17 research outputs found
Chimera states: The Existence Criteria Revisited
Chimera states, representing a spontaneous break-up of a population of
identical oscillators that are identically coupled, into sub-populations
displaying synchronized and desynchronized behavior, have traditionally been
found to exist in weakly coupled systems and with some form of nonlocal
coupling between the oscillators. Here we show that neither the weak-coupling
approximation nor nonlocal coupling are essential conditions for their
existence. We obtain for the first time amplitude-mediated chimera states in a
system of globally coupled complex Ginzburg-Landau oscillators. We delineate
the dynamical origins for the formation of such states from a bifurcation
analysis of a reduced model equation and also discuss the practical
implications of our discovery of this broader class of chimera states.Comment: 5 pages, 5 figure
Stability of networks of delay-coupled delay oscillators
Dynamical networks with time delays can pose a considerable challenge for
mathematical analysis. Here, we extend the approach of generalized modeling to
investigate the stability of large networks of delay-coupled delay oscillators.
When the local dynamical stability of the network is plotted as a function of
the two delays then a pattern of tongues is revealed. Exploiting a link between
structure and dynamics, we identify conditions under which perturbations of the
topology have a strong impact on the stability. If these critical regions are
avoided the local stability of large random networks can be well approximated
analytically
Synchronous solutions and their stability in nonlocally coupled phase oscillators with propagation delays
We study the existence and stability of synchronous solutions in a continuum
field of non-locally coupled identical phase oscillators with
distance-dependent propagation delays. We present a comprehensive stability
diagram in the parameter space of the system. From the numerical results a
heuristic synchronization condition is suggested, and an analytic relation for
the marginal stability curve is obtained. We also provide an expression in the
form of a scaling relation that closely follows the marginal stability curve
over the complete range of the non-locality parameter.Comment: accepted in Phys. Rev. E (2010
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.
Clustered chimera states in delay coupled oscillator systems
We investigate "chimera" states in a ring of identical phase oscillators
coupled in a time-delayed and spatially non-local fashion. We find novel
"clustered chimera" states that have spatially distributed phase coherence
separated by incoherence with adjacent coherent regions in anti-phase. The
existence of such time-delay induced phase clustering is further supported
through solutions of a generalized functional self-consistency equation of the
mean field. Our results highlight an additional mechanism for cluster formation
that may find wider practical applications
Excitable Dynamics in the Presence of Time Delay
The spiking properties of a subcritical Hopf oscillator with a time delayed
nonlinear feedback is investigated. Finite time delay is found to significantly
affect both the statistics and the fine structure of the spiking behavior.
These dynamical changes are explained in terms of the fundamental modifications
occurring in the bifurcation scenario of the system. Our mathematical model can
find useful applications in understanding the dynamical behaviour of various
real life excitable systems where propagation delay effects are ubiquitous.Comment: 10 pages including 7 figure
Multiple novel prostate cancer susceptibility signals identified by fine-mapping of known risk loci among Europeans
Genome-wide association studies (GWAS) have identified numerous common prostate cancer (PrCa) susceptibility loci. We have
fine-mapped 64 GWAS regions known at the conclusion of the iCOGS study using large-scale genotyping and imputation in
25 723 PrCa cases and 26 274 controls of European ancestry. We detected evidence for multiple independent signals at 16
regions, 12 of which contained additional newly identified significant associations. A single signal comprising a spectrum of
correlated variation was observed at 39 regions; 35 of which are now described by a novel more significantly associated lead SNP,
while the originally reported variant remained as the lead SNP only in 4 regions. We also confirmed two association signals in
Europeans that had been previously reported only in East-Asian GWAS. Based on statistical evidence and linkage disequilibrium
(LD) structure, we have curated and narrowed down the list of the most likely candidate causal variants for each region.
Functional annotation using data from ENCODE filtered for PrCa cell lines and eQTL analysis demonstrated significant
enrichment for overlap with bio-features within this set. By incorporating the novel risk variants identified here alongside the
refined data for existing association signals, we estimate that these loci now explain ∼38.9% of the familial relative risk of PrCa,
an 8.9% improvement over the previously reported GWAS tag SNPs. This suggests that a significant fraction of the heritability of
PrCa may have been hidden during the discovery phase of GWAS, in particular due to the presence of multiple independent
signals within the same regio