A coupled system of two singularly perturbed ordinary differential equations of first order with the prescribed initial values are considered. The leading term of each equation is multiplied by a small positive parameter and the parameters may differ. The solution exhibits overlapping layers. A Shishkin mesh is constructed. A classical finite difference scheme applied on this mesh (which is pie...

We extend Lin’s method for use in the setting of parameter-dependent nonlinear functional differential equations of mixed type (MFDEs). We show that the presence of M -homoclinic and M -periodic solutions that bifurcate from a prescribed homoclinic connection can be detected by studying a finite dimensional bifurcation equation. As an application, we describe the codimension two orbit-flip bifu...

We consider a Ginzburg-Landau type functional on S 2 with a 6 th order potential and the corresponding selfduality equations. We study the limiting behavior in the two vortex case when a coupling parameter tends to zero. This two vortex case is a limiting case for the Moser inequality, and we correspondingly detect a rich and varied asymptotic behavior depending on the position of the vortices....

The paper presents an original method of designing state variable feedback in time delay systems assigning the dominant system poles on prescribed positions in the splane. For the feedback parameter adjustment a design method has been developed based on application of sensitivity functions, i.e. gradient derivatives of the characteristic quasipolynomial. The prescription of desired zeros as cru...

A principle in surface sampling and mesh generation is that highly curved area should be sampled densely and vice versa. This paper presents an approach for automated surface sampling and adaptive mesh generation in accordance with the principle. The approach is self-organizing, forming topology-preserving mesh from random initialization. Mesh spacing versus surface curvedness can be easily con...

A system of partial differential equations modeling a van der Waals fluid or an elastic medium with nonmonotone pressure-density relation is studied. As the system changes type, regularizations are considered. The existence of one-dimensional periodic travelling waves with prescribed average density in a certain range, average velocity, and wavelength is proved. They exhibit layer structure whe...

Using a construction similar to an iterated function system, but with functions changing at each step of iteration, we provide a natural example of a continuous one-parameter family of holomorphic functions of infinitely many variables. This family is parametrized by the compact space of positive integer sequences of prescribed growth and hence it can also be viewed as a parametric description ...

This paper investigates the problem of asymptotic state observation for analytic nonlinear discrete-time systems. A new technique for the observer construction, based on the Taylor polynomial approximation of the inverse of the observability map, is presented and discussed. The degree chosen for the approximation is the most important design parameter of the observer, in that it can be chosen s...