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Descalzi O, Carvalho MI, Facão M, Brand HR. Dissipative solitons stabilized by nonlinear gradient terms: Time-dependent behavior and generic properties. CHAOS (WOODBURY, N.Y.) 2022; 32:123107. [PMID: 36587340 DOI: 10.1063/5.0118348] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2022] [Accepted: 11/07/2022] [Indexed: 06/17/2023]
Abstract
We study the time-dependent behavior of dissipative solitons (DSs) stabilized by nonlinear gradient terms. Two cases are investigated: first, the case of the presence of a Raman term, and second, the simultaneous presence of two nonlinear gradient terms, the Raman term and the dispersion of nonlinear gain. As possible types of time-dependence, we find a number of different possibilities including periodic behavior, quasi-periodic behavior, and also chaos. These different types of time-dependence are found to form quite frequently from a window structure of alternating behavior, for example, of periodic and quasi-periodic behaviors. To analyze the time dependence, we exploit extensively time series and Fourier transforms. We discuss in detail quantitatively the question whether all the DSs found for the cubic complex Ginzburg-Landau equation with nonlinear gradient terms are generic, meaning whether they are stable against structural perturbations, for example, to the additions of a small quintic perturbation as it arises naturally in an envelope equation framework. Finally, we examine to what extent it is possible to have different types of DSs for fixed parameter values in the equation by just varying the initial conditions, for example, by using narrow and high vs broad and low amplitudes. These results indicate an overlapping multi-basin structure in parameter space.
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Affiliation(s)
- Orazio Descalzi
- Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Av. Mons. Álvaro del Portillo 12.455, Las Condes, Santiago, Chile
| | - M I Carvalho
- DEEC/FEUP and INESC TEC. Universidade do Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
| | - M Facão
- Departamento de Física, Universidade de Aveiro and I3N Campus Universitário de Santiago, 3810-193 Aveiro, Portugal
| | - Helmut R Brand
- Department of Physics, University of Bayreuth, 95440 Bayreuth, Germany
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2
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Yochelis A, Flemming S, Beta C. Versatile Patterns in the Actin Cortex of Motile Cells: Self-Organized Pulses Can Coexist with Macropinocytic Ring-Shaped Waves. PHYSICAL REVIEW LETTERS 2022; 129:088101. [PMID: 36053696 DOI: 10.1103/physrevlett.129.088101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/24/2022] [Accepted: 08/03/2022] [Indexed: 06/15/2023]
Abstract
Self-organized patterns in the actin cytoskeleton are essential for eukaryotic cellular life. They are the building blocks of many functional structures that often operate simultaneously to facilitate, for example, nutrient uptake and movement of cells. However, identifying how qualitatively distinct actin patterns can coexist remains a challenge. Using bifurcation theory of a mass conserved activator-inhibitor system, we uncover a generic mechanism of how different actin waves-traveling waves and excitable pulses-organize and simultaneously emerge. Live-cell imaging experiments indeed reveal that narrow, planar, and fast-moving excitable pulses may coexist with ring-shaped macropinocytic actin waves in the cortex of motile amoeboid cells.
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Affiliation(s)
- Arik Yochelis
- Department of Solar Energy and Environmental Physics, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus, Midreshet Ben-Gurion 8499000, Israel
- Department of Physics, Ben-Gurion University of the Negev, Be'er Sheva 8410501, Israel
| | - Sven Flemming
- Institute of Physics and Astronomy, University of Potsdam, Potsdam 14476, Germany
| | - Carsten Beta
- Institute of Physics and Astronomy, University of Potsdam, Potsdam 14476, Germany
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Descalzi O, Cartes C, Brand HR. Oscillatory dissipative solitons stabilized by nonlinear gradient terms: The transition to localized spatiotemporal disorder. Phys Rev E 2022; 105:L062201. [PMID: 35854493 DOI: 10.1103/physreve.105.l062201] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2022] [Accepted: 05/24/2022] [Indexed: 11/07/2022]
Abstract
We investigate properties of oscillatory dissipative solitons (DSs) in a cubic complex Ginzburg-Landau equation stabilized by nonlinear gradient terms. As a main result we find a transition to dissipative solitons with spatiotemporal disorder as a function of the diffusion coefficient. This transition proceeds via quasiperiodicity and shows incommensurate satellites next to the fundamental frequency and its harmonics indicating a possible route to localized spatiotemporal chaos. The transition back to oscillatory DSs follows a similar scenario.
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Affiliation(s)
- Orazio Descalzi
- Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Chile.,Department of Physics, University of Bayreuth, 95440 Bayreuth, Germany
| | - Carlos Cartes
- Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Chile
| | - Helmut R Brand
- Department of Physics, University of Bayreuth, 95440 Bayreuth, Germany
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Descalzi O, Cartes C, Brand HR. Multiplicative noise can induce a velocity change of propagating dissipative solitons. Phys Rev E 2021; 103:L050201. [PMID: 34134314 DOI: 10.1103/physreve.103.l050201] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2020] [Accepted: 04/13/2021] [Indexed: 11/07/2022]
Abstract
We investigate the influence of spatially homogeneous multiplicative noise on propagating dissipative solitons (DSs) of the cubic complex Ginzburg-Landau equation stabilized by nonlinear gradient terms. Here we focus on the nonlinear gradient terms, in particular on the influence of the Raman term and the delayed nonlinear gain. We show that a fairly small amount of multiplicative noise can lead to a change in the mean velocity for such systems. This effect is exclusively due to the presence of the stabilizing nonlinear gradient terms. For a range of parameters we find a velocity change proportional to the noise intensity for the Raman term and for delayed nonlinear gain. We note that the dissipative soliton decreases the modulus of its velocity when only one type of nonlinear gradient is present. We present a straightforward mean field analysis to capture this simple scaling law. At sufficiently high noise strength the nonlinear gradient stabilized DSs collapse.
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Affiliation(s)
- Orazio Descalzi
- Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, 7620001, Santiago, Chile.,Department of Physics, University of Bayreuth, 95440 Bayreuth, Germany
| | - Carlos Cartes
- Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, 7620001, Santiago, Chile
| | - Helmut R Brand
- Department of Physics, University of Bayreuth, 95440 Bayreuth, Germany
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Descalzi O, Cartes C, Brand HR. Interaction of dissipative solitons stabilized by nonlinear gradient terms. Phys Rev E 2021; 103:042215. [PMID: 34005884 DOI: 10.1103/physreve.103.042215] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2020] [Accepted: 04/02/2021] [Indexed: 06/12/2023]
Abstract
We study the interaction of stable dissipative solitons of the cubic complex Ginzburg-Landau equation which are stabilized only by nonlinear gradient terms. In this paper we focus for the interactions in particular on the influence of the nonlinear gradient term associated with the Raman effect. Depending on its magnitude, we find up to seven possible outcomes of theses collisions: Stationary bound states, oscillatory bound states, meandering oscillatory bound states, bound states with large-amplitude oscillations, partial annihilation, complete annihilation, and interpenetration. Detailed results and their analysis are presented for one value of the corresponding nonlinear gradient term, while the results for two other values are just mentioned briefly. We compare our results with those obtained for coupled cubic-quintic complex Ginzburg-Landau equations and with the cubic-quintic complex Swift-Hohenberg equation. It turns out that both meandering oscillatory bound states as well as bound states with large-amplitude oscillations appear to be specific for coupled cubic complex Ginzburg-Landau equations with a stabilizing cubic nonlinear gradient term. Remarkably, we find for the large-amplitude oscillations a linear relationship between oscillation amplitude and period.
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Affiliation(s)
- Orazio Descalzi
- Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Santiago 7620001, Chile
- Department of Physics, University of Bayreuth, 95440 Bayreuth, Germany
| | - Carlos Cartes
- Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Santiago 7620001, Chile
| | - Helmut R Brand
- Department of Physics, University of Bayreuth, 95440 Bayreuth, Germany
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Beta C, Gov NS, Yochelis A. Why a Large-Scale Mode Can Be Essential for Understanding Intracellular Actin Waves. Cells 2020; 9:cells9061533. [PMID: 32585983 PMCID: PMC7349605 DOI: 10.3390/cells9061533] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2020] [Revised: 06/16/2020] [Accepted: 06/18/2020] [Indexed: 01/18/2023] Open
Abstract
During the last decade, intracellular actin waves have attracted much attention due to their essential role in various cellular functions, ranging from motility to cytokinesis. Experimental methods have advanced significantly and can capture the dynamics of actin waves over a large range of spatio-temporal scales. However, the corresponding coarse-grained theory mostly avoids the full complexity of this multi-scale phenomenon. In this perspective, we focus on a minimal continuum model of activator-inhibitor type and highlight the qualitative role of mass conservation, which is typically overlooked. Specifically, our interest is to connect between the mathematical mechanisms of pattern formation in the presence of a large-scale mode, due to mass conservation, and distinct behaviors of actin waves.
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Affiliation(s)
- Carsten Beta
- Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany;
| | - Nir S. Gov
- Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot 76100, Israel;
| | - Arik Yochelis
- Department of Solar Energy and Environmental Physics, Blaustein Institutes for Desert Research (BIDR), Ben-Gurion University of the Negev, Sede Boqer Campus, Midreshet Ben-Gurion 8499000, Israel
- Department of Physics, Ben-Gurion University of the Negev, Be’er Sheva 8410501, Israel
- Correspondence:
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Descalzi O, Brand HR. Breaking of symmetry of interacting dissipative solitons can lead to partial annihilation. Phys Rev E 2020; 101:040201. [PMID: 32422738 DOI: 10.1103/physreve.101.040201] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2019] [Accepted: 04/05/2020] [Indexed: 11/07/2022]
Abstract
We show that for a large range of approach velocities and over a large interval of stabilizing cubic cross-coupling between counterpropagating waves, a collision of stationary pulses leads to a partial annihilation of pulses via a spontaneous breaking of symmetry. This result arises for coupled cubic-quintic complex Ginzburg-Landau equations for traveling waves for sufficiently large values of the stabilizing cubic cross-coupling and for large enough approach velocities of the pulses. Briefly, we show in addition that the collision of counterpropagating pulses in a system of two coupled cubic Ginzburg-Landau equations with nonlinear gradients (Raman effect) might also lead to partial annihilation, indicating that this breaking of symmetry is generic. Systems of experimental interest include surface reactions, convective onset, biosolitons, and nonlinear optics.
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Affiliation(s)
- Orazio Descalzi
- Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Avenida Monseñor Álvaro del Portillo 12.455, Las Condes, Santiago, Chile.,Department of Physics, University of Bayreuth, 95440 Bayreuth, Germany
| | - Helmut R Brand
- Department of Physics, University of Bayreuth, 95440 Bayreuth, Germany
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Cisternas J, Albers T, Radons G. Normal and anomalous random walks of 2-d solitons. CHAOS (WOODBURY, N.Y.) 2018; 28:075505. [PMID: 30070531 DOI: 10.1063/1.5021586] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Solitons, which describe the propagation of concentrated beams of light through nonlinear media, can exhibit a variety of behaviors as a result of the intrinsic dissipation, diffraction, and the nonlinear effects. One of these phenomena, modeled by the complex Ginzburg-Landau equation, is chaotic explosions, transient enlargements of the soliton that may induce random transversal displacements, which in the long run lead to a random walk of the soliton center. As we show in this work, the transition from nonmoving to moving solitons is not a simple bifurcation but includes a sequence of normal and anomalous random walks. We analyze their statistics with the distribution of generalized diffusivities, a novel approach that has been used successfully for characterizing anomalous diffusion.
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Affiliation(s)
- Jaime Cisternas
- Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Monseñor Alvaro del Portillo 12455, Las Condes, Santiago, Chile
| | - Tony Albers
- Institute of Physics, Chemnitz University of Technology, Chemnitz 09107, Germany
| | - Günter Radons
- Institute of Physics, Chemnitz University of Technology, Chemnitz 09107, Germany
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Gaskins DK, Soohoo JS, Dolnik M, Epstein IR. Birth and Death of Invading Standing Waves in the BZ‐AOT Reaction‐diffusion System. Isr J Chem 2018. [DOI: 10.1002/ijch.201700142] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Affiliation(s)
| | - Jamie S. Soohoo
- Department of Chemistry, Brandeis University Waltham, MA USA 02453
| | - Milos Dolnik
- Department of Chemistry, Brandeis University Waltham, MA USA 02453
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Bozdech S, Biecher Y, Savinova ER, Schuster R, Krischer K, Bonnefont A. Oscillations in an array of bistable microelectrodes coupled through a globally conserved quantity. CHAOS (WOODBURY, N.Y.) 2018; 28:045113. [PMID: 31906625 DOI: 10.1063/1.5022475] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
The dynamical behavior of an array of microelectrodes is investigated under controlled current conditions during CO electrooxidation, a bistable electrochemical reaction with an S-shaped negative differential resistance (S-NDR) current-potential curve. Under these conditions, the total current constitutes a globally conserved quantity, thus coupling all microelectrodes globally. Upon increasing the total current, the microelectrodes activate one by one, with a single microelectrode being on its intermediate S-NDR current branch and the other ones being either on their passive or their active branches. When a few coupled microelectrodes are activated, the electrochemical system exhibits spontaneous potential oscillations. Mathematical analysis shows that oscillations arise already in a two group approximation of the dynamics, the two groups consisting of 1 electrode and n - 1 electrodes with n ≥ 3, respectively, with each group being described by a single evolution equation. In this minimal representation, oscillations occur when the single electrode is on the intermediate branch and the larger group is on the active branch.
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Affiliation(s)
- S Bozdech
- Institut de Chimie des Procédés, pour l'Energie, l'Environnement et la Santé, UMR7515, CNRS-Université de Strasbourg, 25 rue Becquerel, 67087 Strasbourg, France
| | - Y Biecher
- Institut de Chimie des Procédés, pour l'Energie, l'Environnement et la Santé, UMR7515, CNRS-Université de Strasbourg, 25 rue Becquerel, 67087 Strasbourg, France
| | - E R Savinova
- Institut de Chimie des Procédés, pour l'Energie, l'Environnement et la Santé, UMR7515, CNRS-Université de Strasbourg, 25 rue Becquerel, 67087 Strasbourg, France
| | - R Schuster
- Institut für Physikalische Chemie, Karlsruher Institute of Technology, Fritz-Haber-Weg 2, 76131 Karlsruhe, Germany
| | - K Krischer
- Physik Department, Technische Universität München, James-Franck-Str. 1, 85748 Garching, Germany
| | - A Bonnefont
- Institut de Chimie de Strasbourg, UMR7177, CNRS-Université de Strasbourg, 4 rue Blaise Pascal, 67070 Strasbourg, France
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Nkomo S, Tinsley MR, Showalter K. Chimera and chimera-like states in populations of nonlocally coupled homogeneous and heterogeneous chemical oscillators. CHAOS (WOODBURY, N.Y.) 2016; 26:094826. [PMID: 27781438 DOI: 10.1063/1.4962631] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Chimera and chimera-like states are characterized in populations of photochemically coupled Belousov-Zhabotinsky (BZ) oscillators. Simple chimeras and chimera states with multiple and traveling phase clusters, phase-slip behavior, and chimera-like states with phase waves are described. Simulations with a realistic model of the discrete BZ system of populations of homogeneous and heterogeneous oscillators are compared with each other and with experimental behavior.
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Affiliation(s)
- Simbarashe Nkomo
- C. Eugene Bennett Department of Chemistry, West Virginia University, Morgantown, West Virginia 26506-6045, USA
| | - Mark R Tinsley
- C. Eugene Bennett Department of Chemistry, West Virginia University, Morgantown, West Virginia 26506-6045, USA
| | - Kenneth Showalter
- C. Eugene Bennett Department of Chemistry, West Virginia University, Morgantown, West Virginia 26506-6045, USA
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