This paper is concerned with the asymptotic behavior of solutions of stochastic differential equations dyt = dωt − ∇V (yt ) dt , y0 = 0. When d = 1 and V is not periodic but obtained as a superposition of an infinite number of periodic potentials with geometrically increasing periods [V (x)= ∑∞ k=0 Uk(x/Rk), where Uk are smooth functions of period 1, Uk(0)= 0, and Rk grows exponentially fast wi...

In this paper, we consider hybrid models of mechanical systems undergoing impacts — Lagrangian hybrid systems, and study their periodic orbits in the presence of Zeno behavior, where an infinite sequence of impacts converges in finite time. The main result of this paper is explicit conditions under which the existence of stable periodic orbits for a Lagrangian hybrid system with perfectly plast...

A structured model of bioreactor for an activated sludge process was presented. The stability and bifurcation characteristics of the model are investigated, the bifurcation analysis of the model shows static and complex dynamic behavior (periodic and complex) over a wide range of the model parameters. The model exhibits a new interesting behavior (in some range of parameters) including four sta...

In this work we characterize experimentally the transition between periodic rotating waves and synchronized chaos in a ring of unidirectionally coupled Lorenz oscillators by means of electronic circuits. The study is complemented by numerical and theoretical analysis, and the intermediate states and their transitions are identified. The route linking periodic behavior with synchronous chaos inv...

As the existence theory for solutions of nonlinear partial differential equations becomes better understood, one can begin to ask more detailed questions about the behavior of solutions of such equations. Given the bewildering complexity which can arise from relatively simple systems of ordinary differential equations, it is hopeless to try to describe fully the behavior which might arise from ...

The equations of motion of a two-degrees-of-freedom mass in a magnetic bearing are non-linear in displacement, with geometric coupling of the magnetic bearing coupling the horizontal and vertical components of rotor motion. The non-linear forced response is studied in two ways: (1) using imbalance force; (2) using non-imbalance harmonic force. In the forced response, only periodic motion is inv...

Detecting suspicious or malicious user behavior in large networks is an essential task for administrators which requires significant effort due to the huge amount of log data to be processed. However, several of these activities can be rapidly identified since they usually demonstrate periodic behavior. For instance, periodic activities by specific users accessing the billing system of a financ...

We investigate a type of intermittency that occurs in space as well as time, studying a one dimensional lattice of coupled quadratic maps. This system naturally forms spatial domains. Motion of the domain walls causes spatially localized changes from chaotic to almost periodic behavior. The almost periodic phases have eigenvalues quite close to one, resulting in long-lived laminar bursts with a...

Squeeze film dampers (SFDs) are often used in machines with high rotational speed to reduce non-periodic behavior by creating external damping. There are some structural parameters which are of great importance in designing these systems, such as oil film thickness and inner race mass of SFD. Moreover, there is a crucial parameter associated with manufacturing process, under the title of wavine...

A first generation smoking machine capable of reading and replicating detailed puffing behavior from recorded smoking topography data is presented. Unlike standard smoking machines, which model human puffing behavior as a steady periodic waveform with a fixed puff frequency, volume, and duration, this novel machine generates a mainstream smoke aerosol by automatically "playing-back" puff topogr...