41 research outputs found
Self-organized and driven phase synchronization in coupled maps
We study the phase synchronization and cluster formation in coupled maps on
different networks. We identify two different mechanisms of cluster formation;
(a) {\it Self-organized} phase synchronization which leads to clusters with
dominant intra-cluster couplings and (b) {\it driven} phase synchronization
which leads to clusters with dominant inter-cluster couplings. In the novel
driven synchronization the nodes of one cluster are driven by those of the
others. We also discuss the dynamical origin of these two mechanisms for small
networks with two and three nodes.Comment: 4 pages including 2 figure
Parametric characterisation of a chaotic attractor using the two scale cantor measure
A chaotic attractor is usually characterised by its multifractal spectrum which gives a geometric measure of its complexity. Here we present a characterisation using a minimal set of independent parameters which is uniquely determined by the underlying process that generates the attractor. The method maps the f(α ) spectrum of a chaotic attractor on to that of a general two scale Cantor measure. We show that the mapping can be done in practice with reasonable accuracy for many of the standard chaotic attractors. In order to implement this procedure, we also propose a generalisation of the standard equations for the two scale Cantor set in one dimension to that in higher dimensions. Another interesting result we have obtained both theoretically and numerically is that, the f(α ) characterisation gives information only up to two scales, even when the underlying process generating the multifractal involves more than two scales
Computing the multifractal spectrum from time series: An algorithmic approach
We show that the existing methods for computing the f(\alpha) spectrum from a
time series can be improved by using a new algorithmic scheme. The scheme
relies on the basic idea that the smooth convex profile of a typical f(\alpha)
spectrum can be fitted with an analytic function involving a set of four
independent parameters. While the standard existing schemes [16, 18] generally
compute only an incomplete f(\alpha) spectrum (usually the top portion), we
show that this can be overcome by an algorithmic approach which is automated to
compute the Dq and f(\alpha) spectrum from a time series for any embedding
dimension. The scheme is first tested with the logistic attractor with known
f(\alpha) curve and subsequently applied to higher dimensional cases. We also
show that the scheme can be effectively adapted for analysing practcal time
series involving noise, with examples from two widely different real world
systems. Moreover, some preliminary results indicating that the set of four
independant parameters may be used as diagnostic measures is also included.Comment: 10 pages, 16 figures, submitted to CHAO
Experimental observation of extreme multistability in an electronic system of two coupled R\"{o}ssler oscillators
We report the first experimental observation of extreme multistability in a
controlled laboratory investigation. Extreme multistability arises when
infinitely many attractors coexist for the same set of system parameters. The
behavior was predicted earlier on theoretical grounds, supported by numerical
studies of models of two coupled identical or nearly identical systems. We
construct and couple two analog circuits based on a modified coupled
R\"{o}ssler system and demonstrate the occurrence of extreme multistability
through a controlled switching to different attractor states purely through a
change in initial conditions for a fixed set of system parameters. Numerical
studies of the coupled model equations are in agreement with our experimental
findings.Comment: to be published in Phys. Rev.
Methods for Molecular Modelling of Protein Complexes.
Biological processes are often mediated by complexes formed between proteins and various biomolecules. The 3D structures of such protein-biomolecule complexes provide insights into the molecular mechanism of their action. The structure of these complexes can be predicted by various computational methods. Choosing an appropriate method for modelling depends on the category of biomolecule that a protein interacts with and the availability of structural information about the protein and its interacting partner. We intend for the contents of this chapter to serve as a guide as to what software would be the most appropriate for the type of data at hand and the kind of 3D complex structure required. Particularly, we have dealt with protein-small molecule ligand, protein-peptide, protein-protein, and protein-nucleic acid interactions.Most, if not all, model building protocols perform some sampling and scoring. Typically, several alternate conformations and configurations of the interactors are sampled. Each such sample is then scored for optimization. To boost the confidence in these predicted models, their assessment using other independent scoring schemes besides the inbuilt/default ones would prove to be helpful. This chapter also lists such software and serves as a guide to gauge the fidelity of modelled structures of biomolecular complexes
Kinks Dynamics in One-Dimensional Coupled Map Lattices
We examine the problem of the dynamics of interfaces in a one-dimensional
space-time discrete dynamical system. Two different regimes are studied : the
non-propagating and the propagating one. In the first case, after proving the
existence of such solutions, we show how they can be described using Taylor
expansions. The second situation deals with the assumption of a travelling wave
to follow the kink propagation. Then a comparison with the corresponding
continuous model is proposed. We find that these methods are useful in simple
dynamical situations but their application to complex dynamical behaviour is
not yet understood.Comment: 17pages, LaTex,3 fig available on cpt.univ-mrs.fr directory
pub/preprints/94/dynamical-systems/94-P.307
General mechanism for amplitude death in coupled systems
We introduce a general mechanism for amplitude death in coupled
synchronizable dynamical systems. It is known that when two systems are coupled
directly, they can synchronize under suitable conditions. When an indirect
feedback coupling through an environment or an external system is introduced in
them, it is found to induce a tendency for anti-synchronization. We show that,
for sufficient strengths, these two competing effects can lead to amplitude
death. We provide a general stability analysis that gives the threshold values
for onset of amplitude death. We study in detail the nature of the transition
to death in several specific cases and find that the transitions can be of two
types - continuous and discontinuous. By choosing a variety of dynamics for
example, periodic, chaotic, hyper chaotic, and time-delay systems, we
illustrate that this mechanism is quite general and works for different types
of direct coupling, such as diffusive, replacement, and synaptic couplings and
for different damped dynamics of the environment.Comment: 12 pages, 17 figure
Effect of noise on coupled chaotic systems
Effect of noise in inducing order on various chaotically evolving systems is
reviewed, with special emphasis on systems consisting of coupled chaotic
elements. In many situations it is observed that the uncoupled elements when
driven by identical noise, show synchronization phenomena where chaotic
trajectories exponentially converge towards a single noisy trajectory,
independent of the initial conditions. In a random neural network, with
infinite range coupling, chaos is suppressed due to noise and the system
evolves towards a fixed point. Spatiotemporal stochastic resonance phenomenon
has been observed in a square array of coupled threshold devices where a
temporal characteristic of the system resonates at a given noise strength. In a
chaotically evolving coupled map lattice with logistic map as local dynamics
and driven by identical noise at each site, we report that the number of
structures (a structure is a group of neighbouring lattice sites for whom
values of the variable follow certain predefined pattern) follow a power-law
decay with the length of the structure. An interesting phenomenon, which we
call stochastic coherence, is also reported in which the abundance and
lifetimes of these structures show characteristic peaks at some intermediate
noise strength.Comment: 21 page LaTeX file for text, 5 Postscript files for figure