The inflow problem for the full two-phase model in a half line is investigated this paper. existence and uniqueness of stationary solution shown by applications center manifold theory, its nonlinear stablility established small perturbation.

An improved homoclinic predictor at a generic codim 2 Bogdanov-Takens (BT) bifucation is derived. We use the classical “blow-up” technique to reduce the canonical smooth normal form near a generic BT bifurcation to a perturbed Hamiltonian system. With a simple perturbation method, we derive explicit firstand second-order corrections of the unperturbed homoclinic orbit and parameter value. To ob...

Motivated by an animal territoriality 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 ...

In this paper, we consider a delayed system of differential equations modeling two neurons: one is excitatory, the other is inhibitory. We study the stability and bifurcations of the trivial equilibrium. Using center manifold theory for delay differential equations, we develop the universal unfolding of the system when the trivial equilibrium point has a double zero eigenvalue. In particular, w...

We consider a simple model of the evolution of the concentration of a tracer, subject to a background shear flow by a fluid with viscosity ν 1 in an infinite channel. Taylor observed in the 1950’s that, in such a setting, the tracer diffuses at a rate proportional to 1/ν, rather than the expected rate proportional to ν. We provide a mathematical explanation for this enhanced diffusion using a c...

Multistrain diseases have multiple distinct coexisting serotypes (strains). For some diseases, such as dengue fever, the serotypes interact by antibody-dependent enhancement (ADE), in which infection with a single serotype is asymptomatic, but contact with a second serotype leads to higher viral load and greater infectivity. We present and analyze a dynamic compartmental model for multiple sero...

The frequency-dependent pi criterion of Bittanti et al. [7] is a very important tool that has been used extensively in applications, to predict potential performance improvement under periodic forcing in a nonlinear system. The pi criterion is local in nature and provides an approximate formula for the performance index under small-amplitude periodic forcing. Motivated by basic results from Cen...

The reduction of smooth dynamical systems to lower dimensional center manifolds containing the essential bifurcation dynamics is a very useful approach both for theoretical investigations as well as for numerical computation. Since this approach relies on smoothness properties of the system and on the existence of a basic linearization the question arises if this approach can be carried over to...

Markus Kunze1 Mathematisches Institut der Universit at K oln Weyertal 86, D-50931 K oln, Germany email: [email protected] Herbert Spohn Zentrum Mathematik and Physik Department, TU M unchen D-80290 M unchen, Germany email: [email protected] Abstract We consider the Abraham model of a rigid charge distribution coupled to the electromagnetic eld and subject to, on the scal...