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Luis Ocampo-Espindola J, Singhal B, Li JS, Kiss IZ. Optimal phase-selective entrainment of electrochemical oscillators with different phase response curves. CHAOS (WOODBURY, N.Y.) 2024; 34:073129. [PMID: 38995992 DOI: 10.1063/5.0205480] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/26/2024] [Accepted: 06/25/2024] [Indexed: 07/14/2024]
Abstract
We investigate the entrainment of electrochemical oscillators with different phase response curves (PRCs) using a global signal: the goal is to achieve the desired phase configuration using a minimum-power waveform. Establishing the desired phase relationships in a highly nonlinear networked system exhibiting significant heterogeneities, such as different conditions or parameters for the oscillators, presents a considerable challenge because different units respond differently to the common global entraining signal. In this work, we apply an optimal phase-selective entrainment technique in both a kinetic model and experiments involving electrochemical oscillators in achieving phase synchronized states. We estimate the PRCs of the oscillators at different circuit potentials and external resistance, and entrain pairs and small sets of four oscillators in various phase configurations. We show that for small PRC variations, phase assignment can be achieved using an averaged PRC in the control design. However, when the PRCs are sufficiently different, individual PRCs are needed to entrain the system with the expected phase relationships. The results show that oscillator assemblies with heterogeneous PRCs can be effectively entrained to desired phase configurations in practical settings. These findings open new avenues to applications in biological and engineered oscillator systems where synchronization patterns are essential for system performance.
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Affiliation(s)
| | - Bharat Singhal
- Department of Electrical & Systems Engineering, Washington University in St Louis, St Louis, Missouri 63130, USA
| | - Jr-Shin Li
- Department of Electrical & Systems Engineering, Washington University in St Louis, St Louis, Missouri 63130, USA
| | - István Z Kiss
- Department of Chemistry, Saint Louis University, St. Louis, Missouri 63103, USA
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Liu Y, Pérez-Mercader J, Kiss IZ. Synchronization of Belousov-Zhabotinsky oscillators with electrochemical coupling in a spontaneous process. CHAOS (WOODBURY, N.Y.) 2022; 32:093128. [PMID: 36182363 DOI: 10.1063/5.0096689] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/20/2022] [Accepted: 08/22/2022] [Indexed: 06/16/2023]
Abstract
A passive electrochemical coupling approach is proposed to induce spontaneous synchronization between chemical oscillators. The coupling exploits the potential difference between a catalyst redox couple in the Belousov-Zhabotinsky (BZ) reaction, without external feedback, to induce surface reactions that impact the kinetics of the bulk system. The effect of coupling in BZ oscillators under batch condition is characterized using phase synchronization measures. Although the frequency of the oscillators decreases nonlinearly over time, by a factor of 2 or more within 100 cycles, the coupling is strong enough to maintain synchronization. In such a highly drifting system, the Gibbs-Shannon entropy of the cyclic phase difference distribution can be used to quantify the coupling effect. We extend the Oregonator BZ model to account for the drifting natural frequencies in batch condition and for electrochemical coupling, and numerical simulations of the effect of acid concentration on synchronization patterns are in agreement with the experiments. Because of the passive nature of coupling, the proposed coupling scheme can open avenues for designing pattern recognition and neuromorphic computation systems using chemical reactions in a spontaneous process.
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Affiliation(s)
- Yifan Liu
- Department of Earth and Planetary Sciences, Harvard Origins of Life Initiative, Harvard University, 20 Oxford Street, Cambridge, Massachusetts 02138, USA
| | - Juan Pérez-Mercader
- Department of Earth and Planetary Sciences, Harvard Origins of Life Initiative, Harvard University, 20 Oxford Street, Cambridge, Massachusetts 02138, USA
| | - István Z Kiss
- Department of Chemistry, Saint Louis University, 3501 Laclede Ave., St. Louis, Missouri 63103, USA
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Anesiadis K, Provata A. Synchronization in Multiplex Leaky Integrate-and-Fire Networks With Nonlocal Interactions. FRONTIERS IN NETWORK PHYSIOLOGY 2022; 2:910862. [PMID: 36926067 PMCID: PMC10013047 DOI: 10.3389/fnetp.2022.910862] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2022] [Accepted: 05/25/2022] [Indexed: 11/13/2022]
Abstract
We study synchronization phenomena in a multiplex network composed of two rings with identical Leaky Integrate-and-Fire (LIF) oscillators located on the nodes of the rings. Within each ring the LIF oscillators interact nonlocally, while between rings there are one-to-one inter-ring interactions. This structure is motivated by the observed connectivity between the two hemispheres of the brain: within each hemisphere the various brain regions interact with neighboring regions, while across hemispheres each region interacts, primarily, with the functionally homologous region. We consider both positive (excitatory) and negative (inhibitory) linking. We identify numerically various parameter regimes where the multiplex network develops coexistence of active and subthreshold domains, chimera states, solitary states, full coherence or incoherence. In particular, for weak inter-ring coupling (weak multiplexing) different synchronization patterns on the two rings are supported. These are stable and are obtained when the intra-ring coupling values are near the critical points separating qualitatively distinct synchronization regimes, e.g., between the travelling fronts regime and the chimera state one.
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Affiliation(s)
- K Anesiadis
- Institute of Nanoscience and Nanotechnology, National Center for Scientific Research "Demokritos", Athens, Greece.,School of Applied Mathematical and Physical Sciences, National Technical University of Athens, Athens, Greece
| | - A Provata
- Institute of Nanoscience and Nanotechnology, National Center for Scientific Research "Demokritos", Athens, Greece
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Novičenko V, Ratas I. Unstable delayed feedback control to change sign of coupling strength for weakly coupled limit cycle oscillators. CHAOS (WOODBURY, N.Y.) 2021; 31:093138. [PMID: 34598474 DOI: 10.1063/5.0033391] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2020] [Accepted: 09/07/2021] [Indexed: 06/13/2023]
Abstract
Weakly coupled limit cycle oscillators can be reduced into a system of weakly coupled phase models. These phase models are helpful to analyze the synchronization phenomena. For example, a phase model of two oscillators has a one-dimensional differential equation for the evolution of the phase difference. The existence of fixed points determines frequency-locking solutions. By treating each oscillator as a black-box possessing a single input and a single output, one can investigate various control algorithms to change the synchronization of the oscillators. In particular, we are interested in a delayed feedback control algorithm. Application of this algorithm to the oscillators after a subsequent phase reduction should give the same phase model as in the control-free case, but with a rescaled coupling strength. The conventional delayed feedback control is limited to the change of magnitude but does not allow the change of sign of the coupling strength. In this work, we present a modification of the delayed feedback algorithm supplemented by an additional unstable degree of freedom, which is able to change the sign of the coupling strength. Various numerical calculations performed with Landau-Stuart and FitzHugh-Nagumo oscillators show successful switching between an in-phase and anti-phase synchronization using the provided control algorithm. Additionally, we show that the control force becomes non-invasive if our objective is stabilization of an unstable phase difference for two coupled oscillators.
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Affiliation(s)
- Viktor Novičenko
- Faculty of Physics, Vilnius University, Saulėtekio ave. 3, LT-10222 Vilnius, Lithuania
| | - Irmantas Ratas
- Center for Physical Sciences and Technology, Saulėtekio ave. 3, LT-10222 Vilnius, Lithuania
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Sebek M, Kawamura Y, Nott AM, Kiss IZ. Anti-phase collective synchronization with intrinsic in-phase coupling of two groups of electrochemical oscillators. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2019; 377:20190095. [PMID: 31656145 PMCID: PMC6833994 DOI: 10.1098/rsta.2019.0095] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 09/05/2019] [Indexed: 05/02/2023]
Abstract
The synchronization of two groups of electrochemical oscillators is investigated during the electrodissolution of nickel in sulfuric acid. The oscillations are coupled through combined capacitance and resistance, so that in a single pair of oscillators (nearly) in-phase synchronization is obtained. The internal coupling within each group is relatively strong, but there is a phase difference between the fast and slow oscillators. The external coupling between the two groups is weak. The experiments show that the two groups can exhibit (nearly) anti-phase collective synchronization. Such synchronization occurs only when the external coupling is weak, and the interactions are delayed by the capacitance. When the external coupling is restricted to those between the fast and the slow elements, the anti-phase synchronization is more prominent. The results are interpreted with phase models. The theory predicts that, for anti-phase collective synchronization, there must be a minimum internal phase difference for a given shift in the phase coupling function. This condition is less stringent with external fast-to-slow coupling. The results provide a framework for applications of collective phase synchronization in modular networks where weak coupling between the groups can induce synchronization without rearrangements of the phase dynamics within the groups. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.
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Affiliation(s)
- Michael Sebek
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St Louis, MO 63103, USA
| | - Yoji Kawamura
- Center for Mathematical Science and Advanced Technology, Japan Agency for Marine-Earth Science and Technology, 236-0001 Yokohama, Japan
| | - Ashley M. Nott
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St Louis, MO 63103, USA
| | - István Z. Kiss
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St Louis, MO 63103, USA
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Stankovski T, Pereira T, McClintock PVE, Stefanovska A. Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2019; 377:20190039. [PMID: 31656134 PMCID: PMC6834002 DOI: 10.1098/rsta.2019.0039] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Accepted: 08/13/2019] [Indexed: 06/10/2023]
Abstract
Dynamical systems are widespread, with examples in physics, chemistry, biology, population dynamics, communications, climatology and social science. They are rarely isolated but generally interact with each other. These interactions can be characterized by coupling functions-which contain detailed information about the functional mechanisms underlying the interactions and prescribe the physical rule specifying how each interaction occurs. Coupling functions can be used, not only to understand, but also to control and predict the outcome of the interactions. This theme issue assembles ground-breaking work on coupling functions by leading scientists. After overviewing the field and describing recent advances in the theory, it discusses novel methods for the detection and reconstruction of coupling functions from measured data. It then presents applications in chemistry, neuroscience, cardio-respiratory physiology, climate, electrical engineering and social science. Taken together, the collection summarizes earlier work on coupling functions, reviews recent developments, presents the state of the art, and looks forward to guide the future evolution of the field. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.
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Affiliation(s)
- Tomislav Stankovski
- Department of Physics, Lancaster University, Lancaster LA1 4YB, UK
- Faculty of Medicine, Ss Cyril and Methodius University, Skopje 1000, Macedonia
| | - Tiago Pereira
- Department of Mathematics, Imperial College London, London SW7 2AZ, UK
- Institute of Mathematical and Computer Sciences, University of Sao Paulo, Sao Carlos 13566-590, Brazil
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Fengler E, Totz JF, Kaluza P, Engel H. Directed adaptation of synchronization levels in oscillator communities. CHAOS (WOODBURY, N.Y.) 2019; 29:063101. [PMID: 31266320 DOI: 10.1063/1.5094490] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2019] [Accepted: 05/13/2019] [Indexed: 06/09/2023]
Abstract
We present an adaptive control scheme that realizes desired dynamics of an oscillator network with a given number of communities by adjusting the coupling weights between oscillators accordingly. The scheme allows, for example, to simultaneously establish different pregiven synchronization levels in the particular communities as well as phase relationships between them. We apply the method in numerical simulations with all-to-all and randomly coupled networks. Moreover, we provide an experimental proof of concept validating our numerical findings in a network of optically coupled photosensitive chemical micro-oscillators.
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Affiliation(s)
- Enrico Fengler
- Technische Universität Berlin, Institut für Theoretische Physik, Hardenbergstraße 36, EW 7-1, 10623 Berlin, Germany
| | - Jan Frederik Totz
- Technische Universität Berlin, Institut für Theoretische Physik, Hardenbergstraße 36, EW 7-1, 10623 Berlin, Germany
| | - Pablo Kaluza
- National Scientific and Technical Research Council & Faculty of Exact and Natural Sciences, National University of Cuyo, Padre Contreras 1300, 5500 Mendoza, Argentina
| | - Harald Engel
- Technische Universität Berlin, Institut für Theoretische Physik, Hardenbergstraße 36, EW 7-1, 10623 Berlin, Germany
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