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Irving R. Epstein - One of the best experts on this subject based on the ideXlab platform.
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localized structures in a nonlinear wave equation stabilized by negative Global Feedback one dimensional and quasi two dimensional kinks
Physical Review E, 2006Co-Authors: Horacio G Rotstein, Anatol Zhabotinsky, Irving R. EpsteinAbstract:We study the evolution of fronts in a nonlinear wave equation with Global Feedback. This equation generalizes the Klein-Gordon and sine-Gordon equations. Extending previous work, we describe the derivation of an equation governing the front motion, which is strongly nonlinear, and, for the two-dimensional case, generalizes the damped Born-Infeld equation. We study the motion of one- and two-dimensional fronts, finding a much richer dynamics than for the classical case (with no Global Feedback), leading in most cases to a localized solution; i.e., the stabilization of one phase inside the other. The nature of the localized solution depends on the strength of the Global Feedback as well as on other parameters of the model.
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Canard phenomenon and localization of oscillations in the Belousov-Zhabotinsky reaction with Global Feedback
The Journal of Chemical Physics, 2003Co-Authors: Horacio G Rotstein, Nancy Kopell, Anatol M. Zhabotinsky, Irving R. EpsteinAbstract:The occurrence of spatial domains of large amplitude oscillation on a background of small amplitude oscillation in a reaction–diffusion system is called localization. We study, analytically and numerically, the mechanism of localization in a model of the Belousov–Zhabotinsky reaction subject to Global Feedback. This behavior is found to arise from the canard phenomenon, in which a limit cycle suddenly undergoes a significant change in amplitude as a bifurcation parameter, in this case the Feedback strength, is varied. In the system studied here, the oscillations arise via a supercritical Hopf bifurcation, but our analysis suggests that the same mechanism is relevant for systems undergoing a subcritical Hopf bifurcation.
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oscillatory cluster patterns in a homogeneous chemical system with Global Feedback
Nature, 2000Co-Authors: Vladimir K. Vanag, And Anatol M. Zhabotinsky, Lingfa Yang, Milos Dolnik, Irving R. EpsteinAbstract:Oscillatory clusters are sets of domains in which nearly all elements in a given domain oscillate with the same amplitude and phase1,2,3,4. They play an important role in understanding coupled neuron systems5,6,7,8. In the simplest case, a system consists of two clusters that oscillate in antiphase and can each occupy multiple fixed spatial domains. Examples of cluster behaviour in extended chemical systems are rare, but have been shown to resemble standing waves9,10,11,12,13, except that they lack a characteristic wavelength. Here we report the observation of so-called ‘localized clusters’—periodic antiphase oscillations in one part of the medium, while the remainder appears uniform—in the Belousov–Zhabotinsky reaction–diffusion system with photochemical Global Feedback. We also observe standing clusters with fixed spatial domains that oscillate periodically in time and occupy the entire medium, and irregular clusters with no periodicity in either space or time, with standing clusters transforming into irregular clusters and then into localized clusters as the strength of the Global negative Feedback is gradually increased. By incorporating the effects of Global Feedback into a model of the reaction, we are able to simulate successfully the experimental data.
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Pattern Formation in the Belousov−Zhabotinsky Reaction with Photochemical Global Feedback
The Journal of Physical Chemistry A, 2000Co-Authors: Vladimir K. Vanag, And Anatol M. Zhabotinsky, Irving R. EpsteinAbstract:We have found a variety of oscillating patterns in the Belousov−Zhabotinsky (BZ) reaction−diffusion system with Global negative Feedback. Bulk oscillations and wave patterns arise at low values of the Feedback strength. When the Feedback exceeds a critical value, cluster patterns arise. Besides the standing, irregular, and localized clusters observed earlier, we have found new types of clusters: three-phase, localized irregular, and localized oscillatory clusters. A model of three identical Oregonators with Global negative coupling yields the same bifurcation scenario as found in our experiments.
Stephen Mclaughlin - One of the best experts on this subject based on the ideXlab platform.
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Synthesising natural-sounding vowels using a nonlinear dynamical model
Signal Processing, 2001Co-Authors: Iain Mann, Stephen MclaughlinAbstract:This paper addresses the issue of vowel sound synthesis using a nonlinear model, comprising of a free-running radial basis function (RBF) neural network with Global Feedback. Voiced speech production is modelled as the output of a nonlinear dynamical system, rather than the conventional linear source-filter approach, which, given the nonlinear nature of speech, is expected to produce more natural-sounding synthetic speech. It is shown that the use of regularisation theory when learning the weights allows stable resynthesis when the network is operated with a Global Feedback and no external input, correctly producing the desired vowel sound. Additionally it is found that the dynamics of the vowel sound are well modelled, including the inter-pitch variations (jitter), thus making the synthesised vowel more natural-sounding than is possible with simple linear techniques.
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Using a nonlinear model to synthesise natural-sounding vowels
IEE Seminar on State of the Art in Speech Synthesis, 2000Co-Authors: Iain Mann, Stephen MclaughlinAbstract:This paper describes a nonlinear model that is able to generate vowel sounds of any required duration which also contain jitter and shimmer, and hence are more natural-sounding than the equivalent sounds generated by linear prediction techniques. The model is based on a radial basis function (RBF) neural network, with a Global Feedback loop. The network is trained by first placing the radial basis centres onto either a subset of the input data or a fixed hyper-lattice structure. The network weights are then found so as to minimise the mean square error between the input data (which will be a stationary vowel sound segment) and the network output. Regularisation is used when calculating the weight values, as this ensures stability when the Global Feedback loop is connected for synthesis. (6 pages)
Alexander S. Mikhailov - One of the best experts on this subject based on the ideXlab platform.
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Global Feedback control of Turing patterns in network-organized activator-inhibitor systems
EPL (Europhysics Letters), 2012Co-Authors: Shigefumi Hata, Hiroya Nakao, Alexander S. MikhailovAbstract:Results of the first systematic study on Feedback control of nonequilibrium pattern formation in networks are reported. Effects of Global Feedback control on Turing patterns in network-organized activator-inhibitor system have been investigated. The Feedback signal was introduced into one of the parameters of the system and was proportional to the amplitude of the developing Turing pattern. Without the control, the Turing instability corresponded to a subcritical bifurcation and hysteresis effects were observed. Sufficiently strong Feedback control rendered, however, the bifurcation supercritical and eliminated the hysteresis effects.
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Networks on the edge of chaos: Global Feedback control of turbulence in oscillator networks
Physical Review E, 2009Co-Authors: Santiago Gil, Alexander S. MikhailovAbstract:Random networks of coupled phase oscillators with phase shifts in the interaction functions are considered. In such systems, extensive chaos (turbulence) is observed in a wide range of parameters. We show that, by introducing Global Feedback, the turbulence can be suppressed and a transition to synchronous oscillations can be induced. Our attention is focused on the transition scenario and the properties of patterns, including intermittent turbulence, which are found at the edge of chaos. The emerging coherent patterns represent various self-organized active (sub)networks whose size and behavior can be controlled.
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Controlling turbulence in the complex Ginzburg-Landau equation II. Two-dimensional systems
Physica D: Nonlinear Phenomena, 1997Co-Authors: Dorjsuren Battogtokh, A. Preusser, Alexander S. MikhailovAbstract:Abstract Turbulence in oscillatory distributed systems can be controlled by introducing a delayed Global Feedback and adjusting the Feedback intensity and the delay time. We investigate influence of Global Feedbacks on turbulence in two-dimensional systems described by the complex Ginzburg-Landau equation. Inside a synchronization window, application of such Feedbacks leads to destruction of phase flips and spiral waves, appearance of breathing and stationary cellular structures or stripes, and development of localized turbulent bubbles on the background of uniform oscillations.
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Controlling Spiral Waves in Confined Geometries by Global Feedback
Physical Review Letters, 1997Co-Authors: Vladimir S. Zykov, Alexander S. Mikhailov, Stefan C MullerAbstract:The evolution of spiral waves on a circular domain and on a spherical surface is studied by numerical integration of a reaction-diffusion system with a Global Feedback. It is shown that depending on intensity, sign, and/or time delay in the Feedback loop a Global coupling can be effectively used either to stabilize the rigid rotation of a spiral wave or to completely destroy spiral waves and to suppress self-sustained activity in a confined domain of an excitable medium. An explanation of the numerically observed effects is produced by a kinematical model of spiral wave propagation.
István Z. Kiss - One of the best experts on this subject based on the ideXlab platform.
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Plasticity facilitates pattern selection of networks of chemical oscillations.
Chaos (Woodbury N.Y.), 2019Co-Authors: Michael Sebek, István Z. KissAbstract:Rotating wave synchronization patterns are explored with a ring of 20 electrochemical oscillators during nickel electrodissolution in sulfuric acid. With desynchronized initial states, coupling alone yields predominance of nonrotating solutions, i.e., in-phase synchronization. An experimental technique is presented in which, through a combination of temporary alterations in topology, the application of Global Feedback provides rotational solutions. With phase repulsive Global Feedback, the in-phase synchronization is destabilized and a rotating wave is obtained. This Feedback induced rotating wave can be employed to establish an initial condition for the rotating wave with coupling only. Higher order rotating solutions with 2, 3, and 4 waves corotating around the ring are observed, where the initial conditions are generated by temporary network rewiring to a structure with 2, 3, and 4 loops, respectively, and by Global Feedback. The experimental observations are supported by numerical simulations with a phase model. The results indicate that while network plasticity is thought to be significant in the operation of neural systems, it can also play a role in pattern selection of chemical systems.
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Spatiotemporal Patterns on a Ring Network of Oscillatory Electrochemical Reaction with Negative Global Feedback
Israel Journal of Chemistry, 2018Co-Authors: Michael Sebek, István Z. KissAbstract:The formation of spatiotemporal patterns in chemical systems can often be attributed to local and Global interactions with the nonlinear kinetics, e. g., due to diffusion or an external constraint, respectively. We investigate the dynamics of an oscillatory chemical reaction on a ring of discrete elements, where the positive local coupling and negative Global Feedback can be varied independently to observe the emerging spatiotemporal patterns. With local coupling, the oscillations exhibit nearly in-phase synchronization. When increasing the Global negative Feedback, a transition is seen from nearly sinusoidal phase profile oscillations through rotating and standing waves to amplitude death behavior. The experimental studies are interpreted with a kinetic model of nickel electrodissolution. The results demonstrate the presence of rich spatiotemporal patterns that can be obtained in a network with positive local and negative Global interactions.
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Synchronization and Clustering of Arrays of Electrochemical Oscillators with Global Feedback
Industrial & Engineering Chemistry Research, 2002Co-Authors: Wen Wang, István Z. Kiss, John L. HudsonAbstract:Experiments on chaotically oscillating arrays of nickel electrodes in sulfuric acid were carried out. A Global Feedback is added in which a signal proportional to the difference between the sum of the currents of all elements and a mean current is fed back to the applied potential. The addition of Global Feedback transforms a system of weakly coupled elements to one of complete synchronization. At intermediate Feedback strengths, intermittent, unstable chaotic clusters are observed in which clusters of elements form and break up. Stable clusters or condensates form at somewhat higher Feedback strengths. The stable clusters become periodic at higher gain; both two-cluster and three-cluster states are observed. With a further increase in the Feedback gain, one of the clusters dominates the collective dynamics; its size increases until at some Feedback strength the entire system is synchronized. Delay in the Feedback signal also influences the interaction of the oscillators.
Horacio G Rotstein - One of the best experts on this subject based on the ideXlab platform.
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Dynamic mechanisms of generation of oscillatory cluster patterns in a Globally coupled chemical system.
The Journal of chemical physics, 2012Co-Authors: Horacio G RotsteinAbstract:We use simulations and dynamical systems tools to investigate the mechanisms of generation of phase-locked and localized oscillatory cluster patterns in a Globally coupled Oregonator model where the activator receives Global Feedback from the inhibitor, mimicking experimental results observed in the photosensitive Belousov-Zhabotinsky reaction. A homogeneous two-cluster system (two clusters with equal cluster size) displays antiphase patterns. Heterogenous two-cluster systems (two clusters with different sizes) display both phase-locked and localized patterns depending on the parameter values. In a localized pattern the oscillation amplitude of the largest cluster is roughly an order of magnitude smaller than the oscillation amplitude of the smaller cluster, reflecting the effect of self-inhibition exerted by the Global Feedback term. The transition from phase-locked to localized cluster patterns occurs as the intensity of Global Feedback increases. Three qualitatively different basic mechanisms, described previously for a Globally coupled FitzHugh-Nagumo model, are involved in the generation of the observed patterns. The swing-and-release mechanism is related to the canard phenomenon (canard explosion of limit cycles) in relaxation oscillators. The hold-and-release and hold-and-escape mechanisms are related to the release and escape mechanisms in synaptically connected neural models. The methods we use can be extended to the investigation of oscillatory chemical reactions with other types of non-local coupling.
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Dynamics of one- and two-dimensional fronts in a bistable equation with time-delayed Global Feedback: Propagation failure and control mechanisms
Physical Review E, 2010Co-Authors: Yassine Boubendir, Vicenç Méndez, Horacio G RotsteinAbstract:We study the evolution of fronts in a bistable equation with time-delayed Global Feedback in the fast reaction and slow diffusion regime. This equation generalizes the Hodgkin-Grafstein and Allen-Cahn equations. We derive a nonlinear equation governing the motion of fronts, which includes a term with delay. In the one-dimensional case this equation is linear. We study the motion of one- and two-dimensional fronts, finding a much richer dynamics than for the previously studied cases (without time-delayed Global Feedback). We explain the mechanism by which localized fronts created by inhibitory Global coupling loose stability in a Hopf bifurcation as the delay time increases. We show that for certain delay times, the prevailing phase is different from that corresponding to the system in the absence of Global coupling. Numerical simulations of the partial differential equation are in agreement with the analytical predictions.
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localized structures in a nonlinear wave equation stabilized by negative Global Feedback one dimensional and quasi two dimensional kinks
Physical Review E, 2006Co-Authors: Horacio G Rotstein, Anatol Zhabotinsky, Irving R. EpsteinAbstract:We study the evolution of fronts in a nonlinear wave equation with Global Feedback. This equation generalizes the Klein-Gordon and sine-Gordon equations. Extending previous work, we describe the derivation of an equation governing the front motion, which is strongly nonlinear, and, for the two-dimensional case, generalizes the damped Born-Infeld equation. We study the motion of one- and two-dimensional fronts, finding a much richer dynamics than for the classical case (with no Global Feedback), leading in most cases to a localized solution; i.e., the stabilization of one phase inside the other. The nature of the localized solution depends on the strength of the Global Feedback as well as on other parameters of the model.
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Canard phenomenon and localization of oscillations in the Belousov-Zhabotinsky reaction with Global Feedback
The Journal of Chemical Physics, 2003Co-Authors: Horacio G Rotstein, Nancy Kopell, Anatol M. Zhabotinsky, Irving R. EpsteinAbstract:The occurrence of spatial domains of large amplitude oscillation on a background of small amplitude oscillation in a reaction–diffusion system is called localization. We study, analytically and numerically, the mechanism of localization in a model of the Belousov–Zhabotinsky reaction subject to Global Feedback. This behavior is found to arise from the canard phenomenon, in which a limit cycle suddenly undergoes a significant change in amplitude as a bifurcation parameter, in this case the Feedback strength, is varied. In the system studied here, the oscillations arise via a supercritical Hopf bifurcation, but our analysis suggests that the same mechanism is relevant for systems undergoing a subcritical Hopf bifurcation.