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Title:

Controlling surface morphologies by time-delayed feedback

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We propose a new method to control the roughness of a growing surface, via a time-delayed feedback scheme. As an illustration, we apply this method to the Kardar-Parisi-Zhang equation in 1+1 dimensions and show that the effective growth exponent of the surface width can be stabilized at any desired value in the interval [0.25,0.33], for a signif...

We propose a new method to control the roughness of a growing surface, via a time-delayed feedback scheme. As an illustration, we apply this method to the Kardar-Parisi-Zhang equation in 1+1 dimensions and show that the effective growth exponent of the surface width can be stabilized at any desired value in the interval [0.25,0.33], for a significant length of time. The method is quite general and can be applied to a wide range of growth phenomena. A possible experimental realization is suggested. ; Comment: 4 pages, 3 figures Minimize

Year of Publication:

2007-01-09

Document Type:

text

Subjects:

Condensed Matter - Materials Science

Condensed Matter - Materials Science Minimize

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Title:

Noise-induced cooperative dynamics and its control in coupled neuron models

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We investigate feedback control of the cooperative dynamics of two coupled neural oscillators that is induced merely by external noise. The interacting neurons are modelled as FitzHugh-Nagumo systems with parameter values at which no autonomous oscillations occur, and each unit is forced by its own source of random fluctuations. Application of d...

We investigate feedback control of the cooperative dynamics of two coupled neural oscillators that is induced merely by external noise. The interacting neurons are modelled as FitzHugh-Nagumo systems with parameter values at which no autonomous oscillations occur, and each unit is forced by its own source of random fluctuations. Application of delayed feedback to only one of two subsystems is shown to be able to change coherence and timescales of noise induced oscillations either in the given subsystem, or globally. It is also able to induce or to suppress stochastic synchronization under certain conditions. ; Comment: 12 pages, 17 figures, Phys. Rev. E accepted Minimize

Year of Publication:

2006-10-04

Document Type:

text

Subjects:

Nonlinear Sciences - Chaotic Dynamics

Nonlinear Sciences - Chaotic Dynamics Minimize

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Title:

Synchronization of networks of oscillators with distributed delay coupling

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This paper studies the stability of synchronized states in networks where couplings between nodes are characterized by some distributed time delay, and develops a generalized master stability function approach. Using a generic example of Stuart-Landau oscillators, it is shown how the stability of synchronized solutions in networks with distribut...

This paper studies the stability of synchronized states in networks where couplings between nodes are characterized by some distributed time delay, and develops a generalized master stability function approach. Using a generic example of Stuart-Landau oscillators, it is shown how the stability of synchronized solutions in networks with distributed delay coupling can be determined through a semi-analytic computation of Floquet exponents. The analysis of stability of fully synchronized and of cluster or splay states is illustrated for several practically important choices of delay distributions and network topologies. ; Comment: 18 pages, 4 figures Minimize

Year of Publication:

2014-06-20

Document Type:

text

Subjects:

Nonlinear Sciences - Chaotic Dynamics

Nonlinear Sciences - Chaotic Dynamics Minimize

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Title:

Delayed feedback as a means of control of noise-induced motion

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Time--delayed feedback is exploited for controlling noise--induced motion in coherence resonance oscillators. Namely, under the proper choice of time delay, one can either increase or decrease the regularity of motion. It is shown that in an excitable system, delayed feedback can stabilize the frequency of oscillations against variation of noise...

Time--delayed feedback is exploited for controlling noise--induced motion in coherence resonance oscillators. Namely, under the proper choice of time delay, one can either increase or decrease the regularity of motion. It is shown that in an excitable system, delayed feedback can stabilize the frequency of oscillations against variation of noise strength. Also, for fixed noise intensity, the phenomenon of entrainment of the basic oscillation period by the delayed feedback occurs. This allows one to steer the timescales of noise-induced motion by changing the time delay. ; Comment: 4 pages, 4 figures. In the replacement file Fig. 2 and Fig. 4(b),(d) were amended. The reason is numerical error found, that affected the quantitative estimates of correlation time, but did not affect the main message Minimize

Year of Publication:

2003-09-09

Document Type:

text

Subjects:

Condensed Matter - Statistical Mechanics

Condensed Matter - Statistical Mechanics Minimize

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Title:

Amplitude and phase dynamics in oscillators with distributed-delay coupling

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This paper studies the effects of distributed delay coupling on the dynamics in a system of non-identical coupled Stuart-Landau oscillators. For uniform and gamma delay distribution kernels, conditions for amplitude death are obtained in terms of average frequency, frequency detuning and parameters of the coupling, including coupling strength an...

This paper studies the effects of distributed delay coupling on the dynamics in a system of non-identical coupled Stuart-Landau oscillators. For uniform and gamma delay distribution kernels, conditions for amplitude death are obtained in terms of average frequency, frequency detuning and parameters of the coupling, including coupling strength and phase, as well as the mean time delay and the width of the delay distribution. To gain further insight into the dynamics inside amplitude death regions, eigenvalues of the corresponding characteristic equations are computed numerically. Oscillatory dynamics of the system is also investigated using amplitude and phase representation. Various branches of phase-locked solutions are identified, and their stability is analysed for different types of delay distributions. ; Comment: 25 pages, 13 figures Minimize

Year of Publication:

2012-09-01

Document Type:

text

Subjects:

Nonlinear Sciences - Chaotic Dynamics

Nonlinear Sciences - Chaotic Dynamics Minimize

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Title:

Asymptotic properties of the spectrum of neutral delay differential equations

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Spectral properties and transition to instability in neutral delay differential equations are investigated in the limit of large delay. An approximation of the upper boundary of stability is found and compared to an analytically derived exact stability boundary. The approximate and exact stability borders agree quite well for the large time dela...

Spectral properties and transition to instability in neutral delay differential equations are investigated in the limit of large delay. An approximation of the upper boundary of stability is found and compared to an analytically derived exact stability boundary. The approximate and exact stability borders agree quite well for the large time delay, and the inclusion of a time-delayed velocity feedback improves this agreement for small delays. Theoretical results are complemented by a numerically computed spectrum of the corresponding characteristic equations. ; Comment: 14 pages, 6 figures Minimize

Year of Publication:

2012-01-28

Document Type:

text

Subjects:

Nonlinear Sciences - Chaotic Dynamics ; Mathematics - Dynamical Systems

Nonlinear Sciences - Chaotic Dynamics ; Mathematics - Dynamical Systems Minimize

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Title:

Control of unstable steady states in neutral time-delayed systems

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We present an analysis of time-delayed feedback control used to stabilize an unstable steady state of a neutral delay differential equation. Stability of the controlled system is addressed by studying the eigenvalue spectrum of a corresponding characteristic equation with two time delays. An analytic expression for the stabilizing control streng...

We present an analysis of time-delayed feedback control used to stabilize an unstable steady state of a neutral delay differential equation. Stability of the controlled system is addressed by studying the eigenvalue spectrum of a corresponding characteristic equation with two time delays. An analytic expression for the stabilizing control strength is derived in terms of original system parameters and the time delay of the control. Theoretical and numerical results show that the interplay between the control strength and two time delays provides a number of regions in the parameter space where the time-delayed feedback control can successfully stabilize an otherwise unstable steady state. ; Comment: 11 pages, 8 figures Minimize

Year of Publication:

2012-01-28

Document Type:

text

Subjects:

Nonlinear Sciences - Chaotic Dynamics ; Mathematics - Dynamical Systems

Nonlinear Sciences - Chaotic Dynamics ; Mathematics - Dynamical Systems Minimize

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Title:

Amplitude death in systems of coupled oscillators with distributed-delay coupling

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This paper studies the effects of coupling with distributed delay on the suppression of oscillations in a system of coupled Stuart-Landau oscillators. Conditions for amplitude death are obtained in terms of strength and phase of the coupling, as well as the mean time delay and the width of the delay distribution for uniform and gamma distributio...

This paper studies the effects of coupling with distributed delay on the suppression of oscillations in a system of coupled Stuart-Landau oscillators. Conditions for amplitude death are obtained in terms of strength and phase of the coupling, as well as the mean time delay and the width of the delay distribution for uniform and gamma distributions. Analytical results are confirmed by numerical computation of the eigenvalues of the corresponding characteristic equations. These results indicate that larger widths of delay distribution increase the regions of amplitude death in the parameter space. In the case of a uniformly distributed delay kernel, for sufficiently large width of the delay distribution it is possible to achieve amplitude death for an arbitrary value of the average time delay, provided that the coupling strength has a value in the appropriate range. For a gamma distribution of delay, amplitude death is also possible for an arbitrary value of the average time delay, provided that it exceeds a certain value as determined by the coupling phase and the power law of the distribution. The coupling phase has a destabilizing effect and reduces the regions of amplitude death. ; Comment: 15 pages, 7 figures Minimize

Year of Publication:

2012-02-01

Document Type:

text

Subjects:

Nonlinear Sciences - Chaotic Dynamics ; Mathematics - Dynamical Systems

Nonlinear Sciences - Chaotic Dynamics ; Mathematics - Dynamical Systems Minimize

DDC:

535 Light & infrared & ultraviolet phenomena *(computed)*

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Title:

Refuting the odd number limitation of time-delayed feedback control

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We refute an often invoked theorem which claims that a periodic orbit with an odd number of real Floquet multipliers greater than unity can never be stabilized by time-delayed feedback control in the form proposed by Pyragas. Using a generic normal form, we demonstrate that the unstable periodic orbit generated by a subcritical Hopf bifurcation,...

We refute an often invoked theorem which claims that a periodic orbit with an odd number of real Floquet multipliers greater than unity can never be stabilized by time-delayed feedback control in the form proposed by Pyragas. Using a generic normal form, we demonstrate that the unstable periodic orbit generated by a subcritical Hopf bifurcation, which has a single real unstable Floquet multiplier, can in fact be stabilized. We derive explicit analytical conditions for the control matrix in terms of the amplitude and the phase of the feedback control gain, and present a numerical example. Our results are of relevance for a wide range of systems in physics, chemistry, technology,and life sciences, where subcritical Hopf bifurcations occur. ; Comment: 4 pages, 3 figures, in print at Phys Rev Lett Minimize

Year of Publication:

2006-09-22

Document Type:

text

Subjects:

Nonlinear Sciences - Chaotic Dynamics

Nonlinear Sciences - Chaotic Dynamics Minimize

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Title:

Time delay control of symmetry-breaking primary and secondary oscillation death

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We show that oscillation death as a specific type of oscillation suppression, which implies symmetry breaking, can be controlled by introducing time-delayed coupling. In particular, we demonstrate that time delay influences the stability of an inhomogeneous steady state, providing the opportunity to modulate the threshold for oscillation death. ...

We show that oscillation death as a specific type of oscillation suppression, which implies symmetry breaking, can be controlled by introducing time-delayed coupling. In particular, we demonstrate that time delay influences the stability of an inhomogeneous steady state, providing the opportunity to modulate the threshold for oscillation death. Additionally, we find a novel type of oscillation death representing a secondary bifurcation of an inhomogeneous steady state. ; Comment: 6 pages, 4 figures Minimize

Year of Publication:

2013-09-23

Document Type:

text

Subjects:

Nonlinear Sciences - Chaotic Dynamics ; Nonlinear Sciences - Adaptation and Self-Organizing Systems

Nonlinear Sciences - Chaotic Dynamics ; Nonlinear Sciences - Adaptation and Self-Organizing Systems Minimize

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