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Vanag VK, Epstein IR. Out-of-phase oscillatory Turing patterns in a bistable reaction-diffusion system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:066212. [PMID: 16089854 DOI: 10.1103/physreve.71.066212] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2005] [Indexed: 05/03/2023]
Abstract
A new type of out-of-phase oscillatory Turing pattern is found in simulations of a simple two-variable model of a bistable reaction-diffusion system consisting of an autocatalytic activator reacting with a substrate that is replenished by a flow. This class of models can describe pH oscillators or enzymatic reactions. No Hopf instability is necessary for this type of oscillatory Turing pattern.
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Affiliation(s)
- Vladimir K Vanag
- Department of Chemistry and Volen Center for Complex Systems, MS 015, Brandeis University, Waltham, Massachusetts 02454, USA
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Pineda M, Cosenza MG. Synchronization in driven versus autonomous coupled chaotic maps. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:057201. [PMID: 16089699 DOI: 10.1103/physreve.71.057201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2004] [Revised: 12/02/2004] [Indexed: 05/03/2023]
Abstract
The phenomenon of synchronization occurring in a locally coupled map lattice subject to an external drive is compared to the synchronization process in an autonomous coupled map system with similar local couplings plus a global interaction. It is shown that chaotic synchronized states in both systems are equivalent, but the collective states arising after the chaotic synchronized state becomes unstable can be different in these two systems. It is found that the external drive induces chaotic synchronization as well as synchronization of unstable periodic orbits of the local dynamics in the driven lattice. On the other hand, the addition of a global interaction in the autonomous system allows for chaotic synchronization which is not possible in a large coupled map system possessing only local couplings.
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Affiliation(s)
- M Pineda
- Max-Planck-Institut für Physik Komplexer Systeme, Nöthnizer Strasse 38, 01187 Dresden, Germany
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Miyakita Y, Nakabayashi S, Karantonis A. Spatiotemporal coding in an electrochemical oscillatory network. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:056207. [PMID: 16089634 DOI: 10.1103/physreve.71.056207] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/08/2004] [Indexed: 05/03/2023]
Abstract
A network consisting of N relaxation electrochemical oscillators, mutually coupled by all-to-all inhibitory connections, can have (N-1) ! coexisting out-of-phase states, each state being a permutation of a periodic spiking sequence. The modification of the out-of-phase states by shots of laser pulse perturbations is shown. In such networks the phase relation of the oscillators is stored as a coded pattern. The ability of the network to function as a rewritable memory of (N-1) ! different spatiotemporal patterns is demonstrated experimentally for N=4.
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Affiliation(s)
- Yasuyuki Miyakita
- Department of Chemistry, Faculty of Science, Saitama University, Saitama 338-8570, Japan
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Karantonis A, Pagitsas M, Miyakita Y, Nakabayashi S. From Excitatory to Inhibitory Connections in Networks of Discrete Electrochemical Oscillators. J Phys Chem B 2003. [DOI: 10.1021/jp036595c] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- A. Karantonis
- Department of Materials Science and Engineering, School of Chemical Engineering, National Technical University of Athens, Zografou 15780, Athens, Greece, Department of Chemistry, Faculty of Science, Aristotle University of Thessaloniki, Thessaloniki 54006, Greece, and Department of Chemistry, Faculty of Science, Saitama University, Saitama 338-8570, Japan
| | - M. Pagitsas
- Department of Materials Science and Engineering, School of Chemical Engineering, National Technical University of Athens, Zografou 15780, Athens, Greece, Department of Chemistry, Faculty of Science, Aristotle University of Thessaloniki, Thessaloniki 54006, Greece, and Department of Chemistry, Faculty of Science, Saitama University, Saitama 338-8570, Japan
| | - Y. Miyakita
- Department of Materials Science and Engineering, School of Chemical Engineering, National Technical University of Athens, Zografou 15780, Athens, Greece, Department of Chemistry, Faculty of Science, Aristotle University of Thessaloniki, Thessaloniki 54006, Greece, and Department of Chemistry, Faculty of Science, Saitama University, Saitama 338-8570, Japan
| | - S. Nakabayashi
- Department of Materials Science and Engineering, School of Chemical Engineering, National Technical University of Athens, Zografou 15780, Athens, Greece, Department of Chemistry, Faculty of Science, Aristotle University of Thessaloniki, Thessaloniki 54006, Greece, and Department of Chemistry, Faculty of Science, Saitama University, Saitama 338-8570, Japan
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Cosenza MG, Pineda M, Parravano A. Emergence of patterns in driven and in autonomous spatiotemporal systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:066217. [PMID: 16241336 DOI: 10.1103/physreve.67.066217] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2002] [Indexed: 05/04/2023]
Abstract
The relationship between a driven extended system and an autonomous spatiotemporal system is investigated in the context of coupled map lattice models. Specifically, a locally coupled map lattice subjected to an external drive is compared to a coupled map system with similar local couplings plus a global interaction. It is shown that, under some conditions, the emergent patterns in both systems are analogous. Based on the knowledge of the dynamical responses of the driven lattice, we present a method that allows the prediction of parameter values for the emergence of ordered spatiotemporal patterns in a class of coupled map systems having local coupling and general forms of global interactions.
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Affiliation(s)
- M G Cosenza
- Centro de Astrofísica Teórica, Facultad de Ciencias Universidad de Los Andes, Mérida, Apartado Postal 26, Mérida 5251, Venezuela
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Bîrzu A, Plenge F, Jaeger NI, Hudson JL, Krischer K. Complex Spatiotemporal Antiphase Oscillations during Electrodissolution of a Metal Disk Electrode: Model Calculations. J Phys Chem B 2003. [DOI: 10.1021/jp022457w] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Adrian Bîrzu
- Department of Physics, Technical University of München, James-Franck-Strasse 1, 85748 Garching, Germany, Fritz Haber Institute of the Max Planck Society, Faradayweg 4-6, 14195 Berlin, Germany, Institute for Applied and Physical Chemistry, University of Bremen, FB 2-Biology/Chemistry, Postfach 330 440, 28334 Bremen, Germany, and Department of Chemical Engineering, 102 Engineers' Way, University of Virginia, Charlottesville, Virginia 22904-4741
| | - Florian Plenge
- Department of Physics, Technical University of München, James-Franck-Strasse 1, 85748 Garching, Germany, Fritz Haber Institute of the Max Planck Society, Faradayweg 4-6, 14195 Berlin, Germany, Institute for Applied and Physical Chemistry, University of Bremen, FB 2-Biology/Chemistry, Postfach 330 440, 28334 Bremen, Germany, and Department of Chemical Engineering, 102 Engineers' Way, University of Virginia, Charlottesville, Virginia 22904-4741
| | - Nils I. Jaeger
- Department of Physics, Technical University of München, James-Franck-Strasse 1, 85748 Garching, Germany, Fritz Haber Institute of the Max Planck Society, Faradayweg 4-6, 14195 Berlin, Germany, Institute for Applied and Physical Chemistry, University of Bremen, FB 2-Biology/Chemistry, Postfach 330 440, 28334 Bremen, Germany, and Department of Chemical Engineering, 102 Engineers' Way, University of Virginia, Charlottesville, Virginia 22904-4741
| | - John L. Hudson
- Department of Physics, Technical University of München, James-Franck-Strasse 1, 85748 Garching, Germany, Fritz Haber Institute of the Max Planck Society, Faradayweg 4-6, 14195 Berlin, Germany, Institute for Applied and Physical Chemistry, University of Bremen, FB 2-Biology/Chemistry, Postfach 330 440, 28334 Bremen, Germany, and Department of Chemical Engineering, 102 Engineers' Way, University of Virginia, Charlottesville, Virginia 22904-4741
| | - Katharina Krischer
- Department of Physics, Technical University of München, James-Franck-Strasse 1, 85748 Garching, Germany, Fritz Haber Institute of the Max Planck Society, Faradayweg 4-6, 14195 Berlin, Germany, Institute for Applied and Physical Chemistry, University of Bremen, FB 2-Biology/Chemistry, Postfach 330 440, 28334 Bremen, Germany, and Department of Chemical Engineering, 102 Engineers' Way, University of Virginia, Charlottesville, Virginia 22904-4741
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Karantonis A, Miyakita Y, Nakabayashi S. Synchronization of coupled assemblies of relaxation oscillatory electrode pairs. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:046213. [PMID: 12005982 DOI: 10.1103/physreve.65.046213] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2001] [Indexed: 05/23/2023]
Abstract
Spatiotemporal patterns emerging through coupling of identical relaxation oscillatory electrode pairs are studied. Each pair, consisting of an iron anode and a copper cathode, oscillates periodically under fixed applied potential difference conditions. It is shown that the system synchronizes rapidly (within few oscillatory cycles) and differences of natural frequencies as well as boundary effects are compensated. The effect of the geometrical configuration on the dynamic modes is investigated for relatively large assemblies of such oscillatory pairs. When oscillators are coupled through neighboring electrodes, the response is synchronized by a simultaneous formation of groups. The formation of groups due to enhancement or inhibition of the oscillations depends on the relative position of interacting anodes and cathodes. The behavior of the system is compared with the response of coupled relaxation cells of neurophysiological interest.
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Affiliation(s)
- Antonis Karantonis
- Department of Chemistry, Faculty of Science, Saitama University, Saitama City, Saitama 338-8570, Japan.
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Christoph J, Eiswirth M. Theory of electrochemical pattern formation. CHAOS (WOODBURY, N.Y.) 2002; 12:215-230. [PMID: 12779549 DOI: 10.1063/1.1449956] [Citation(s) in RCA: 39] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
The spatial coupling in electrochemical systems is mediated by ion migration under the influence of the electric field. Since field effects spread very rapidly, every point of an electrode can communicate with every other one practically instantaneously through migration coupling. Based on mathematical potential theory we present the derivation of a generally applicable reaction-migration equation, which describes the coupling via an integral over the whole electrode area. The corresponding coupling function depends only on the geometry of the electrode setup and has been computed for commonly used electrode shapes (such as ring, disk, ribbon or rectangle). The pattern formation observed in electrochemical systems in the bistable, excitable and oscillatory regime can be reproduced in computer simulations, and the types of patterns occurring under different geometries can be rationalized. (c) 2002 American Institute of Physics.
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Affiliation(s)
- J. Christoph
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany
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Jaeger NI, Otterstedt RD, Birzu A, Green BJ, Hudson JL. Evolution of spatiotemporal patterns during the electrodissolution of metals: Experiments and simulations. CHAOS (WOODBURY, N.Y.) 2002; 12:231-239. [PMID: 12779550 DOI: 10.1063/1.1436502] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Spatiotemporal patterns including accelerating fronts, rotating waves, and homogeneous oscillations evolve during the electrodissolution of metals like cobalt and iron that exhibit passivity under potentiostatic control. The nature of the patterns is determined by long-range (nonlocal) coupling through the electric field which in turn is influenced by the geometry of the electrochemical cell, the applied potential, and the conductivity of the electrolyte. A two-variable model in a three-dimensional geometry is presented which is able to simulate the essential features of the experimental system.(c) 2002 American Institute of Physics.
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Affiliation(s)
- Nils I. Jaeger
- Institut fur Angewandte und Physikalische Chemie, FB 2-Universitat Bremen, Postfach 330 440, D-28334 Bremen, Germany
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Parmananda P, Green BJ, Hudson JL. Suppressing spatiotemporal disorder via local perturbations in an electrochemical cell. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:035202. [PMID: 11909145 DOI: 10.1103/physreve.65.035202] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2001] [Indexed: 05/23/2023]
Abstract
We report experimental results depicting suppression of complex spatiotemporal dynamics under the influence of local periodic stimulations. In an experimental electrochemical system, applying a continuous forcing signal to one of the sites in an array of eight coupled oscillators, the naturally complex behavior of the remaining seven electrodes can be converted to periodic responses. The oscillations remain periodic as long as the forcing is active and revert back to exhibiting chaotic dynamics after the control is switched off. These results can also be interpreted as experimental realization of "phase-synchronization" induced via local driving in an extended system. A possible relevance to the experimentally observed calcium wave patterns is pointed out.
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Affiliation(s)
- P Parmananda
- Facultad de Ciencias, UAEM, Avenida Universidad 1001, Col. Chamilpa, Cuernavaca, Morelos, Mexico
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Shiomi Y, Karantonis A, Nakabayashi S. Reaction Propagation over a Ring Electrode during Self-Sustained Current Oscillations in the Fe/H2SO4System. CHEM LETT 2001. [DOI: 10.1246/cl.2001.1276] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Green BJ, Hudson JL. Spatiotemporal patterns and symmetry breaking on a ring electrode. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:026214. [PMID: 11308565 DOI: 10.1103/physreve.63.026214] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/28/2000] [Indexed: 05/23/2023]
Abstract
A series of experiments on a ring electrode with changes in a parameter, the applied potential, are described. Spatiotemporal patterns are investigated in a region of parameter space in which relaxation oscillations occur. The simplest state is a period 2Pi oscillation that has full O(2) symmetry so that at each instant the pattern is unchanged by rotations or reflections of the ring. With change in parameter a spatiotemporal period doubling occurs to period 4Pi. This is followed by a symmetry breaking to another state with period 4Pi and subsequently by a second period doubling to period 8Pi. Proper orthogonal decomposition is used as an aid in elucidating the nature of the transitions.
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Affiliation(s)
- B J Green
- Department of Chemical Engineering, University of Virginia, 102 Engineers' Way, Charlottesville, Virginia 22904-4741, USA
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Vanag VK, Zhabotinsky AM, Epstein IR. Pattern Formation in the Belousov−Zhabotinsky Reaction with Photochemical Global Feedback. J Phys Chem A 2000. [DOI: 10.1021/jp002390h] [Citation(s) in RCA: 59] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Vladimir K. Vanag
- Department of Chemistry and Volen Center for Complex Systems, MS 015, Brandeis University, P.O. Box 549110, Waltham, Massachusetts 02454-9110
| | - Anatol M. Zhabotinsky
- Department of Chemistry and Volen Center for Complex Systems, MS 015, Brandeis University, P.O. Box 549110, Waltham, Massachusetts 02454-9110
| | - Irving R. Epstein
- Department of Chemistry and Volen Center for Complex Systems, MS 015, Brandeis University, P.O. Box 549110, Waltham, Massachusetts 02454-9110
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Wang W, Kiss IZ, Hudson JL. Experiments on arrays of globally coupled chaotic electrochemical oscillators: Synchronization and clustering. CHAOS (WOODBURY, N.Y.) 2000; 10:248-256. [PMID: 12779380 DOI: 10.1063/1.166470] [Citation(s) in RCA: 68] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Experiments on chaotically oscillating arrays of 64 nickel electrodes in sulfuric acid were carried out. External resistors in parallel and series are added to vary the extent of global coupling among the oscillators without changing the other properties of the system. The array is heterogeneous due to small variations in the properties of the electrodes and there is also a small amount of noise. The addition of global coupling transforms a system of independent elements to a state of complete synchronization. At intermediate coupling strengths stable clusters, or condensates of elements, form. All the elements in a cluster follow the same chaotic trajectory but each cluster has its own dynamics; the system is thus temporally chaotic but spatially ordered. Many cluster configurations occur under the same conditions and transitions among them can be produced. For values of the coupling parameter on either side of the stable cluster region a non-stationary behavior occurs in which clustered and synchronized states alternately form and break up. Some statistical properties of the cluster states are determined. (c) 2000 American Institute of Physics.
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Affiliation(s)
- Wen Wang
- Department of Chemical Engineering, Thornton Hall, University of Virginia, Charlottesville, Virginia 22903-2442
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Kiss IZ, Wang W, Hudson JL. Experiments on Arrays of Globally Coupled Periodic Electrochemical Oscillators. J Phys Chem B 1999. [DOI: 10.1021/jp992471h] [Citation(s) in RCA: 88] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- István Z. Kiss
- Department of Chemical Engineering, Thornton Hall, University of Virginia, Charlottesville, Virginia 22903-2442
| | - Wen Wang
- Department of Chemical Engineering, Thornton Hall, University of Virginia, Charlottesville, Virginia 22903-2442
| | - J. L. Hudson
- Department of Chemical Engineering, Thornton Hall, University of Virginia, Charlottesville, Virginia 22903-2442
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