12,124 research outputs found
Stochastic Synchronization of Genetic Oscillator Networks
The study of synchronization among genetic oscillators is essential for the
understanding of the rhythmic phenomena of living organisms at both molecular
and cellular levels. Genetic networks are intrinsically noisy due to natural
random intra- and inter-cellular fluctuations. Therefore, it is important to
study the effects of noise perturbation on the synchronous dynamics of genetic
oscillators. From the synthetic biology viewpoint, it is also important to
implement biological systems that minimizing the negative influence of the
perturbations. In this paper, based on systems biology approach, we provide a
general theoretical result on the synchronization of genetic oscillators with
stochastic perturbations. By exploiting the specific properties of many genetic
oscillator models, we provide an easy-verified sufficient condition for the
stochastic synchronization of coupled genetic oscillators, based on the Lur'e
system approach in control theory. A design principle for minimizing the
influence of noise is also presented. To demonstrate the effectiveness of our
theoretical results, a population of coupled repressillators is adopted as a
numerical example. In summary, we present an efficient theoretical method for
analyzing the synchronization of genetic oscillator networks, which is helpful
for understanding and testing the synchronization phenomena in biological
organisms. Besides, the results are actually applicable to general oscillator
networks.Comment: 14 pages, 4 figure
Synchronization processes in complex networks
We present an extended analysis, based on the dynamics towards
synchronization of a system of coupled oscillators, of the hierarchy of
communities in complex networks. In the synchronization process, different
structures corresponding to well defined communities of nodes appear in a
hierarchical way. The analysis also provides a useful connection between
synchronization dynamics, complex networks topology and spectral graph
analysis.Comment: 16 pages, 4 figures. To appear in Physica D "Special Issue on
dynamics on complex networks
Synchronization of Coupled Nonidentical Genetic Oscillators
The study on the collective dynamics of synchronization among genetic
oscillators is essential for the understanding of the rhythmic phenomena of
living organisms at both molecular and cellular levels. Genetic oscillators are
biochemical networks, which can generally be modelled as nonlinear dynamic
systems. We show in this paper that many genetic oscillators can be transformed
into Lur'e form by exploiting the special structure of biological systems. By
using control theory approach, we provide a theoretical method for analyzing
the synchronization of coupled nonidentical genetic oscillators. Sufficient
conditions for the synchronization as well as the estimation of the bound of
the synchronization error are also obtained. To demonstrate the effectiveness
of our theoretical results, a population of genetic oscillators based on the
Goodwin model are adopted as numerical examples.Comment: 16 pages, 3 figure
The development of generalized synchronization on complex networks
In this paper, we investigate the development of generalized synchronization
(GS) on typical complex networks, such as scale-free networks, small-world
networks, random networks and modular networks. By adopting the
auxiliary-system approach to networks, we show that GS can take place in
oscillator networks with both heterogeneous and homogeneous degree
distribution, regardless of whether the coupled chaotic oscillators are
identical or nonidentical. For coupled identical oscillators on networks, we
find that there exists a general bifurcation path from initial
non-synchronization to final global complete synchronization (CS) via GS as the
coupling strength is increased. For coupled nonidentical oscillators on
networks, we further reveal how network topology competes with the local
dynamics to dominate the development of GS on networks. Especially, we analyze
how different coupling strategies affect the development of GS on complex
networks. Our findings provide a further understanding for the occurrence and
development of collective behavior in complex networks.Comment: 10 pages, 13 figure
Synchronization reveals topological scales in complex networks
We study the relationship between topological scales and dynamic time scales
in complex networks. The analysis is based on the full dynamics towards
synchronization of a system of coupled oscillators. In the synchronization
process, modular structures corresponding to well defined communities of nodes
emerge in different time scales, ordered in a hierarchical way. The analysis
also provides a useful connection between synchronization dynamics, complex
networks topology and spectral graph analysis.Comment: 4 pages, 3 figure
Sufficient Conditions for Fast Switching Synchronization in Time Varying Network Topologies
In previous work, empirical evidence indicated that a time-varying network
could propagate sufficient information to allow synchronization of the
sometimes coupled oscillators, despite an instantaneously disconnected
topology. We prove here that if the network of oscillators synchronizes for the
static time-average of the topology, then the network will synchronize with the
time-varying topology if the time-average is achieved sufficiently fast. Fast
switching, fast on the time-scale of the coupled oscillators, overcomes the
descychnronizing decoherence suggested by disconnected instantaneous networks.
This result agrees in spirit with that of where empirical evidence suggested
that a moving averaged graph Laplacian could be used in the master-stability
function analysis. A new fast switching stability criterion here-in gives
sufficiency of a fast-switching network leading to synchronization. Although
this sufficient condition appears to be very conservative, it provides new
insights about the requirements for synchronization when the network topology
is time-varying. In particular, it can be shown that networks of oscillators
can synchronize even if at every point in time the frozen-time network topology
is insufficiently connected to achieve synchronization.Comment: Submitted to SIAD
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