We study reaction-di¤usion systems of propagator-controller type in the one-dimensional unit interval. When propagator di¤uses slowly, we establish the existence of transition layer equilibria by using singular perturbation expansions and a Lyapunov-Schmidt reduction method. Our approach to the existence also enables us to simultaneously obtain a stability criterion for the layer equilibria.

We construct the most general form of axially symmetric SU (2)-Yang-Mills fields in Bianchi cosmologies. The dynamical evolution of axially symmetric YM fields in Bianchi I model is compared with the dynamical evolution of the electromagnetic field in Bianchi I and the fully isotropic YM field in Friedmann-Robertson-Walker cosmolo-gies. The stochastic properties of axially symmetric Bianchi I-E...

We show that the feedback from the macroscopic dynamics of a system of coupled units can synchronize the dynamics of these units. We studied the dynamics of maps coupled through their variables and control parameters. The feedback adjusted the values of the parameters of each map by using a function that depended on the difference between the Liapunov exponent of each unit and the Liapunov expo...

Hamrick (2002) contested the conclusion of our recent article on evolutionary constraints on digit numbers that in tetrapods limb reduction usually occurs via arrest of the initial development followed by degeneration (Galis et al 2001). Firstly, we agree with Hamrick that we unfortunately illustrated this phenomenon with the wrong figure: the digits in the hand of Didelphis marsupialis are ind...

In this work, the modified Lyapunov-Schmidt reduction is used to find a nonlinear Ritz approximation of Fredholm functional defined by nonhomogeneous Camassa-Holm equation and Benjamin-Bona-Mahony. We introduced for problems when dimension null space equal two. The has been found as function codimension twenty-four.

We find a canonical form for pure states of a general multipartite system, in which the constraints on the coordinates (with respect to a factorisable orthonormal basis) are simply that certain ones vanish and certain others are real. For identical particles they are invariant under permutations of the particles. As an application, we find the dimension of the generic local equivalence class.

We introduce a class of difference/differential equations which is sufficiently large to include systems of interest for applications, but at the same time sufficiently easy to handle. In this framework, we give in particular a detailed and rather complete study of the asymptotic behavior of pairs of oscillators. We finally introduce appropriate notions of stability and extend Liapunov first an...

For one-dimensional system of dissipative balance laws endowed with a convex entropy we prove, under natural assumptions, that a constant equilibrium state is asymptotically L 2 ?stable under a zero-mass initial disturbance. The technique is based on the construction of an appropriate Liapunov functional involving the entropy and a so-called compensation term.