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Ocampo-Espindola JL, Nikhil KL, Li JS, Herzog ED, Kiss IZ. Synchronization, clustering, and weak chimeras in a densely coupled transcription-based oscillator model for split circadian rhythms. CHAOS (WOODBURY, N.Y.) 2023; 33:083105. [PMID: 37535024 PMCID: PMC10403273 DOI: 10.1063/5.0156135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2023] [Accepted: 07/08/2023] [Indexed: 08/04/2023]
Abstract
The synchronization dynamics for the circadian gene expression in the suprachiasmatic nucleus is investigated using a transcriptional circadian clock gene oscillator model. With global coupling in constant dark (DD) conditions, the model exhibits a one-cluster phase synchronized state, in dim light (dim LL), bistability between one- and two-cluster states and in bright LL, a two-cluster state. The two-cluster phase synchronized state, where some oscillator pairs synchronize in-phase, and some anti-phase, can explain the splitting of the circadian clock, i.e., generation of two bouts of daily activities with certain species, e.g., with hamsters. The one- and two-cluster states can be reached by transferring the animal from DD or bright LL to dim LL, i.e., the circadian synchrony has a memory effect. The stability of the one- and two-cluster states was interpreted analytically by extracting phase models from the ordinary differential equation models. In a modular network with two strongly coupled oscillator populations with weak intragroup coupling, with appropriate initial conditions, one group is synchronized to the one-cluster state and the other group to the two-cluster state, resulting in a weak-chimera state. Computational modeling suggests that the daily rhythms in sleep-wake depend on light intensity acting on bilateral networks of suprachiasmatic nucleus (SCN) oscillators. Addition of a network heterogeneity (coupling between the left and right SCN) allowed the system to exhibit chimera states. The simulations can guide experiments in the circadian rhythm research to explore the effect of light intensity on the complexities of circadian desynchronization.
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Affiliation(s)
| | - K. L. Nikhil
- Department of Biology, Washington University in St. Louis, One Brookings Drive, St. Louis, Missouri 63130-4899, USA
| | - Jr-Shin Li
- Department of Electrical and Systems Engineering, Washington University in St Louis, 1 Brookings Drive, St. Louis, Missouri 63130, USA
| | - Erik D. Herzog
- Department of Biology, Washington University in St. Louis, One Brookings Drive, St. Louis, Missouri 63130-4899, USA
| | - István Z. Kiss
- Department of Chemistry, Saint Louis University, 3501 Laclede Ave., St. Louis, Missouri 63103, USA
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2
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Mallphanov IL, Vanag VK. Chemical micro-oscillators based on the Belousov–Zhabotinsky reaction. RUSSIAN CHEMICAL REVIEWS 2021. [DOI: 10.1070/rcr5009] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
Abstract
The results of studies on the development of micro-oscillators (MOs) based on the Belousov –Zhabotinsky (BZ) oscillatory chemical reaction are integrated and systematized. The mechanisms of the BZ reaction and the methods of immobilization of the catalyst of the BZ reaction in micro-volumes are briefly discussed. Methods for creating BZ MOs based on water microdroplets in the oil phase and organic and inorganic polymer microspheres are considered. Methods of control and management of the dynamics of BZ MO networks are described, including methods of MO synchronization. The prospects for the design of neural networks of MOs with intelligent-like behaviour are outlined. Such networks present a new area of nonlinear chemistry, including, in particular, the creation of a chemical ‘computer’.
The bibliography includes 250 references.
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Ohno K, Ogawa T, Suematsu NJ. Competition between global feedback and diffusion in coupled Belousov-Zhabotinsky oscillators. Phys Rev E 2019; 99:012208. [PMID: 30780237 DOI: 10.1103/physreve.99.012208] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2018] [Indexed: 11/07/2022]
Abstract
The Belousov-Zhabotinsky (BZ) reaction is a famous experimental model for chemical oscillatory reaction and pattern formation. We herein study a diffusive coupled system of two oscillators with global feedback using the photosensitive BZ reaction both experimentally and theoretically. The coupled oscillator showed in-phase and antiphase oscillations depending on the strength of diffusive coupling and light feedback. Moreover, we analyzed our model to locate the bifurcational origin and found the reconnection of the bifurcation branches for antiphase oscillation, which was induced by the competition between global feedback and the diffusion effect.
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Affiliation(s)
- Kota Ohno
- Graduate School of Advanced Mathematical Science, Meiji University, Nakano, Tokyo 164-8525, Japan and Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Nakano, Tokyo 164-8525, Japan
| | - Toshiyuki Ogawa
- Graduate School of Advanced Mathematical Science, Meiji University, Nakano, Tokyo 164-8525, Japan and Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Nakano, Tokyo 164-8525, Japan
| | - Nobuhiko J Suematsu
- Graduate School of Advanced Mathematical Science, Meiji University, Nakano, Tokyo 164-8525, Japan and Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Nakano, Tokyo 164-8525, Japan
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4
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Szabo E. Oregonator generalization as a minimal model of quorum sensing in Belousov–Zhabotinsky reaction with catalyst confinement in large populations of particles. RSC Adv 2015. [DOI: 10.1039/c5ra12841b] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023] Open
Abstract
The Oregonator demonstrates that quorum sensing in populations of Belousov–Zhabotinsky oscillators arises from modification of the stoichiometry by catalyst confinement.
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Affiliation(s)
- E. Szabo
- Department of Earth and Planetary Sciences
- Harvard University
- Cambridge
- USA
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Zeyer KP, Holz R, Schneider FW. Continuous Coupling of Chaotic and Periodic States of Chemical Oscillators With and Without Time Delay. ACTA ACUST UNITED AC 2010. [DOI: 10.1002/bbpc.19930970908] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Miyazaki J, Kinoshita S. Method for determining a coupling function in coupled oscillators with application to Belousov-Zhabotinsky oscillators. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:056209. [PMID: 17279986 DOI: 10.1103/physreve.74.056209] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2006] [Indexed: 05/13/2023]
Abstract
A coupling function that describes the interaction between self-sustained oscillators in a phase equation is derived and applied experimentally to Belousov-Zhabotinsky (BZ) oscillators. It is demonstrated that the synchronous behavior of coupled BZ reactors is explained extremely well in terms of the coupling function thus obtained. This method does not require comprehensive knowledge of either the oscillation mechanism or the interaction among the oscillators, both of these being often difficult to elucidate in an actual system. These facts enable us to accurately analyze the weakly coupled entrainment phenomenon through the direct measurement of the coupling function.
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Affiliation(s)
- J Miyazaki
- Graduate School of Frontier Biosciences, Osaka University, Suita 565-0871, Japan.
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7
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Recent developments in chemical oscillations. Top Curr Chem (Cham) 2005. [DOI: 10.1007/3-540-12575-2_2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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8
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Tatara E, Birol İ, Çınar A, Teymour F. Measuring Complexity in Reactor Networks with Cubic Autocatalytic Reactions. Ind Eng Chem Res 2005. [DOI: 10.1021/ie049246t] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Eric Tatara
- Department of Chemical and Environmental Engineering, Illinois Institute of Technology, 10 West 33rd Street, Chicago, Illinois 60616
| | - İnanç Birol
- Department of Chemical and Environmental Engineering, Illinois Institute of Technology, 10 West 33rd Street, Chicago, Illinois 60616
| | - Ali Çınar
- Department of Chemical and Environmental Engineering, Illinois Institute of Technology, 10 West 33rd Street, Chicago, Illinois 60616
| | - Fouad Teymour
- Department of Chemical and Environmental Engineering, Illinois Institute of Technology, 10 West 33rd Street, Chicago, Illinois 60616
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Tatara E, Birol I, Teymour F, Çınar A. Static and Dynamic Behavior of Autocatalytic Replicators in Reactor Networks. Ind Eng Chem Res 2004. [DOI: 10.1021/ie030802d] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Eric Tatara
- Department of Chemical and Environmental Engineering, Illinois Institute of Technology, 10 West 33rd Street, Chicago, Illinois 60616
| | - Inanc Birol
- Department of Chemical and Environmental Engineering, Illinois Institute of Technology, 10 West 33rd Street, Chicago, Illinois 60616
| | - Fouad Teymour
- Department of Chemical and Environmental Engineering, Illinois Institute of Technology, 10 West 33rd Street, Chicago, Illinois 60616
| | - Ali Çınar
- Department of Chemical and Environmental Engineering, Illinois Institute of Technology, 10 West 33rd Street, Chicago, Illinois 60616
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10
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Horsthemke W, Moore PK. Turing Instability in Inhomogeneous Arrays of Diffusively Coupled Reactors. J Phys Chem A 2004. [DOI: 10.1021/jp037029k] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Werner Horsthemke
- Department of Chemistry and Center for Scientific Computation, Southern Methodist University, Dallas, Texas 75275-0314
| | - Peter K. Moore
- Department of Mathematics and Center for Scientific Computation, Southern Methodist University, Dallas, Texas 75275-0156
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Abstract
A simple two compartment model system composed of a reservoir and a reactor is studied by means of numerical bifurcation analysis. An enzyme reaction involving ionic species is assumed to take place in the reactor connected to the reservoir
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12
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Zhong S, Xin H. Effects of Noise and Coupling on the Spatiotemporal Dynamics in a Linear Array of Coupled Chemical Reactors. J Phys Chem A 2000. [DOI: 10.1021/jp002600q] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Shi Zhong
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui, 230026, P. R. China, and National Laboratory of Theoretical and Computational Chemistry of China, Changchun, Jilin, 130023, P. R. China
| | - Houwen Xin
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui, 230026, P. R. China, and National Laboratory of Theoretical and Computational Chemistry of China, Changchun, Jilin, 130023, P. R. China
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14
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Branca M, Brunetti A, Caravati C, Rustici M. Coupling of erratic Belousov-Zhabotinsky oscillators observed by spectrophotometric measure. Ann N Y Acad Sci 1999; 879:228-34. [PMID: 10415832 DOI: 10.1111/j.1749-6632.1999.tb10424.x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- M Branca
- Università di Sassari, Dipartimento di Chimica, Italy.
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15
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Schreiber I, Hasal P, Marek M. Chaotic patterns in a coupled oscillator-excitator biochemical cell system. CHAOS (WOODBURY, N.Y.) 1999; 9:43-54. [PMID: 12779800 DOI: 10.1063/1.166400] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
In this paper we examine dynamical modes resulting from diffusion-like interaction of two model biochemical cells. Kinetics in each of the cells is given by the ICC model of calcium ions in the cytosol. Constraints for one of the cells are set so that it is excitable. One of the constraints in the other cell - a fraction of activated cell surface receptors-is varied so that the dynamics in the cell is either excitable or oscillatory or a stable focus. The cells are interacting via mass transfer and dynamics of the coupled system are studied as two parameters are varied-the fraction of activated receptors and the coupling strength. We find that (i) the excitator-excitator interaction does not lead to oscillatory patterns, (ii) the oscillator-excitator interaction leads to alternating phase-locked periodic and quasiperiodic regimes, well known from oscillator-oscillator interactions; torus breaking bifurcation generates chaos when the coupling strength is in an intermediate range, (iii) the focus-excitator interaction generates compound oscillations arranged as period adding sequences alternating with chaotic windows; the transition to chaos is accompanied by period doublings and folding of branches of periodic orbits and is associated with a Shilnikov homoclinic orbit. The nature of spontaneous self-organized oscillations in the focus-excitator range is discussed. (c) 1999 American Institute of Physics.
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Affiliation(s)
- Igor Schreiber
- Department of Chemical Engineering and Center for Nonlinear Dynamics of Chemical and Biological Systems, Institute of Chemical Technology in Prague, 166 28 Prague 6, Czech Republic
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16
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Votrubová V, Hasal P, Schreiberová L, Marek M. Dynamical Patterns in Arrays of Coupled Chemical Oscillators and Excitators. J Phys Chem A 1998. [DOI: 10.1021/jp973041z] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- V. Votrubová
- Department of Chemical Engineering and Center for Nonlinear Dynamics of Chemical and Biological Systems, Faculty of Chemical Engineering, Institute of Chemical Technology, Prague, 166 28 Prague 6, Czech Republic
| | - P. Hasal
- Department of Chemical Engineering and Center for Nonlinear Dynamics of Chemical and Biological Systems, Faculty of Chemical Engineering, Institute of Chemical Technology, Prague, 166 28 Prague 6, Czech Republic
| | - L. Schreiberová
- Department of Chemical Engineering and Center for Nonlinear Dynamics of Chemical and Biological Systems, Faculty of Chemical Engineering, Institute of Chemical Technology, Prague, 166 28 Prague 6, Czech Republic
| | - M. Marek
- Department of Chemical Engineering and Center for Nonlinear Dynamics of Chemical and Biological Systems, Faculty of Chemical Engineering, Institute of Chemical Technology, Prague, 166 28 Prague 6, Czech Republic
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17
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Yoshimoto M. Phase-death mode in two-coupled chemical oscillators studied with reactors of different volume and by simulation. Chem Phys Lett 1997. [DOI: 10.1016/s0009-2614(97)01175-5] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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18
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Affiliation(s)
- A. Lekebusch
- Institute of Physical Chemistry, University of Würzburg, Am Hubland, D-97074 Würzburg, Germany
| | - F. W. Schneider
- Institute of Physical Chemistry, University of Würzburg, Am Hubland, D-97074 Würzburg, Germany
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19
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Nevoral V, Votrubová V, Hasal P, Schreiberová L, Marek M. Synchronization of Oscillations and Propagation of Excitations in Circular and Linear Arrays of Coupled CSTRs. J Phys Chem A 1997. [DOI: 10.1021/jp970672k] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- V. Nevoral
- Department of Chemical Engineering and Center for Nonlinear Dynamics of Chemical and Biological Systems, Faculty of Chemical Engineering, Institute of Chemical Technology, Prague, 166 28 Prague 6, Czech Republic
| | - V. Votrubová
- Department of Chemical Engineering and Center for Nonlinear Dynamics of Chemical and Biological Systems, Faculty of Chemical Engineering, Institute of Chemical Technology, Prague, 166 28 Prague 6, Czech Republic
| | - P. Hasal
- Department of Chemical Engineering and Center for Nonlinear Dynamics of Chemical and Biological Systems, Faculty of Chemical Engineering, Institute of Chemical Technology, Prague, 166 28 Prague 6, Czech Republic
| | - L. Schreiberová
- Department of Chemical Engineering and Center for Nonlinear Dynamics of Chemical and Biological Systems, Faculty of Chemical Engineering, Institute of Chemical Technology, Prague, 166 28 Prague 6, Czech Republic
| | - M. Marek
- Department of Chemical Engineering and Center for Nonlinear Dynamics of Chemical and Biological Systems, Faculty of Chemical Engineering, Institute of Chemical Technology, Prague, 166 28 Prague 6, Czech Republic
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Miyakawa K, Okabe T, Mizoguchi M, Sakamoto F. Synchronization in the discrete chemical oscillation system. J Chem Phys 1995. [DOI: 10.1063/1.469977] [Citation(s) in RCA: 27] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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21
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Nishiyama N. Spatial phase pattern in one-dimensional arrays of limit cycle oscillators with discrete coupling. Biophys Chem 1994; 52:139-43. [PMID: 17020828 DOI: 10.1016/0301-4622(94)00090-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/1994] [Accepted: 05/09/1994] [Indexed: 11/23/2022]
Abstract
We present a model of limit cycle oscillators for collective oscillations in intracellular calcium concentration in cell communities. A phase-dependent discrete coupling between nearest neighbors is introduced into the model on the basis of the experimental observation that intercellular transmission of calcium or calcium mobilizing messenger is effected by gap junction and gap junctional permeability is affected by intracellular calcium concentration. The spatial phase pattern of several clusters in which oscillations are in phase is found with the phase-dependent discrete coupling.
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Affiliation(s)
- N Nishiyama
- Department of Chemistry, Fukuoka University of Education 729 Akama, Munakata, Fukuoka 811-41, Japan
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22
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Taylor MA, Pavlou S, Kevrekidis IG. Microbial predation in coupled chemostats: a global study of two coupled nonlinear oscillators. Math Biosci 1994; 122:25-66. [PMID: 8081048 DOI: 10.1016/0025-5564(94)90081-7] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Abstract
Predator-prey systems in continuously operated chemostats exhibit sustained oscillations over a wide range of operating conditions. When two such chemostats interact through flow exchange, the interplay of the oscillation frequencies gives rise to a wealth of dynamic behavior patterns. Using numerical bifurcation techniques, we perform a detailed computational study of these patterns and the transitions between them as the coupling strength and relative frequencies of the two chemostats vary. We concentrate on certain strong resonance phenomena between the two frequencies as well as their mutual extinction and provide a representative sampling of possible phase portraits for our model system. Our observations corroborate recent mathematical results and case studies of coupled nonlinear chemical oscillators in which regions of mutual extinction as well as the Arnol'd structure for two-parameter families of maps of the plane have been observed. We highlight certain unexpected features of the operating diagram discovered through our computational study and discuss their implication for the dynamic response of the chemostat system.
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Affiliation(s)
- M A Taylor
- Department of Chemical Engineering, Princeton University, New Jersey
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23
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Nishiyama N, Eto K. Experimental study on three chemical oscillators coupled with time delay. J Chem Phys 1994. [DOI: 10.1063/1.467015] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Park I, Woo S. Computer simulation of spatial coupling in chemical oscillations of CO oxidation on two Pd(110) single crystals. Chem Phys Lett 1993. [DOI: 10.1016/0009-2614(93)87237-w] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Yoshimoto M, Yoshikawa K, Mori Y. Coupling among three chemical oscillators: Synchronization, phase death, and frustration. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 47:864-874. [PMID: 9960081 DOI: 10.1103/physreve.47.864] [Citation(s) in RCA: 38] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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27
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Yoshimoto M, Yoshikawa K, Mori Y, Hanazaki I. Asymmetric coupling stabilizes the out-of-phase mode: experimental evidence in the Belousov—Zhabotinsky reaction. Chem Phys Lett 1992. [DOI: 10.1016/0009-2614(92)85146-2] [Citation(s) in RCA: 23] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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Electrically Coupled Belousov-Zhabotinskii Oscillators: Experimental Observation of Chaos in a Chemical System and Identification of its Source in the Field-Noyes Equations. ACTA ACUST UNITED AC 1986. [DOI: 10.1007/978-3-642-93318-9_5] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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31
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Crowley MF, Field RJ. Electrically Coupled Belousov-Zhabotinsky Oscillators: A Potential Chaos Generator. NONLINEAR PHENOMENA IN CHEMICAL DYNAMICS 1981. [DOI: 10.1007/978-3-642-81778-6_21] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
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32
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Tagawa S, Schnabel W, Washio M, Tabata Y. Picosecond pulse radiolysis and laser flash photolysis studies on polymer degradation of polystyrene and poly-α-methylstyrene. ACTA ACUST UNITED AC 1981. [DOI: 10.1016/0146-5724(81)90300-9] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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