This paper modelles job search mechanism at individual level by a determinstic-stochastic approach in a economy with perfect competion and rational agents. Each single unit, firm or worker, is analyzed over time; aggregate dynamics comes directly from the micro-structure of the economy. We show that the unemployment as well as vacancy rate converge in the long run to an ergodic distribution who...

We study the controllability properties of the class of stochastic differential systems characterized by a linear controlled diffusion perturbed by a smooth, bounded, uniformly Lipschitz nonlinearity. We obtain conditions that guarantee the weak and strong controllability of the system. Also, given any open set in the state space we construct a control, depending only on the Lipschitz constant ...

We present a theory for describing the evolution of a galaxy caused by stochastic events such as weak mergers, transient spiral structure, orbiting blobs, etc. This noise excites large-scale patterns that drives the evolution of the galactic density profile. In dark-matter haloes, the repeated stochastic perturbations preferentially ring the lowest-order modes of the halo with only a very weak ...

We present a theory for describing the evolution of a galaxy caused by stochastic events such as weak mergers, transient spiral structure, orbiting blobs, etc. This noise excites large-scale patterns that drives the evolution of the galactic density profile. In dark-matter haloes, the repeated stochastic perturbations preferentially ring the lowest-order modes of the halo with only a very weak ...

The present paper introduces a new technique to generate several independent chaotic attractors by designing a switching piecewise-constant controller in continuous-time systems. This controller can create chaos using an anticontrol of chaos feedback. It is shown that nonlinear continuous-time systems have several attractors, depending on initial conditions. We demonstrate that the state space ...

It is proposed that any dynamical system with coexisting chaotic attractors has an emergent property. This provides a nonreductive explanation of mental states and their high sensitivity to noise and initial conditions. If metaphysical terms result from the mental states and these are emergent properties of dynamical systems with coexisting attractors, such as the brain, it is suggested that th...

We consider the concept of Reachability for systems described by PMDs, generalizing various known results from the theory of generalized state space systems using time domain analysis,which takes into account the finite and infinite pole-zero structure of the associated matrix. We extend also the theory of admissible initial conditions and we introduce the concept of Reachable subspace for PMDs...

Bewley considers a dynamic general equilibrium model with heterogeneous consumers. Assuming that the future is sufficiently important, he shows that an equilibrium path converges to a limit which depends upon initial conditions. This study shows that the limit lies near the stationary state independent of initial conditions. This state is the economy’s so-called turnpike ~ a turnpike is usually...

The famous Lorenz system is studied and analyzed for a particular set of parameters originally proposed by Lorenz. With those parameters, the system has a single globally attracting strange attractor, meaning that almost all initial conditions in its 3D state space approach the attractor as time advances. However, with a slight change in one of the parameters, the chaotic attractor coexists wit...

Model equations for the description of chemical reactions of dissociation and recombination through a transition state constitute necessarily singular perturbation problems because of the very short lifetime of the excited molecules, compared to all other characteristic times. Asymptotic solutions are derived and tested versus an accurate numerical solution by resorting to different expansion a...