2,640 research outputs found
Excitability in autonomous Boolean networks
We demonstrate theoretically and experimentally that excitable systems can be
built with autonomous Boolean networks. Their experimental implementation is
realized with asynchronous logic gates on a reconfigurabe chip. When these
excitable systems are assembled into time-delay networks, their dynamics
display nanosecond time-scale spike synchronization patterns that are
controllable in period and phase.Comment: 6 pages, 5 figures, accepted in Europhysics Letters
(epljournal.edpsciences.org
Control of coherence resonance by self-induced stochastic resonance in a multiplex neural network
We consider a two-layer multiplex network of diffusively coupled
FitzHugh-Nagumo (FHN) neurons in the excitable regime. It is shown, in contrast
to SISR in a single isolated FHN neuron, that the maximum noise amplitude at
which SISR occurs in the network of coupled FHN neurons is controllable,
especially in the regime of strong coupling forces and long time delays. In
order to use SISR in the first layer of the multiplex network to control CR in
the second layer, we first choose the control parameters of the second layer in
isolation such that in one case CR is poor and in another case, non-existent.
It is then shown that a pronounced SISR cannot only significantly improve a
poor CR, but can also induce a pronounced CR, which was non-existent in the
isolated second layer. In contrast to strong intra-layer coupling forces,
strong inter-layer coupling forces are found to enhance CR. While long
inter-layer time delays just as long intra-layer time delays, deteriorates CR.
Most importantly, we find that in a strong inter-layer coupling regime, SISR in
the first layer performs better than CR in enhancing CR in the second layer.
But in a weak inter-layer coupling regime, CR in the first layer performs
better than SISR in enhancing CR in the second layer. Our results could find
novel applications in noisy neural network dynamics and engineering
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.
Coherence resonance in a network of FitzHugh-Nagumo systems: interplay of noise, time-delay and topology
We systematically investigate the phenomena of coherence resonance in
time-delay coupled networks of FitzHugh-Nagumo elements in the excitable
regime. Using numerical simulations, we examine the interplay of noise,
time-delayed coupling and network topology in the generation of coherence
resonance. In the deterministic case, we show that the delay-induced dynamics
is independent of the number of nearest neighbors and the system size. In the
presence of noise, we demonstrate the possibility of controlling coherence
resonance by varying the time-delay and the number of nearest neighbors. For a
locally coupled ring, we show that the time-delay weakens coherence resonance.
For nonlocal coupling with appropriate time-delays, both enhancement and
weakening of coherence resonance are possible
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
Time-delayed feedback in neurosystems
The influence of time delay in systems of two coupled excitable neurons is
studied in the framework of the FitzHugh-Nagumo model. Time-delay can occur in
the coupling between neurons or in a self-feedback loop. The stochastic
synchronization of instantaneously coupled neurons under the influence of white
noise can be deliberately controlled by local time-delayed feedback. By
appropriate choice of the delay time synchronization can be either enhanced or
suppressed. In delay-coupled neurons, antiphase oscillations can be induced for
sufficiently large delay and coupling strength. The additional application of
time-delayed self-feedback leads to complex scenarios of synchronized in-phase
or antiphase oscillations, bursting patterns, or amplitude death.Comment: 13 pages, 13 figure
Synchronization of coupled neural oscillators with heterogeneous delays
We investigate the effects of heterogeneous delays in the coupling of two
excitable neural systems. Depending upon the coupling strengths and the time
delays in the mutual and self-coupling, the compound system exhibits different
types of synchronized oscillations of variable period. We analyze this
synchronization based on the interplay of the different time delays and support
the numerical results by analytical findings. In addition, we elaborate on
bursting-like dynamics with two competing timescales on the basis of the
autocorrelation function.Comment: 18 pages, 14 figure
Mean field approximation of two coupled populations of excitable units
The analysis on stability and bifurcations in the macroscopic dynamics
exhibited by the system of two coupled large populations comprised of
stochastic excitable units each is performed by studying an approximate system,
obtained by replacing each population with the corresponding mean-field model.
In the exact system, one has the units within an ensemble communicating via the
time-delayed linear couplings, whereas the inter-ensemble terms involve the
nonlinear time-delayed interaction mediated by the appropriate global
variables. The aim is to demonstrate that the bifurcations affecting the
stability of the stationary state of the original system, governed by a set of
4N stochastic delay-differential equations for the microscopic dynamics, can
accurately be reproduced by a flow containing just four deterministic
delay-differential equations which describe the evolution of the mean-field
based variables. In particular, the considered issues include determining the
parameter domains where the stationary state is stable, the scenarios for the
onset and the time-delay induced suppression of the collective mode, as well as
the parameter domains admitting bistability between the equilibrium and the
oscillatory state. We show how analytically tractable bifurcations occurring in
the approximate model can be used to identify the characteristic mechanisms by
which the stationary state is destabilized under different system
configurations, like those with symmetrical or asymmetrical inter-population
couplings.Comment: 5 figure
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