In this technical note we calculate the dynamics of a linear feedback model of progression in the cell cycle in the case that the cells are organized into k = 3 clusters. We examine the dynamics in detail for a specific subset of parameters with non-empty interior. There is an interior fixed point of the Poincaré map defined by the system. This fixed point corresponds to a periodic solution wit...

In this paper we present time dependent solution of the open bosonic string field theory describing the motion of the tachyon on unstable D-brane.

In this paper we construct a string-like classical solution, the pion-string, in the linear sigma model. We then study the stability of the pion-string, and find that it is unstable in the parameter space allowed experimentally. We also speculate on the existance of an unstable eta-string, associated with spontaneous breakdown of the anomalous UA(1) symmetry in QCD at high temperatures. The imp...

We follow the unstable manifold of periodic and quasi-periodic solutions for the Poiseuille problem, using two formulations: holding constant flux or mean pressure gradient. By means of a numerical integrator of the Navier-Stokes equations, we let the fluid evolve from a perturbed unstable solution. We detect several connections among different configurations of the flow such as laminar, period...

A new transition mechanism to Alfvén chaos via boundary crisis is reported. This crisis appears in a complex plasma region in the presence of a large number of coexisting attractors. We characterize an example of double boundary crises using the unstable periodic orbit determined from the numerical solution of the driven-dissipative derivative nonlinear Schrödinger equation, and demonstrate how...

We show that the solution of fully nonlinear lasing equations for stadium cavities exhibits a highly directional emission pattern. This directionality can be well explained by a ray-dynamical model, where the dominant ray-escape dynamics is governed by the unstable manifolds of the unstable short periodic orbits for the stadium cavity. Investigating the cold-cavity modes relevant for the lasing...

Using a scalar reaction-diffusion equation with drift and a cubic nonlinearity as a simple model problem, we investigate the effect of domain size on stability and bifurcations of steady states. We focus on two parameter regimes, namely the regions where the steady state is convectively or absolutely unstable. In the convective-instability regime, the trivial stationary solution is asymptotical...

This article is a sequel to [M.Z.Z.1] aimed at completing the characterization of the pathwise local structure of solutions of semi-linear stochastic evolution equations (see’s) and stochastic partial differential equations (spde’s) near stationary solutions. The characterization is expressed in terms of the almost sure long-time behavior of trajectories of the equation in relation to the stati...