342 research outputs found
Transmitting a signal by amplitude modulation in a chaotic network
We discuss the ability of a network with non linear relays and chaotic
dynamics to transmit signals, on the basis of a linear response theory
developed by Ruelle \cite{Ruelle} for dissipative systems. We show in
particular how the dynamics interfere with the graph topology to produce an
effective transmission network, whose topology depends on the signal, and
cannot be directly read on the ``wired'' network. This leads one to reconsider
notions such as ``hubs''. Then, we show examples where, with a suitable choice
of the carrier frequency (resonance), one can transmit a signal from a node to
another one by amplitude modulation, \textit{in spite of chaos}. Also, we give
an example where a signal, transmitted to any node via different paths, can
only be recovered by a couple of \textit{specific} nodes. This opens the
possibility for encoding data in a way such that the recovery of the signal
requires the knowledge of the carrier frequency \textit{and} can be performed
only at some specific node.Comment: 19 pages, 13 figures, submitted (03-03-2005
A three-scale model of spatio-temporal bursting
© 2016 Society for Industrial and Applied Mathematics. We study spatio-temporal bursting in a three-scale reaction diffusion equation organized by the winged cusp singularity. For large time-scale separation the model exhibits traveling bursts, whereas for large space-scale separation the model exhibits standing bursts. Both behaviors exhibit a common singular skeleton, whose geometry is fully determined by persistent bifurcation diagrams of the winged cusp. The modulation of spatio-temporal bursting in such a model naturally translates into paths in the universal unfolding of the winged cusp.The research leading to these results has received funding from the European Research Council under the Advanced ERC Grant Agreement Switchlet 670645 and from DGAPA-Universidad Nacional Aut onoma de Mexico under the PAPIIT Grant IA105816
Stable resonances and signal propagation in a chaotic network of coupled units
We apply the linear response theory developed in \cite{Ruelle} to analyze how
a periodic signal of weak amplitude, superimposed upon a chaotic background, is
transmitted in a network of non linearly interacting units. We numerically
compute the complex susceptibility and show the existence of specific poles
(stable resonances) corresponding to the response to perturbations transverse
to the attractor. Contrary to the poles of correlation functions they depend on
the pair emitting/receiving units. This dynamic differentiation, induced by non
linearities, exhibits the different ability that units have to transmit a
signal in this network.Comment: 10 pages, 3 figures, to appear in Phys. rev.
An operator-theoretic approach to differential positivity
Differentially positive systems are systems whose linearization along
trajectories is positive. Under mild assumptions, their solutions
asymptotically converge to a one-dimensional attractor, which must be a limit
cycle in the absence of fixed points in the limit set. In this paper, we
investigate the general connections between the (geometric) properties of
differentially positive systems and the (spectral) properties of the Koopman
operator. In particular, we obtain converse results for differential
positivity, showing for instance that any hyperbolic limit cycle is
differentially positive in its basin of attraction. We also provide the
construction of a contracting cone field.A. Mauroy holds a BELSPO Return Grant and F. Forni holds a FNRS fellowship. This paper presents research results of the Belgian Network DYSCO, funded by the Interuniversity Attraction Poles Programme initiated by the Belgian Science Policy Office.This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/CDC.2015.740332
Dominance margins for feedback systems
The paper introduces notions of robustness margins geared towards the
analysis and design of systems that switch and oscillate. While such phenomena
are ubiquitous in nature and in engineering, a theory of robustness for
behaviors away from equilibria is lacking. The proposed framework addresses
this need in the framework of p-dominance theory, which aims at generalizing
stability theory for the analysis of systems with low-dimensional attractors.
Dominance margins are introduced as natural generalisations of stability
margins in the context of p-dominance analysis. In analogy with stability
margins, dominance margins are shown to admit simple interpretations in terms
of familiar frequency domain tools and to provide quantitative measures of
robustness for multistable and oscillatory behaviors in Lure systems. The
theory is illustrated by means of an elementary mechanical example.The research leading to these results has received funding from the European Research Council under the Advanced ERC Grant Agreement Switchlet n. 670645
Control Across Scales by Positive and Negative Feedback
Feedback is a key element of regulation, as it shapes the sensitivity of a process to its environment. Positive feedback upregulates, and negative feedback downregulates. Many regulatory processes involve a mixture of both, whether in nature or in engineering. This article revisits the mixed-feedback paradigm, with the aim of investigating control across scales. We propose that mixed feedback regulates excitability and that excitability plays a central role in multiscale neuronal signaling. We analyze this role in a multiscale network architecture inspired by neurophysiology. The nodal behavior defines a mesoscale that connects actuation at the microscale to regulation at the macroscale. We show that mixed-feedback nodal control provides regulatory principles at the network scale, with a nodal resolution. In this sense, the mixed-feedback paradigm is a control principle across scales. </jats:p
Dominance analysis of linear complementarity systems
The paper extends the concepts of dominance and p-dissipativity to the
non-smooth family of linear complementarity systems. Dominance generalizes
incremental stability whereas p-dissipativity generalizes incremental
passivity. The generalization aims at an interconnection theory for the design
and analysis of switching and oscillatory systems. The approach is illustrated
by a detailed study of classical electrical circuits that switch and oscillate
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