2,275 research outputs found
Complex and unexpected dynamics in simple genetic regulatory networks
Peer reviewedPublisher PD
Synchronization in complex networks
Synchronization processes in populations of locally interacting elements are
in the focus of intense research in physical, biological, chemical,
technological and social systems. The many efforts devoted to understand
synchronization phenomena in natural systems take now advantage of the recent
theory of complex networks. In this review, we report the advances in the
comprehension of synchronization phenomena when oscillating elements are
constrained to interact in a complex network topology. We also overview the new
emergent features coming out from the interplay between the structure and the
function of the underlying pattern of connections. Extensive numerical work as
well as analytical approaches to the problem are presented. Finally, we review
several applications of synchronization in complex networks to different
disciplines: biological systems and neuroscience, engineering and computer
science, and economy and social sciences.Comment: Final version published in Physics Reports. More information
available at http://synchronets.googlepages.com
Electronically--implemented coupled logistic maps
The logistic map is a paradigmatic dynamical system originally conceived to
model the discrete-time demographic growth of a population, which shockingly,
shows that discrete chaos can emerge from trivial low-dimensional non-linear
dynamics. In this work, we design and characterize a simple, low-cost,
easy-to-handle, electronic implementation of the logistic map. In particular,
our implementation allows for straightforward circuit-modifications to behave
as different one-dimensional discrete-time systems. Also, we design a coupling
block in order to address the behavior of two coupled maps, although, our
design is unrestricted to the discrete-time system implementation and it can be
generalized to handle coupling between many dynamical systems, as in a complex
system. Our findings show that the isolated and coupled maps' behavior has a
remarkable agreement between the experiments and the simulations, even when
fine-tuning the parameters with a resolution of . We support
these conclusions by comparing the Lyapunov exponents, periodicity of the
orbits, and phase portraits of the numerical and experimental data for a wide
range of coupling strengths and map's parameters.Comment: 8 pages, 10 figure
Stability and chaos in coupled two-dimensional maps on Gene Regulatory Network of bacterium E.Coli
The collective dynamics of coupled two-dimensional chaotic maps on complex
networks is known to exhibit a rich variety of emergent properties which
crucially depend on the underlying network topology. We investigate the
collective motion of Chirikov standard maps interacting with time delay through
directed links of Gene Regulatory Network of bacterium Escherichia Coli.
Departures from strongly chaotic behavior of the isolated maps are studied in
relation to different coupling forms and strengths. At smaller coupling
intensities the network induces stable and coherent emergent dynamics. The
unstable behavior appearing with increase of coupling strength remains confined
within a connected sub-network. For the appropriate coupling, network exhibits
statistically robust self-organized dynamics in a weakly chaotic regime
Geometrical Properties of Coupled Oscillators at Synchronization
We study the synchronization of nearest neighbors coupled oscillators in
a ring. We derive an analytic form for the phase difference among neighboring
oscillators which shows the dependency on the periodic boundary conditions. At
synchronization, we find two distinct quantities which characterize four of the
oscillators, two pairs of nearest neighbors, which are at the border of the
clusters before total synchronization occurs. These oscillators are responsible
for the saddle node bifurcation, of which only two of them have a phase-lock of
phase difference equals /2. Using these properties we build a
technique based on geometric properties and numerical observations to arrive to
an exact analytic expression for the coupling strength at full synchronization
and determine the two oscillators that have a phase-lock condition of
/2.Comment: accepted for publication in "Communications in Nonlinear Science and
Numerical Simulations
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