1,714 research outputs found
Coherent regimes of globally coupled dynamical systems
The paper presents a method by which the mean field dynamics of a population
of dynamical systems with parameter diversity and global coupling can be
described in terms of a few macroscopic degrees of freedom. The method applies
to populations of any size and functional form in the region of coherence. It
requires linear variation or a narrow distribution for the dispersed parameter.
Although being an approximation, the method allows us to quantitatively study
the collective regimes that arise as a result of diversity and coupling and to
interpret the transitions among these regimes as bifurcations of the effective
macroscopic degrees of freedom. To illustrate, the phenomenon of oscillator
death and the route to full locking are examined for chaotic oscillators with
time scale mismatch.Comment: 5 pages, 3 figure
The interaction of thin-film flow, bacterial swarming and cell differentiation in colonies of Serratia liquefaciens
The rate of expansion of bacterial colonies of S. liquefaciens is investigated in terms of a mathematical model that combines biological as well as hydrodynamic processes. The relative importance of cell differentiation and production of an extracellular wetting agent to bacterial swarming is explored using a continuum representation. The model incorporates aspects of thin film flow with variable suspension viscosity, wetting, and cell differentiation. Experimental evidence suggests that the bacterial colony is highly sensitive to its environment and that a variety of mechanisms are exploited in order to proliferate on a variety of surfaces. It is found that a combination of effects are required to reproduce the variation of bacterial colony motility over a large range of nutrient availability and medium hardness
Low-dimensional chaos in populations of strongly-coupled noisy maps
We characterize the macroscopic attractor of infinite populations of noisy
maps subjected to global and strong coupling by using an expansion in order
parameters. We show that for any noise amplitude there exists a large region of
strong coupling where the macroscopic dynamics exhibits low-dimensional chaos
embedded in a hierarchically-organized, folded, infinite-dimensional set. Both
this structure and the dynamics occuring on it are well-captured by our
expansion. In particular, even low-degree approximations allow to calculate
efficiently the first macroscopic Lyapunov exponents of the full system.Comment: 16 pages, 9 figures. Progress of Theoretical Physics, to appea
Cluster and group synchronization in delay-coupled networks
We investigate the stability of synchronized states in delay-coupled networks
where synchronization takes place in groups of different local dynamics or in
cluster states in networks with identical local dynamics. Using a master
stability approach, we find that the master stability function shows a discrete
rotational symmetry depending on the number of groups. The coupling matrices
that permit solutions on group or cluster synchronization manifolds show a very
similar symmetry in their eigenvalue spectrum, which helps to simplify the
evaluation of the master stability function. Our theory allows for the
characterization of stability of different patterns of synchronized dynamics in
networks with multiple delay times, multiple coupling functions, but also with
multiple kinds of local dynamics in the networks' nodes. We illustrate our
results by calculating stability in the example of delay-coupled semiconductor
lasers and in a model for neuronal spiking dynamics.Comment: 11 pages, 7 figure
Enhance synchronizability via age-based coupling
In this brief report, we study the synchronization of growing scale-free
networks. An asymmetrical age-based coupling method is proposed with only one
free parameter . Although the coupling matrix is asymmetric, our
coupling method could guarantee that all the eigenvalues are non-negative
reals. The eigneratio R will approach to 1 in the large limit of .Comment: 3 pages, 1 figur
Loss of coherence in dynamical networks: spatial chaos and chimera states
We discuss the breakdown of spatial coherence in networks of coupled
oscillators with nonlocal interaction. By systematically analyzing the
dependence of the spatio-temporal dynamics on the range and strength of
coupling, we uncover a dynamical bifurcation scenario for the
coherence-incoherence transition which starts with the appearance of narrow
layers of incoherence occupying eventually the whole space. Our findings for
coupled chaotic and periodic maps as well as for time-continuous R\"ossler
systems reveal that intermediate, partially coherent states represent
characteristic spatio-temporal patterns at the transition from coherence to
incoherence.Comment: 4 pages, 4 figure
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