Abstract. In this paper we present a simple and efficient method for computing center manifold and normal forms of differential equations. The main attention is focused on general semi-simple singularities, that is, the Jacobian of a given system evaluated at an equilibrium contains semi-simple eigenvalues. The method combines the computation of center manifold and normal form in one unified pr...

Abstract. Center manifold and normal form theories as well as numerical simulations are employed to analyse the bifurcation and stability of a 13-dimensional deterministic model associated with the transmission dynamics of two diseases within a host population. The stability of the multiple equilibrium solutions together with the associated possible critical points are discussed. It is shown th...

We consider a stochastic susceptible-exposed-infected-recovered (SEIR) epidemiological model. Through the use of a normal form coordinate transform, we are able to analytically derive the stochastic center manifold along with the associated, reduced set of stochastic evolution equations. The transformation correctly projects both the dynamics and the noise onto the center manifold. Therefore, t...

Motivated by an animal territorlality model, we consider a centroidal Voronoi tessellation algorithm from a dynamical systems perspective. In doing so, we discuss the stability of an aligned equilibrium configuration for a rectangular domain that exhibits interesting symmetry properties. We also demonstrate the procedure for performing a center manifold reduction on the system to extract a set ...

We consider the three-dimensional Poiseuille problem of a viscous incompressible uid ow between parallel plates. The ows under investigation are assumed to be traveling waves in streamwise direction with spatial periodicity 2==. In spanwise direction they are assumed to be uniformly close to the basic ow which enables us to use the spatial center{manifold reduction, where the spanwise variable ...

In this paper, a delayed plankton-nutrient interaction model consisting of phytoplankton, zooplankton and dissolved nutrient is considered. It is assumed that some species of phytoplankton releases toxin (known as toxin producing phytoplankton (TPP)) which is harmful for zooplankton growth and this toxin releasing process follows a discrete time variation. Using delay as bifurcation parameter, ...

despite recent advances in video inpainting techniques, reconstructing large missing regions of a moving subject while its scale changes remains an elusive goal. in this paper, we have introduced a scale-change invariant method for large missing regions to tackle this problem. using this framework, first the moving foreground is separated from the background and its scale is equalized. then, a ...

Nonlinear symmetries of nite dimensional dynamical systems are related to nonlinear normal forms and center manifolds in the neighbourhood of a singular point. Certain abstract results can be used algorith-mically to construct the normal forms and/or the center manifold up to a given order in the perturbation expansion. We also argue that for this task, approximate symmetries are as useful as e...

Investigated are J̃-holomorphic cylinders in R ×M , where M is a contact manifold. It is shown that a sufficiently long cylinder having small area is close to a constant map, if its center action vanishes. If its center action is positive, it is close to a cylinder over a periodic orbit of the Reeb vector field, and has a well determined shape. A compactness result is deduced, which is useful in...