84 research outputs found
Chimera states in pulse coupled neural networks: the influence of dilution and noise
We analyse the possible dynamical states emerging for two symmetrically pulse
coupled populations of leaky integrate-and-fire neurons. In particular, we
observe broken symmetry states in this set-up: namely, breathing chimeras,
where one population is fully synchronized and the other is in a state of
partial synchronization (PS) as well as generalized chimera states, where both
populations are in PS, but with different levels of synchronization. Symmetric
macroscopic states are also present, ranging from quasi-periodic motions, to
collective chaos, from splay states to population anti-phase partial
synchronization. We then investigate the influence disorder, random link
removal or noise, on the dynamics of collective solutions in this model. As a
result, we observe that broken symmetry chimera-like states, with both
populations partially synchronized, persist up to 80 \% of broken links and up
to noise amplitudes 8 \% of threshold-reset distance. Furthermore, the
introduction of disorder on symmetric chaotic state has a constructive effect,
namely to induce the emergence of chimera-like states at intermediate dilution
or noise level.Comment: 15 pages, 7 figure, contribution for the Workshop "Nonlinear Dynamics
in Computational Neuroscience: from Physics and Biology to ICT" held in Turin
(Italy) in September 201
Effect of disorder and noise in shaping the dynamics of power grids
The aim of this paper is to investigate complex dynamic networks which can
model high-voltage power grids with renewable, fluctuating energy sources. For
this purpose we use the Kuramoto model with inertia to model the network of
power plants and consumers. In particular, we analyse the synchronization
transition of networks of phase oscillators with inertia (rotators) whose
natural frequencies are bimodally distributed, corresponding to the
distribution of generator and consumer power. First, we start from globally
coupled networks whose links are successively diluted, resulting in a random
Erd\"os-Renyi network. We focus on the changes in the hysteretic loop while
varying inertial mass and dilution. Second, we implement Gaussian white noise
describing the randomly fluctuating input power, and investigate its role in
shaping the dynamics. Finally, we briefly discuss power grid networks under the
impact of both topological disorder and external noise sources.Comment: 7 pages, 6 figure
Linear stability in networks of pulse-coupled neurons
In a first step towards the comprehension of neural activity, one should
focus on the stability of the various dynamical states. Even the
characterization of idealized regimes, such as a perfectly periodic spiking
activity, reveals unexpected difficulties. In this paper we discuss a general
approach to linear stability of pulse-coupled neural networks for generic
phase-response curves and post-synaptic response functions. In particular, we
present: (i) a mean-field approach developed under the hypothesis of an
infinite network and small synaptic conductances; (ii) a "microscopic" approach
which applies to finite but large networks. As a result, we find that no matter
how large is a neural network, its response to most of the perturbations
depends on the system size. There exists, however, also a second class of
perturbations, whose evolution typically covers an increasingly wide range of
time scales. The analysis of perfectly regular, asynchronous, states reveals
that their stability depends crucially on the smoothness of both the
phase-response curve and the transmitted post-synaptic pulse. The general
validity of this scenarion is confirmed by numerical simulations of systems
that are not amenable to a perturbative approach.Comment: 13 pages, 7 figures, submitted to Frontiers in Computational
Neuroscienc
Stability of the splay state in networks of pulse-coupled neurons
We analytically investigate the stability of {\it splay states} in networks
of pulse-coupled phase-like models of neurons. By developing a perturbative
technique, we find that, in the limit of large , the Floquet spectrum scales
as for generic discontinuous velocity fields. Moreover, the stability
of the so-called short-wavelength component is determined by the sign of the
jump at the discontinuity. Altogether, the form of the spectrum depends on the
pulse shape but is independent of the velocity field.Comment: 22 pages, no figures and 120 equation
Collective behavior of oscillating electric dipoles
The present work reports about the dynamics of a collection of randomly
distributed, and randomly oriented, oscillators in 3D space, coupled by an
interaction potential falling as , where r stands for the inter-particle
distance. This model schematically represents a collection of identical
biomolecules, coherently vibrating at some common frequency, coupled with a
potential stemming from the electrodynamic interaction between
oscillating dipoles. The oscillating dipole moment of each molecule being a
direct consequence of its coherent (collective) vibration. By changing the
average distance among the molecules, neat and substantial changes in the power
spectrum of the time variation of a collective observable are found. As the
average intermolecular distance can be varied by changing the concentration of
the solvated molecules, and as the collective variable investigated is
proportional to the projection of the total dipole moment of the model
biomolecules on a coordinate plane, we have found a prospective experimental
strategy of spectroscopic kind to check whether the mentioned intermolecular
electrodynamic interactions can be strong enough to be detectable, and thus to
be of possible relevance to biology.Comment: 20 pages, 4 figure
Qualitative stability and synchronicity analysis of power network models in port-Hamiltonian form
This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Chaos 28, 101102 (2018) and may be found at https://doi.org/10.1063/1.5054850.In view of highly decentralized and diversified power generation concepts, in particular with renewable energies, the analysis and control of the stability and the synchronization of power networks is an important topic that requires different levels of modeling detail for different tasks. A frequently used qualitative approach relies on simplified nonlinear network models like the Kuramoto model with inertia. The usual formulation in the form of a system of coupled ordinary differential equations is not always adequate. We present a new energy-based formulation of the Kuramoto model with inertia as a polynomial port-Hamiltonian system of differential-algebraic equations, with a quadratic Hamiltonian function including a generalized order parameter. This leads to a robust representation of the system with respect to disturbances: it encodes the underlying physics, such as the dissipation inequality or the deviation from synchronicity, directly in the structure of the equations, and it explicitly displays all possible constraints and allows for robust simulation methods. The model is immersed into a system of model hierarchies that will be helpful for applying adaptive simulations in future works. We illustrate the advantages of the modified modeling approach with analytics and numerical results.
To reach the goal of temperature reduction to limit the climate change, as stipulated at the Paris Conference in 2015, it is necessary to integrate renewable energy sources into the existing power networks. Wind and solar power are the most promising ones, but the integration into the electric power grid remains an enormous challenge due to their variability that requires storage facilities, back-up plants, and accurate control processing. The current approach to describe the dynamics of power grids in terms of simplified nonlinear models, like the Kuramoto model with inertia, may not be appropriate when different control and optimization tasks are needed to be addressed. Under this aspect, we present a new energy-based formulation of the Kuramoto model with inertia that allows for an easy extension if further effects have to be included and higher fidelity is required for qualitative analysis. We illustrate the new modeling approach with analytic results and numerical simulations carried out for a semi-realistic model of the Italian grid and indicate how this approach can be generalized to models of finer granularity.DFG, 163436311, SFB 910: Kontrolle selbstorganisierender nichtlinearer Systeme: Theoretische Methoden und Anwendungskonzept
Chimera states in pulse coupled neural networks: The influence of dilution and noise
We analyse the possible dynamical states emerging for two symmetrically
pulse coupled populations of leaky integrate-and-fire neurons. In particular,
we observe broken symmetry states in this set-up: namely, breathing chimeras,
where one population is fully synchronized and the other is in a state of
partial synchronization (PS) as well as generalized chimera states, where
both populations are in PS, but with different levels of synchronization.
Symmetric macroscopic states are also present, ranging from quasi-periodic
motions, to collective chaos, from splay states to population anti-phase
partial synchronization. We then investigate the influence disorder, random
link removal or noise, on the dynamics of collective solutions in this model.
As a result, we observe that broken symmetry chimeralike states, with both
populations partially synchronized, persist up to 80% of broken links and up
to noise ï¸ amplitude
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