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Ghosh A, Mondal S, Sujith RI. Occasional coupling enhances amplitude death in delay-coupled oscillators. CHAOS (WOODBURY, N.Y.) 2022; 32:101106. [PMID: 36319273 DOI: 10.1063/5.0110203] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2022] [Accepted: 09/14/2022] [Indexed: 06/16/2023]
Abstract
This paper aims to study amplitude death in time delay coupled oscillators using the occasional coupling scheme that implies intermittent interaction among the oscillators. An enhancement of amplitude death regions (i.e., an increment of the width of the amplitude death regions along the control parameter axis) can be possible using the occasional coupling in a pair of delay-coupled oscillators. Our study starts with coupled limit cycle oscillators (Stuart-Landau) and coupled chaotic oscillators (Rössler). We further examine coupled horizontal Rijke tubes, a prototypical model of thermoacoustic systems. Oscillatory states are highly detrimental to thermoacoustic systems such as combustors. Consequently, a state of amplitude death is always preferred. We employ the on-off coupling (i.e., a square wave function), as an occasional coupling scheme, to these coupled oscillators. On monotonically varying the coupling strength (as a control parameter), we observe an enhancement of amplitude death regions using the occasional coupling scheme compared to the continuous coupling scheme. In order to study the contribution of the occasional coupling scheme, we perform a detailed linear stability analysis and analytically explain this enhancement of the amplitude death region for coupled limit cycle oscillators. We also adopt the frequency ratio of the oscillators and the time delay between the oscillators as the control parameters. Intriguingly, we obtain a similar enhancement of the amplitude death regions using the frequency ratio and time delay as the control parameters in the presence of the occasional coupling. Finally, we use a half-wave rectified sinusoidal wave function (motivated by practical reality) to introduce the occasional coupling in time delay coupled oscillators and get similar results.
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Affiliation(s)
- Anupam Ghosh
- Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai, Tamil Nadu 600036, India
| | - Sirshendu Mondal
- Department of Mechanical Engineering, National Institute of Technology Durgapur, Durgapur, West Bengal 713209, India
| | - R I Sujith
- Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai, Tamil Nadu 600036, India
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2
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Doranehgard MH, Gupta V, Li LKB. Quenching and amplification of thermoacoustic oscillations in two nonidentical Rijke tubes interacting via time-delay and dissipative coupling. Phys Rev E 2022; 105:064206. [PMID: 35854581 DOI: 10.1103/physreve.105.064206] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2022] [Accepted: 05/23/2022] [Indexed: 06/15/2023]
Abstract
We numerically explore the quenching and amplification of self-excited thermoacoustic oscillations in two nonidentical Rijke tubes interacting via time-delay and dissipative coupling. On applying either type of coupling separately, we find that the presence of nonidentical heater powers can shrink the regions of amplitude death in both oscillators, while producing new regions of amplitude amplification in the weaker oscillator. We find that the magnitude of amplitude amplification grows with the heater power mismatch and with the total power input. These effects are also present when both types of coupling are applied simultaneously. This study highlights the critical role that nonidentical thermal loads can play in determining the amplitude response of coupled thermoacoustic systems, facilitating the design of control strategies for coupled oscillatorlike devices such as gas turbines.
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Affiliation(s)
- Mohammad Hossein Doranehgard
- Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong
| | - Vikrant Gupta
- Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, China and Guangdong-Hong-Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications, Southern University of Science and Technology, Shenzhen, China
| | - Larry K B Li
- Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong and Guangdong-Hong-Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong
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3
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Exothermic reactions on the heterogeneous catalysts: Features of research and implementation. Chem Eng Res Des 2021. [DOI: 10.1016/j.cherd.2021.07.021] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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4
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Dixit S, Asir M P, Dev Shrimali M. Aging in global networks with competing attractive-Repulsive interaction. CHAOS (WOODBURY, N.Y.) 2020; 30:123112. [PMID: 33380009 DOI: 10.1063/5.0026968] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2020] [Accepted: 11/10/2020] [Indexed: 06/12/2023]
Abstract
We study the dynamical inactivity of the global network of identical oscillators in the presence of mixed attractive and repulsive coupling. We consider that the oscillators are a priori in all to all attractive coupling and then upon increasing the number of oscillators interacting via repulsive interaction, the whole network attains a steady state at a critical fraction of repulsive nodes, pc. The macroscopic inactivity of the network is found to follow a typical aging transition due to competition between attractive-repulsive interactions. The analytical expression connecting the coupling strength and pc is deduced and corroborated with numerical outcomes. We also study the influence of asymmetry in the attractive-repulsive interaction, which leads to symmetry breaking. We detect chimera-like and mixed states for a certain ratio of coupling strengths. We have verified sequential and random modes to choose the repulsive nodes and found that the results are in agreement. The paradigmatic networks with diverse dynamics, viz., limit cycle (Stuart-Landau), chaos (Rössler), and bursting (Hindmarsh-Rose neuron), are analyzed.
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Affiliation(s)
- Shiva Dixit
- Department of Physics, Central University of Rajasthan, NH-8, Bandar Sindri, Ajmer 305 817, India
| | - Paul Asir M
- Department of Physics, Central University of Rajasthan, NH-8, Bandar Sindri, Ajmer 305 817, India
| | - Manish Dev Shrimali
- Department of Physics, Central University of Rajasthan, NH-8, Bandar Sindri, Ajmer 305 817, India
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Lei X, Liu W, Zou W, Kurths J. Coexistence of oscillation and quenching states: Effect of low-pass active filtering in coupled oscillators. CHAOS (WOODBURY, N.Y.) 2019; 29:073110. [PMID: 31370423 DOI: 10.1063/1.5093919] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2019] [Accepted: 06/21/2019] [Indexed: 06/10/2023]
Abstract
Effects of a low-pass active filter (LPAF) on the transition processes from oscillation quenching to asymmetrical oscillation are explored for diffusively coupled oscillators. The low-pass filter part and the active part of LPAF exhibit different effects on the dynamics of these coupled oscillators. With the amplifying active part only, LPAF keeps the coupled oscillators staying in a nontrivial amplitude death (NTAD) and oscillation state. However, the additional filter is beneficial to induce a transition from a symmetrical oscillation death to an asymmetrical oscillation death and then to an asymmetrical oscillation state which is oscillating with different amplitudes for two oscillators. Asymmetrical oscillation state is coexisting with a synchronous oscillation state for properly presented parameters. With the attenuating active part only, LPAF keeps the coupled oscillators in rich oscillation quenching states such as amplitude death (AD), symmetrical oscillation death (OD), and NTAD. The additional filter tends to enlarge the AD domains but to shrink the symmetrical OD domains by increasing the areas of the coexistence of the oscillation state and the symmetrical OD state. The stronger filter effects enlarge the basin of the symmetrical OD state which is coexisting with the synchronous oscillation state. Moreover, the effects of the filter are general in globally coupled oscillators. Our results are important for understanding and controlling the multistability of coupled systems.
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Affiliation(s)
- Xiaoqi Lei
- School of Science, Jiangxi University of Science and Technology, Ganzhou341000, China
| | - Weiqing Liu
- School of Science, Jiangxi University of Science and Technology, Ganzhou341000, China
| | - Wei Zou
- School of Mathematical Sciences, South China Normal University, Guangzhou510631, People's Republic of China
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, Telegraphenberg, D-14415 Potsdam, Germany
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6
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Liu W, Lei X, Chen J. Effects of periodically modulated coupling on amplitude death in nonidentical oscillators. ACTA ACUST UNITED AC 2019. [DOI: 10.1209/0295-5075/125/50004] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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7
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Sathiyadevi K, Chandrasekar VK, Senthilkumar DV, Lakshmanan M. Distinct collective states due to trade-off between attractive and repulsive couplings. Phys Rev E 2018; 97:032207. [PMID: 29776099 DOI: 10.1103/physreve.97.032207] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2018] [Indexed: 06/08/2023]
Abstract
We investigate the effect of repulsive coupling together with an attractive coupling in a network of nonlocally coupled oscillators. To understand the complex interaction between these two couplings we introduce a control parameter in the repulsive coupling which plays a crucial role in inducing distinct complex collective patterns. In particular, we show the emergence of various cluster chimera death states through a dynamically distinct transition route, namely the oscillatory cluster state and coherent oscillation death state as a function of the repulsive coupling in the presence of the attractive coupling. In the oscillatory cluster state, the oscillators in the network are grouped into two distinct dynamical states of homogeneous and inhomogeneous oscillatory states. Further, the network of coupled oscillators follow the same transition route in the entire coupling range. Depending upon distinct coupling ranges, the system displays different number of clusters in the death state and oscillatory state. We also observe that the number of coherent domains in the oscillatory cluster state exponentially decreases with increase in coupling range and obeys a power-law decay. Additionally, we show analytical stability for observed solitary state, synchronized state, and incoherent oscillation death state.
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Affiliation(s)
- K Sathiyadevi
- Centre for Nonlinear Science & Engineering, School of Electrical & Electronics Engineering, SASTRA Deemed University, Thanjavur-613 401, Tamil Nadu, India
| | - V K Chandrasekar
- Centre for Nonlinear Science & Engineering, School of Electrical & Electronics Engineering, SASTRA Deemed University, Thanjavur-613 401, Tamil Nadu, India
| | - D V Senthilkumar
- School of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram-695016, India
| | - M Lakshmanan
- Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli-620 024, Tamil Nadu, India
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Thomas N, Mondal S, Pawar SA, Sujith RI. Effect of time-delay and dissipative coupling on amplitude death in coupled thermoacoustic oscillators. CHAOS (WOODBURY, N.Y.) 2018; 28:033119. [PMID: 29604646 DOI: 10.1063/1.5009999] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We here systematically investigate amplitude death (AD) phenomenon in a thermoacoustic system using a mathematical model of coupled prototypical thermoacoustic oscillators, the horizontal Rijke tubes. AD has recently been identified as a relatively simple phenomenon, which can be exploited to stop the unwanted high amplitude pressure oscillations resulting from the occurrence of thermoacoustic instability. We examine the effect of time-delay and dissipative couplings on a system of two Rijke tubes when they are symmetrically and asymmetrically coupled. The regions where appropriate combinations of delay time, detuning, and the strengths of time-delay and dissipative coupling lead to AD are identified. The relative ease of attaining AD when both the couplings are applied simultaneously is inferred from the model. In the presence of strong enough coupling, AD is observed even when the oscillators of dissimilar amplitudes are coupled, while a significant reduction in the amplitudes of both the oscillators is observed when the coupling strength is not enough to attain AD.
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Affiliation(s)
- Nevin Thomas
- Indian Institute of Technology Madras, Chennai 600036, India
| | | | | | - R I Sujith
- Indian Institute of Technology Madras, Chennai 600036, India
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Schneider I, Kapeller M, Loos S, Zakharova A, Fiedler B, Schöll E. Stable and transient multicluster oscillation death in nonlocally coupled networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:052915. [PMID: 26651770 DOI: 10.1103/physreve.92.052915] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2015] [Indexed: 05/03/2023]
Abstract
In a network of nonlocally coupled Stuart-Landau oscillators with symmetry-breaking coupling, we study numerically, and explain analytically, a family of inhomogeneous steady states (oscillation death). They exhibit multicluster patterns, depending on the cluster distribution prescribed by the initial conditions. Besides stable oscillation death, we also find a regime of long transients asymptotically approaching synchronized oscillations. To explain these phenomena analytically in dependence on the coupling range and the coupling strength, we first use a mean-field approximation, which works well for large coupling ranges but fails for coupling ranges, which are small compared to the cluster size. Going beyond standard mean-field theory, we predict the boundaries of the different stability regimes as well as the transient times analytically in excellent agreement with numerical results.
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Affiliation(s)
- Isabelle Schneider
- Institut für Mathematik, Freie Universität Berlin, Arnimallee 7, 14195 Berlin, Germany
| | - Marie Kapeller
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
| | - Sarah Loos
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
| | - Anna Zakharova
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
| | - Bernold Fiedler
- Institut für Mathematik, Freie Universität Berlin, Arnimallee 7, 14195 Berlin, Germany
| | - Eckehard Schöll
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
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10
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Kamal NK, Sharma PR, Shrimali MD. Oscillation suppression in indirectly coupled limit cycle oscillators. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:022928. [PMID: 26382496 DOI: 10.1103/physreve.92.022928] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2015] [Indexed: 06/05/2023]
Abstract
We study the phenomena of oscillation quenching in a system of limit cycle oscillators which are coupled indirectly via a dynamic environment. The dynamics of the environment is assumed to decay exponentially with some decay parameter. We show that for appropriate coupling strength, the decay parameter of the environment plays a crucial role in the emergent dynamics such as amplitude death (AD) and oscillation death (OD). The critical curves for the regions of oscillation quenching as a function of coupling strength and decay parameter of the environment are obtained analytically using linear stability analysis and are found to be consistent with the numerics.
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Affiliation(s)
- Neeraj Kumar Kamal
- Department of Physics, Central University of Rajasthan, Ajmer 305 817, India
| | - Pooja Rani Sharma
- Department of Physics, Central University of Rajasthan, Ajmer 305 817, India
| | - Manish Dev Shrimali
- Department of Physics, Central University of Rajasthan, Ajmer 305 817, India
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11
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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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12
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Banerjee T, Ghosh D. Experimental observation of a transition from amplitude to oscillation death in coupled oscillators. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:062902. [PMID: 25019846 DOI: 10.1103/physreve.89.062902] [Citation(s) in RCA: 32] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2014] [Indexed: 06/03/2023]
Abstract
We report the experimental evidence of an important transition scenario, namely the transition from amplitude death (AD) to oscillation death (OD) state in coupled limit cycle oscillators. We consider two Van der Pol oscillators coupled through mean-field diffusion and show that this system exhibits a transition from AD to OD, which was earlier shown for Stuart-Landau oscillators under the same coupling scheme [T. Banerjee and D. Ghosh, Phys. Rev. E 89, 052912 (2014)]. We show that the AD-OD transition is governed by the density of mean-field and beyond a critical value this transition is destroyed; further, we show the existence of a nontrivial AD state that coexists with OD. Next, we implement the system in an electronic circuit and experimentally confirm the transition from AD to OD state. We further characterize the experimental parameter zone where this transition occurs. The present study may stimulate the search for the practical systems where this important transition scenario can be observed experimentally.
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Affiliation(s)
- Tanmoy Banerjee
- Department of Physics, University of Burdwan, Burdwan 713 104, West Bengal, India
| | - Debarati Ghosh
- Department of Physics, University of Burdwan, Burdwan 713 104, West Bengal, India
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13
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Zakharova A, Kapeller M, Schöll E. Chimera death: symmetry breaking in dynamical networks. PHYSICAL REVIEW LETTERS 2014; 112:154101. [PMID: 24785041 DOI: 10.1103/physrevlett.112.154101] [Citation(s) in RCA: 152] [Impact Index Per Article: 15.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2014] [Indexed: 05/03/2023]
Abstract
For a network of generic oscillators with nonlocal topology and symmetry-breaking coupling we establish novel partially coherent inhomogeneous spatial patterns, which combine the features of chimera states (coexisting incongruous coherent and incoherent domains) and oscillation death (oscillation suppression), which we call "chimera death". We show that due to the interplay of nonlocality and breaking of rotational symmetry by the coupling, two distinct scenarios from oscillatory behavior to a stationary state regime are possible: a transition from an amplitude chimera to chimera death via in-phase synchronized oscillations and a direct abrupt transition for larger coupling strength.
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Affiliation(s)
- Anna Zakharova
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
| | - Marie Kapeller
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
| | - Eckehard Schöll
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
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Zou W, Senthilkumar DV, Koseska A, Kurths J. Generalizing the transition from amplitude to oscillation death in coupled oscillators. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:050901. [PMID: 24329205 DOI: 10.1103/physreve.88.050901] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2013] [Indexed: 06/03/2023]
Abstract
Amplitude death (AD) and oscillation death (OD) are two structurally different oscillation quenching types in coupled nonlinear oscillators. The transition from AD to OD has been recently realized due to the interplay between heterogeneity and coupling strength [A. Koseska et al., Phys. Rev. Lett. 111, 024103 (2013)]. We identify here the transition from AD to OD in nonlinear oscillators with couplings of distinct natures. It is demonstrated that the presence of time delay in the coupling cannot induce such a transition in identical oscillators, but it can indeed facilitate its occurrence with a low degree of heterogeneity. Moreover, it is further shown that the AD to OD transition is reliably observed in identical oscillators with dynamic and conjugate couplings. The coexistence of AD and OD and rich stable OD configurations after the transition are revealed, which are of great significance for potential applications in physics, biology, and control studies.
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Affiliation(s)
- Wei Zou
- School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
| | - D V Senthilkumar
- Potsdam Institute for Climate Impact Research, Telegraphenberg, Potsdam D-14415, Germany
| | - Aneta Koseska
- Department of Systemic Cell Biology, Max Planck Institute of Molecular Physiology, Dortmund D-44227, Germany
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, Telegraphenberg, Potsdam D-14415, Germany and Institute of Physics, Humboldt University Berlin, Berlin D-12489, Germany and Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB24 3FX, United Kingdom
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15
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Kohout M, Hasal P, Schreiber I. Modeling of coupled enzyme membrane oscillators—Effects of an electric field. Chem Eng Sci 2012. [DOI: 10.1016/j.ces.2012.01.041] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
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16
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Krasnyk M, Ginkel M, Mangold M, Kienle A. Numerical analysis of higher order singularities in chemical process models. Comput Chem Eng 2007. [DOI: 10.1016/j.compchemeng.2006.09.010] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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17
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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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Zeyer KP, Mangold M, Shah S, Kienle A, Gilles ED. Yield Effects in Single and Coupled Nonlinear Thermokinetic Reaction Systems. Z PHYS CHEM 2002. [DOI: 10.1524/zpch.2002.216.4.403] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
Abstract
The influence of nonlinear dynamic effects on yield is considered for consecutive-parallel reaction schemes in a single phase CSTR. In the first part, the behavior of a single uncoupled reactor is investigated. Emphasis is on the reaction dynamics and the yield of the intermediate ethanal using continuation and optimization techniques. We characterize regions of periodic, complex periodic, and chaotic oscillations. The chaotic region is reached by type III intermittency. In all cases, the global optimum yield of the intermediate is a steady state, which is unstable or stable due to the location of the stability boundary. It is found that autonomous periodic operation is only locally better than steady state operation. In the second part, different types of mass and energy coupling between two reactors are studied. The results obtained for a simple consecutive parallel reaction scheme are validated by a more detailed model of the ethanol oxidation by hydrogen peroxide under iron(III) catalysis, which can be described by an extended consecutive-parallel reaction scheme. Analogies are found with respect to the dynamics and the yield of the intermediate.
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