477 research outputs found
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
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
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
The emergence of coherence in complex networks of heterogeneous dynamical systems
We present a general theory for the onset of coherence in collections of
heterogeneous maps interacting via a complex connection network. Our method
allows the dynamics of the individual uncoupled systems to be either chaotic or
periodic, and applies generally to networks for which the number of connections
per node is large. We find that the critical coupling strength at which a
transition to synchrony takes place depends separately on the dynamics of the
individual uncoupled systems and on the largest eigenvalue of the adjacency
matrix of the coupling network. Our theory directly generalizes the Kuramoto
model of equal strength, all-to-all coupled phase oscillators to the case of
oscillators with more realistic dynamics coupled via a large heterogeneous
network.Comment: 4 pages, 1 figure. Published versio
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
Quantitative effects of medium hardness and nutrient availability on the swarming motility of <i>Serratia liquefaciens</i>
We report the first controlled measurements of expansion rates for swarming colonies of Serratia liquefaciens under different growth conditions, combined with qualitative observations of the organization of the colony into regions of differentiated cell types. Significantly, the results reveal that swarming colonies of S. liquefaciens can have an increasing expansion rate with time. We compare and contrast the expansion rate results with predictions from a recent mathematical model which coupled key hydrodynamical and biological mechanisms. Furthermore, we investigate whether the swarming colonies grow according to a power law or exponentially (for large times), as suggested by recent theoretical results
The onset of synchronization in large networks of coupled oscillators
We study the transition from incoherence to coherence in large networks of
coupled phase oscillators. We present various approximations that describe the
behavior of an appropriately defined order parameter past the transition, and
generalize recent results for the critical coupling strength. We find that,
under appropriate conditions, the coupling strength at which the transition
occurs is determined by the largest eigenvalue of the adjacency matrix. We show
how, with an additional assumption, a mean field approximation recently
proposed is recovered from our results. We test our theory with numerical
simulations, and find that it describes the transition when our assumptions are
satisfied. We find that our theory describes the transition well in situations
in which the mean field approximation fails. We study the finite size effects
caused by nodes with small degree and find that they cause the critical
coupling strength to increase.Comment: To appear in PRE; Added an Appendix, a reference, modified two
figures and improved the discussion of the range of validity of perturbative
approache
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