b)].

In this paper, we estimate Liapunov-type integral inequalities for a single, cycled, and coupled dynamic system of one-dimensional p-Laplacian problems with weight functions having stronger singularities.

Consider a communications network consisting of mobiles, each of which can be scheduled to serve as a receiver and/or transmitter. There are random external data processes arriving at some of the mobiles, each destined for some set of destinations. Each mobile can serve as a node in the possibly multi-hop path from source to destination. At each mobile the data is queued according to the source...