28,912 research outputs found
Synchronization problems for unidirectional feedback coupled nonlinear systems
In this paper we consider three different synchronization problems consisting
in designing a nonlinear feedback unidirectional coupling term for two
(possibly chaotic) dynamical systems in order to drive the trajectories of one
of them, the slave system, to a reference trajectory or to a prescribed
neighborhood of the reference trajectory of the second dynamical system: the
master system. If the slave system is chaotic then synchronization can be
viewed as the control of chaos; namely the coupling term allows to suppress the
chaotic motion by driving the chaotic system to a prescribed reference
trajectory. Assuming that the entire vector field representing the velocity of
the state can be modified, three different methods to define the nonlinear
feedback synchronizing controller are proposed: one for each of the treated
problems. These methods are based on results from the small parameter
perturbation theory of autonomous systems having a limit cycle, from nonsmooth
analysis and from the singular perturbation theory respectively. Simulations to
illustrate the effectiveness of the obtained results are also presented.Comment: To appear in Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Ana
Properties of generalized synchronization of chaos
A review of recent ideas in the field of generalized synchronization of chaos is presented. This field is concerned with a generalization of the concept of conventional (identical) chaotic synchronization to the case of one-way coupled nonidentical chaotic systems. Generalized synchronization is taken to occur if, ignoring transients, the response system becomes uniquely determined by the current state of the driving system, i. e., all trajectories in the phase space are attracted to a complex synchronization manifold that may have a fractal structure. Different tools for detecting and analyzing the properties of this type of synchronization are discussed
Time-delayed feedback control in astrodynamics
In this paper we present time-delayed feedback control (TDFC) for the purpose of autonomously driving trajectories of nonlinear systems into periodic orbits. As the generation of periodic orbits is a major component of many problems in astodynamics we propose this method as a useful tool in such applications. To motivate the use of this method we apply it to a number of well known problems in the astrodynamics literature. Firstly, TDFC is applied to control in the chaotic attitude motion of an asymmetric satellite in an elliptical orbit. Secondly, we apply TDFC to the problem of maintaining a spacecraft in a periodic orbit about a body with large ellipticity (such as an asteroid) and finally, we apply TDFC to eliminate the drift between two satellites in low Earth orbits to ensure their relative motion is bounded
Anticipated synchronization in coupled inertia ratchets with time-delayed feedback: a numerical study
We investigate anticipated synchronization between two periodically driven
deterministic, dissipative inertia ratchets that are able to exhibit directed
transport with a finite velocity. The two ratchets interact through an
unidirectional delay coupling: one is acting as a master system while the other
one represents the slave system. Each of the two dissipative deterministic
ratchets is driven externally by a common periodic force. The delay coupling
involves two parameters: the coupling strength and the (positive-valued) delay
time. We study the synchronization features for the unbounded, current carrying
trajectories of the master and the slave, respectively, for four different
strengths of the driving amplitude. These in turn characterize differing phase
space dynamics of the transporting ratchet dynamics: regular, intermittent and
a chaotic transport regime. We find that the slave ratchet can respond in
exactly the same way as the master will respond in the future, thereby
anticipating the nonlinear directed transport
Directed transport and localization in phase-modulated driven lattices
We explore the dynamics of non-interacting particles loaded into a
phase-modulated one-dimensional lattice formed by laterally oscillating square
barriers. Tuning the parameters of the driven unit cell of the lattice selected
parts of the classical phase space can be manipulated in a controllable manner.
We find superdiffusion in position space for all parameters regimes. A directed
current of an ensemble of particles can be created through locally breaking the
spatiotemporal symmetries of the time-driven potential. Magnitude and direction
of the current are tunable. Several mechanisms for transient localization and
trapping of particles in different wells of the driven unit cell are presented
and analyzed
Chaos in a double driven dissipative nonlinear oscillator
We propose an anharmonic oscillator driven by two periodic forces of
different frequencies as a new time-dependent model for investigating quantum
dissipative chaos. Our analysis is done in the frame of statistical ensemble of
quantum trajectories in quantum state diffusion approach. Quantum dynamical
manifestation of chaotic behavior, including the emergence of chaos, properties
of strange attractors, and quantum entanglement are studied by numerical
simulation of ensemble averaged Wigner function and von Neumann entropy.Comment: 9 pages, 18 figure
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