130 research outputs found
Amplitude Death: The emergence of stationarity in coupled nonlinear systems
When nonlinear dynamical systems are coupled, depending on the intrinsic
dynamics and the manner in which the coupling is organized, a host of novel
phenomena can arise. In this context, an important emergent phenomenon is the
complete suppression of oscillations, formally termed amplitude death (AD).
Oscillations of the entire system cease as a consequence of the interaction,
leading to stationary behavior. The fixed points that the coupling stabilizes
can be the otherwise unstable fixed points of the uncoupled system or can
correspond to novel stationary points. Such behaviour is of relevance in areas
ranging from laser physics to the dynamics of biological systems. In this
review we discuss the characteristics of the different coupling strategies and
scenarios that lead to AD in a variety of different situations, and draw
attention to several open issues and challenging problems for further study.Comment: Physics Reports (2012
Amplitude death phenomena in delay--coupled Hamiltonian systems
Hamiltonian systems, when coupled {\it via} time--delayed interactions, do
not remain conservative. In the uncoupled system, the motion can typically be
periodic, quasiperiodic or chaotic. This changes drastically when delay
coupling is introduced since now attractors can be created in the phase space.
In particular for sufficiently strong coupling there can be amplitude death
(AD), namely the stabilization of point attractors and the cessation of
oscillatory motion. The approach to the state of AD or oscillation death is
also accompanied by a phase--flip in the transient dynamics. A discussion and
analysis of the phenomenology is made through an application to the specific
cases of harmonic as well as anharmoniccoupled oscillators, in particular the
H\'enon-Heiles system.Comment: To be appeared in Phys. Rev. E (2013
Synchronization of coupled stochastic oscillators: the effect of topology
We study sets of genetic networks having stochastic oscillatory dynamics. Depending on the coupling topology we find regimes of phase synchronization of the dynamical variables. We consider the effect of time-delay in the interaction and show that for suitable choices of delay parameter, either in-phase or anti-phase synchronization can occur
Genome-wide analysis of mobile genetic element insertion sites
Mobile genetic elements (MGEs) account for a significant fraction of eukaryotic genomes and are implicated in altered gene expression and disease. We present an efficient computational protocol for MGE insertion site analysis. ELAN, the suite of tools described here uses standard techniques to identify different MGEs and their distribution on the genome. One component, DNASCANNER analyses known insertion sites of MGEs for the presence of signals that are based on a combination of local physical and chemical properties. ISF (insertion site finder) is a machine-learning tool that incorporates information derived from DNASCANNER. ISF permits classification of a given DNA sequence as a potential insertion site or not, using a support vector machine. We have studied the genomes of Homo sapiens, Mus musculus, Drosophila melanogaster and Entamoeba histolytica via a protocol whereby DNASCANNER is used to identify a common set of statistically important signals flanking the insertion sites in the various genomes. These are used in ISF for insertion site prediction, and the current accuracy of the tool is over 65%. We find similar signals at gene boundaries and splice sites. Together, these data are suggestive of a common insertion mechanism that operates in a variety of eukaryotes
Design strategies for the creation of aperiodic nonchaotic attractors
Parametric modulation in nonlinear dynamical systems can give rise to
attractors on which the dynamics is aperiodic and nonchaotic, namely with
largest Lyapunov exponent being nonpositive. We describe a procedure for
creating such attractors by using random modulation or pseudo-random binary
sequences with arbitrarily long recurrence times. As a consequence the
attractors are geometrically fractal and the motion is aperiodic on
experimentally accessible timescales. A practical realization of such
attractors is demonstrated in an experiment using electronic circuits.Comment: 9 pages. CHAOS, In Press, (2009
Driving--induced bistability in coupled chaotic attractors
We examine the effects of symmetry--preserving and breaking interactions in a
drive--response system where the response has an invariant symmetry in the
absence of the drive. Subsequent to the onset of generalized synchronization,
we find that there can be more than one stable attractor. Numerical, as well as
analytical results establish the presence of phase synchrony in such coexisting
attractors. These results are robust to external noise.Comment: To be published in Phys. Rev. E. 201
The effect of finite response–time in coupled dynamical systems
The paper investigates synchronization in unidirectionally coupled dynamical systems wherein the influence of drive on response is cumulative: coupling signals are integrated over a time interval τ. A major consequence of integrative coupling is that the onset of the generalized and phase synchronization occurs at higher coupling compared to the instantaneous (τ = 0) case. The critical coupling strength at which synchronization sets in is found to increase with τ. The systems explored are the chaotic Rössler and limit cycle (the Landau–Stuart model) oscillators. For coupled Rössler oscillators the region of generalized synchrony in the phase space is intercepted by an asynchronous region which corresponds to anomalous generalized synchronization
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