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

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.

Switchable slow cellular conductances determine robustness and tunability of network states.

Neuronal information processing is regulated by fast and localized fluctuations of brain states. Brain states reliably switch between distinct spatiotemporal signatures at a network scale even though they are composed of heterogeneous and variable rhythms at a cellular scale. We investigated the mechanisms of this network control in a conductance-based population model that reliably switches between active and oscillatory mean-fields. Robust control of the mean-field properties relies critically on a switchable negative intrinsic conductance at the cellular level. This conductance endows circuits with a shared cellular positive feedback that can switch population rhythms on and off at a cellular resolution. The switch is largely independent from other intrinsic neuronal properties, network size and synaptic connectivity. It is therefore compatible with the temporal variability and spatial heterogeneity induced by slower regulatory functions such as neuromodulation, synaptic plasticity and homeostasis. Strikingly, the required cellular mechanism is available in all cell types that possess T-type calcium channels but unavailable in computational models that neglect the slow kinetics of their activation

Neuronal behaviors: A control perspective

The purpose of this tutorial is to introduce and analyze models of neurons from a control perspective and to show how recently developed analytical tools help to address important biological questions. A first objective is to review the basic modeling principles of neurophysiology in which neurons are modeled as equivalent nonlinear electrical circuits that capture their excitable properties. The specific architecture of the models is key to the tractability of their analysis: in spite of their high-dimensional and nonlinear nature, the model properties can be understood in terms of few canonical positive and negative feedback motifs localized in distinct timescales. We use this insight to shed light on a key problem in experimental neurophysiology, the challenge of understanding the sensitivity of neuronal behaviors to underlying parameters in empirically-derived models. Finally, we show how sensitivity analysis of neuronal excitability relates to robustness and regulation of neuronal behaviors.This paper presents research results of the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization), funded by the Interuniversity Attraction Poles Programme, initiated by the Belgian State, Science Policy Office. G.D. is a Marie-Curie COFUND postdoctoral fellow at the University of Liege. Co-funded by the European Union. J.D. is supported by the F.R.S.-FNRS (Belgian Fund for Scientific Research. The scientific responsibility rests with its authors.This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/CDC.2015.740249

Stability properties of the collective stationary motion of self-propelling particles with conservative kinematic constraints

In our previous papers we proposed a continuum model for the dynamics of the systems of self-propelling particles with conservative kinematic constraints on the velocities. We have determined a class of stationary solutions of this hydrodynamic model and have shown that two types of stationary flow, linear and radially symmetric (vortical) flow, are possible. In this paper we consider the stability properties of these stationary flows. We show, using a linear stability analysis, that the linear solutions are neutrally stable with respect to the imposed velocity and density perturbations. A similar analysis of the stability of the vortical solution is found to be not conclusive.Comment: 13 pages, 3 figure

Bifurcations of discrete breathers in a diatomic Fermi-Pasta-Ulam chain

Discrete breathers are time-periodic, spatially localized solutions of the equations of motion for a system of classical degrees of freedom interacting on a lattice. Such solutions are investigated for a diatomic Fermi-Pasta-Ulam chain, i. e., a chain of alternate heavy and light masses coupled by anharmonic forces. For hard interaction potentials, discrete breathers in this model are known to exist either as ``optic breathers'' with frequencies above the optic band, or as ``acoustic breathers'' with frequencies in the gap between the acoustic and the optic band. In this paper, bifurcations between different types of discrete breathers are found numerically, with the mass ratio m and the breather frequency omega as bifurcation parameters. We identify a period tripling bifurcation around optic breathers, which leads to new breather solutions with frequencies in the gap, and a second local bifurcation around acoustic breathers. These results provide new breather solutions of the FPU system which interpolate between the classical acoustic and optic modes. The two bifurcation lines originate from a particular ``corner'' in parameter space (omega,m). As parameters lie near this corner, we prove by means of a center manifold reduction that small amplitude solutions can be described by a four-dimensional reversible map. This allows us to derive formally a continuum limit differential equation which characterizes at leading order the numerically observed bifurcations.Comment: 30 pages, 10 figure

Discrete breathers in nonlinear lattices: Experimental detection in a Josephson array

We present an experimental study of discrete breathers in an underdamped Josephson-junction array. Breathers exist under a range of dc current biases and temperatures, and are detected by measuring dc voltages. We find the maximum allowable bias current for the breather is proportional to the array depinning current while the minimum current seems to be related to a junction retrapping mechanism. We have observed that this latter instability leads to the formation of multi-site breather states in the array. We have also studied the domain of existence of the breather at different values of the array parameters by varying the temperature.Comment: 5 pages, 5 figures, submitted to Physical Revie

Quasiperiodic Patterns in Boundary-Modulated Excitable Waves

We investigate the impact of the domain shape on wave propagation in excitable media. Channelled domains with sinusoidal boundaries are considered. Trains of fronts generated periodically at an extreme of the channel are found to adopt a quasiperiodic spatial configuration stroboscopically frozen in time. The phenomenon is studied in a model for the photo-sensitive Belousov-Zabotinsky reaction, but we give a theoretical derivation of the spatial return maps prescribing the height and position of the successive fronts that is valid for arbitrary excitable reaction-diffusion systems.Comment: 4 pages (figures included

Kinase inhibitors can produce off-target effects and activate linked pathways by retroactivity

Abstract Background It has been shown in experimental and theoretical work that covalently modified signaling cascades naturally exhibit bidirectional signal propagation via a phenomenon known as retroactivity. An important consequence of retroactivity, which arises due to enzyme sequestration in covalently modified signaling cascades, is that a downstream perturbation can produce a response in a component upstream of the perturbation without the need for explicit feedback connections. Retroactivity may, therefore, play an important role in the cellular response to a targeted therapy. Kinase inhibitors are a class of targeted therapies designed to interfere with a specific kinase molecule in a dysregulated signaling pathway. While extremely promising as anti-cancer agents, kinase inhibitors may produce undesirable off-target effects by non-specific interactions or pathway cross-talk. We hypothesize that targeted therapies such as kinase inhibitors can produce off-target effects as a consequence of retroactivity alone. Results We used a computational model and a series of simple signaling motifs to test the hypothesis. Our results indicate that within physiologically and therapeutically relevant ranges for all parameters, a targeted inhibitor can naturally induce an off-target effect via retroactivity. The kinetics governing covalent modification cycles in a signaling network were more important for propagating an upstream off-target effect in our models than the kinetics governing the targeted therapy itself. Our results also reveal the surprising and crucial result that kinase inhibitors have the capacity to turn "on" an otherwise "off" parallel cascade when two cascades share an upstream activator. Conclusions A proper and detailed characterization of a pathway's structure is important for identifying the optimal protein to target as well as what concentration of the targeted therapy is required to modulate the pathway in a safe and effective manner. We believe our results support the position that such characterizations should consider retroactivity as a robust potential source of off-target effects induced by kinase inhibitors and other targeted therapies.http://deepblue.lib.umich.edu/bitstream/2027.42/112707/1/12918_2011_Article_826.pd