3,346 research outputs found
Cluster synchronization of diffusively-coupled nonlinear systems: A contraction based approach
Finding the conditions that foster synchronization in networked oscillatory
systems is critical to understanding a wide range of biological and mechanical
systems. However, the conditions proved in the literature for synchronization
in nonlinear systems with linear coupling, such as has been used to model
neuronal networks, are in general not strict enough to accurately determine the
system behavior. We leverage contraction theory to derive new sufficient
conditions for cluster synchronization in terms of the network structure, for a
network where the intrinsic nonlinear dynamics of each node may differ. Our
result requires that network connections satisfy a cluster-input-equivalence
condition, and we explore the influence of this requirement on network
dynamics. For application to networks of nodes with neuronal spiking dynamics,
we show that our new sufficient condition is tighter than those found in
previous analyses which used nonsmooth Lyapunov functions. Improving the
analytical conditions for when cluster synchronization will occur based on
network configuration is a significant step toward facilitating understanding
and control of complex oscillatory systems
Global convergence of quorum-sensing networks
In many natural synchronization phenomena, communication between individual
elements occurs not directly, but rather through the environment. One of these
instances is bacterial quorum sensing, where bacteria release signaling
molecules in the environment which in turn are sensed and used for population
coordination. Extending this motivation to a general non- linear dynamical
system context, this paper analyzes synchronization phenomena in networks where
communication and coupling between nodes are mediated by shared dynamical quan-
tities, typically provided by the nodes' environment. Our model includes the
case when the dynamics of the shared variables themselves cannot be neglected
or indeed play a central part. Applications to examples from systems biology
illustrate the approach.Comment: Version 2: minor editions, added section on noise. Number of pages:
36
Symmetries, Stability, and Control in Nonlinear Systems and Networks
This paper discusses the interplay of symmetries and stability in the
analysis and control of nonlinear dynamical systems and networks. Specifically,
it combines standard results on symmetries and equivariance with recent
convergence analysis tools based on nonlinear contraction theory and virtual
dynamical systems. This synergy between structural properties (symmetries) and
convergence properties (contraction) is illustrated in the contexts of network
motifs arising e.g. in genetic networks, of invariance to environmental
symmetries, and of imposing different patterns of synchrony in a network.Comment: 16 pages, second versio
Endogenous driving and synchronization in cardiac and uterine virtual tissues: bifurcations and local coupling
Cardiac and uterine muscle cells and tissue can be either autorhythmic or excitable. These behaviours exchange stability at bifurcations produced by changes in parameters, which if spatially localized can produce an ectopic pacemaking focus. The effects of these parameters on cell dynamics have been identified and quantified using continuation algorithms and by numerical solutions of virtual cells. The ability of a compact pacemaker to drive the surrounding excitable tissues depends on both the size of the pacemaker and the strength of electrotonic coupling between cells within, between, and outside the pacemaking region.
We investigate an ectopic pacemaker surrounded by normal excitable tissue. Cell–cell coupling is simulated by the diffusion coefficient for voltage. For uniformly coupled tissues, the behaviour of the hybrid tissue can take one of the three forms: (i) the surrounding tissue electrotonically suppresses the pacemaker; (ii) depressed rate oscillatory activity in the pacemaker but no propagation; and (iii) pacemaker driving propagations into the excitable region.
However, real tissues are heterogeneous with spatial changes in cell–cell coupling. In the gravid uterus during early pregnancy, cells are weakly coupled, with the cell–cell coupling increasing during late pregnancy, allowing synchronous contractions during labour. These effects are investigated for a caricature uterine tissue by allowing both excitability and diffusion coefficient to vary stochastically with space, and for cardiac tissues by spatial gradients in the diffusion coefficient
Control of coupled oscillator networks with application to microgrid technologies
The control of complex systems and network-coupled dynamical systems is a
topic of vital theoretical importance in mathematics and physics with a wide
range of applications in engineering and various other sciences. Motivated by
recent research into smart grid technologies we study here control of
synchronization and consider the important case of networks of coupled phase
oscillators with nonlinear interactions--a paradigmatic example that has guided
our understanding of self-organization for decades. We develop a method for
control based on identifying and stabilizing problematic oscillators, resulting
in a stable spectrum of eigenvalues, and in turn a linearly stable synchronized
state. Interestingly, the amount of control, i.e., number of oscillators,
required to stabilize the network is primarily dictated by the coupling
strength, dynamical heterogeneity, and mean degree of the network, and depends
little on the structural heterogeneity of the network itself
High performance computing of explicit schemes for electrofusion jointing process based on message-passing paradigm
The research focused on heterogeneous cluster workstations comprising of a number of CPUs in single and shared architecture platform. The problem statements under consideration involved one dimensional parabolic equations. The thermal process of electrofusion jointing was also discussed. Numerical schemes of explicit type such as AGE, Brian, and Charlies Methods were employed. The parallelization of these methods were based on the domain decomposition technique. Some parallel performance measurement for these methods were also addressed. Temperature profile of the one dimensional radial model of the electrofusion process were also given
Limits and dynamics of randomly connected neuronal networks
Networks of the brain are composed of a very large number of neurons
connected through a random graph and interacting after random delays that both
depend on the anatomical distance between cells. In order to comprehend the
role of these random architectures on the dynamics of such networks, we analyze
the mesoscopic and macroscopic limits of networks with random correlated
connectivity weights and delays. We address both averaged and quenched limits,
and show propagation of chaos and convergence to a complex integral
McKean-Vlasov equations with distributed delays. We then instantiate a
completely solvable model illustrating the role of such random architectures in
the emerging macroscopic activity. We particularly focus on the role of
connectivity levels in the emergence of periodic solutions
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