4,393 research outputs found
Geometric Analysis of Synchronization in Neuronal Networks with Global Inhibition and Coupling Delays
We study synaptically coupled neuronal networks to identify the role of
coupling delays in network's synchronized behaviors. We consider a network of
excitable, relaxation oscillator neurons where two distinct populations, one
excitatory and one inhibitory, are coupled and interact with each other. The
excitatory population is uncoupled, while the inhibitory population is tightly
coupled. A geometric singular perturbation analysis yields existence and
stability conditions for synchronization states under different firing patterns
between the two populations, along with formulas for the periods of such
synchronous solutions. Our results demonstrate that the presence of coupling
delays in the network promotes synchronization. Numerical simulations are
conducted to supplement and validate analytical results. We show the results
carry over to a model for spindle sleep rhythms in thalamocortical networks,
one of the biological systems which motivated our study. The analysis helps to
explain how coupling delays in either excitatory or inhibitory synapses
contribute to producing synchronized rhythms.Comment: 43 pages, 12 figure
Dynamics of FitzHugh-Nagumo excitable systems with delayed coupling
Small lattices of nearest neighbor coupled excitable FitzHugh-Nagumo
systems, with time-delayed coupling are studied, and compared with systems of
FitzHugh-Nagumo oscillators with the same delayed coupling. Bifurcations of
equilibria in N=2 case are studied analytically, and it is then numerically
confirmed that the same bifurcations are relevant for the dynamics in the case
. Bifurcations found include inverse and direct Hopf and fold limit cycle
bifurcations. Typical dynamics for different small time-lags and coupling
intensities could be excitable with a single globally stable equilibrium,
asymptotic oscillatory with symmetric limit cycle, bi-stable with stable
equilibrium and a symmetric limit cycle, and again coherent oscillatory but
non-symmetric and phase-shifted. For an intermediate range of time-lags inverse
sub-critical Hopf and fold limit cycle bifurcations lead to the phenomenon of
oscillator death. The phenomenon does not occur in the case of FitzHugh-Nagumo
oscillators with the same type of coupling.Comment: accepted by Phys.Rev.
Phaselocked patterns and amplitude death in a ring of delay coupled limit cycle oscillators
We study the existence and stability of phaselocked patterns and amplitude
death states in a closed chain of delay coupled identical limit cycle
oscillators that are near a supercritical Hopf bifurcation. The coupling is
limited to nearest neighbors and is linear. We analyze a model set of discrete
dynamical equations using the method of plane waves. The resultant dispersion
relation, which is valid for any arbitrary number of oscillators, displays
important differences from similar relations obtained from continuum models. We
discuss the general characteristics of the equilibrium states including their
dependencies on various system parameters. We next carry out a detailed linear
stability investigation of these states in order to delineate their actual
existence regions and to determine their parametric dependence on time delay.
Time delay is found to expand the range of possible phaselocked patterns and to
contribute favorably toward their stability. The amplitude death state is
studied in the parameter space of time delay and coupling strength. It is shown
that death island regions can exist for any number of oscillators N in the
presence of finite time delay. A particularly interesting result is that the
size of an island is independent of N when N is even but is a decreasing
function of N when N is odd.Comment: 23 pages, 12 figures (3 of the figures in PNG format, separately from
TeX); minor additions; typos correcte
Nonlinearity of local dynamics promotes multi-chimeras
Chimera states are complex spatio-temporal patterns in which domains of
synchronous and asynchronous dynamics coexist in coupled systems of
oscillators. We examine how the character of the individual elements influences
chimera states by studying networks of nonlocally coupled Van der Pol
oscillators. Varying the bifurcation parameter of the Van der Pol system, we
can interpolate between regular sinusoidal and strongly nonlinear relaxation
oscillations, and demonstrate that more pronounced nonlinearity induces
multi-chimera states with multiple incoherent domains. We show that the
stability regimes for multi-chimera states and the mean phase velocity profiles
of the oscillators change significantly as the nonlinearity becomes stronger.
Furthermore, we reveal the influence of time delay on chimera patterns
Restoration of rhythmicity in diffusively coupled dynamical networks
We acknowledge financial support from the National Natural Science Foundation of China (No. 11202082, No. 61203235, No. 11371367 and No. 11271290), the Fundamental Research Funds for the Central Universities of China under Grant No. 2014QT005, IRTG1740(DFG-FAPESP), and SERB-DST Fast Track scheme for young scientist under Grant No. ST/FTP/PS-119/2013, NSF CHE-0955555 and Grant No. 229171/2013-3 (CNPq).Peer reviewedPublisher PD
Synchronization of stochastic genetic oscillator networks with time delays and Markovian jumping parameters
The official published version of the article can be found at the link below.Genetic oscillator networks (GONs) are inherently coupled complex systems where the nodes indicate the biochemicals and the couplings represent the biochemical interactions. This paper is concerned with the synchronization problem of a general class of stochastic GONs with time delays and Markovian jumping parameters, where the GONs are subject to both the stochastic disturbances and the Markovian parameter switching. The regulatory functions of the addressed GONs are described by the sector-like nonlinear functions. By applying up-to-date âdelay-fractioningâ approach for achieving delay-dependent conditions, we construct novel matrix functional to derive the synchronization criteria for the GONs that are formulated in terms of linear matrix inequalities (LMIs). Note that LMIs are easily solvable by the Matlab toolbox. A simulation example is used to demonstrate the synchronization phenomena within biological organisms of a given GON and therefore shows the applicability of the obtained results.This work was supported in part by the Biotechnology and Biological Sciences Research Council (BBSRC) of the UK under Grants BB/C506264/1 and 100/EGM17735, the Royal Society of the UK, the National Natural Science Foundation of China under Grant 60804028, the Teaching and Research Fund for Excellent Young Teachers at Southeast University of China, the International Science and Technology Cooperation Project of China under Grant 2009DFA32050, and the Alexander von Humboldt Foundation of Germany
Synchronization in the presence of distributed delays
We study systems of identical coupled oscillators introducing a distribution
of delay times in the coupling. For arbitrary network topologies, we show that
the frequency and stability of the fully synchronized states depend only on the
mean of the delay distribution. However, synchronization dynamics is sensitive
to the shape of the distribution. In the presence of coupling delays, the
synchronization rate can be maximal for a specific value of the coupling
strength.Comment: 6 pages, 3 figure
Pulse-coupled relaxation oscillators: from biological synchronization to Self-Organized Criticality
It is shown that globally-coupled oscillators with pulse interaction can
synchronize under broader conditions than widely believed from a theorem of
Mirollo \& Strogatz \cite{MirolloII}. This behavior is stable against frozen
disorder. Beside the relevance to biology, it is argued that synchronization in
relaxation oscillator models is related to Self-Organized Criticality in
Stick-Slip-like models.Comment: 4 pages, RevTeX, 1 uuencoded postscript figure in separate file,
accepted for publication in Phys. Rev. Lett
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