1
|
Parra-Rivas P, Matías MA, Colet P, Gelens L, Walgraef D, Gomila D. Front interaction induces excitable behavior. Phys Rev E 2017; 95:020201. [PMID: 28297869 DOI: 10.1103/physreve.95.020201] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2016] [Indexed: 11/07/2022]
Abstract
Spatially extended systems can support local transient excitations in which just a part of the system is excited. The mechanisms reported so far are local excitability and excitation of a localized structure. Here we introduce an alternative mechanism based on the coexistence of two homogeneous stable states and spatial coupling. We show the existence of a threshold for perturbations of the homogeneous state. Subthreshold perturbations decay exponentially. Superthreshold perturbations induce the emergence of a long-lived structure formed by two back to back fronts that join the two homogeneous states. While in typical excitability the trajectory follows the remnants of a limit cycle, here reinjection is provided by front interaction, such that fronts slowly approach each other until eventually annihilating. This front-mediated mechanism shows that extended systems with no oscillatory regimes can display excitability.
Collapse
Affiliation(s)
- P Parra-Rivas
- Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain.,Applied Physics Research Group, APHY, Vrije Universiteit Brussel, 1050 Brussels, Belgium
| | - M A Matías
- Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
| | - P Colet
- Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
| | - L Gelens
- Applied Physics Research Group, APHY, Vrije Universiteit Brussel, 1050 Brussels, Belgium.,Laboratory of Dynamics in Biological Systems, Department of Cellular and Molecular Medicine, University of Leuven (KU Leuven), B-3000 Leuven, Belgium
| | - D Walgraef
- Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
| | - D Gomila
- Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
| |
Collapse
|
2
|
Chapter 9 Non-linear Dynamics in Catalytic Reactions. ACTA ACUST UNITED AC 2008. [DOI: 10.1016/s1573-4331(08)00009-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
|
3
|
Yang L, Berenstein I, Epstein IR. Segmented waves from a spatiotemporal transverse wave instability. PHYSICAL REVIEW LETTERS 2005; 95:038303. [PMID: 16090777 DOI: 10.1103/physrevlett.95.038303] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2005] [Indexed: 05/03/2023]
Abstract
We observe traveling waves emitted from Turing spots in the chlorine dioxide-iodine-malonic acid reaction. The newborn waves are continuous, but they break into segments as they propagate, and the propagation of these segments ultimately gives rise to spatiotemporal chaos. We model the wave-breaking process and the motion of the chaotic segments. We find stable segmented spirals as well. We attribute the segmentation to an interaction between front rippling via a transverse instability and front symmetry breaking by a fast-diffusing inhibitor far from the codimension-2 Hopf-Turing bifurcation, and the chaos to a secondary instability of the periodic segmentation.
Collapse
Affiliation(s)
- Lingfa Yang
- Department of Chemistry and Volen Center for Complex Systems, MS 015, Brandeis University, Waltham, MA 02454-9110, USA
| | | | | |
Collapse
|
4
|
Monine M, Pismen L. Reconstruction and roughening of a catalytic Pt(110) surface coupled to kinetic oscillations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:051601. [PMID: 12513492 DOI: 10.1103/physreve.66.051601] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2002] [Indexed: 05/24/2023]
Abstract
Three-dimensional reconstruction and roughening of a Pt(110) surface is studied with the help of a qualitative Monte Carlo model. A distinct CO adsorption uptake on different surface phases is taken into account. The computations show that a "missing row" structure with defects relaxes to a more stable (111)-faceted structure. The CO+O2 reaction kinetics is modeled by a phenomenological equation with a cubic nonlinearity reproducing a correct qualitative picture of oscillations. The surface roughening developing under the reaction conditions causes slow changes in catalytic activity of the surface. A nanoscale front between the 1x1 and 1x2 phases disintegrates due to repeated phase transitions caused by CO coverage oscillations. Defect formation and roughening dominate the dynamics of surface phase transitions. A one-dimensional extension of the model reproduces microscopic traveling waves on the CO diffusion scale.
Collapse
Affiliation(s)
- Michael Monine
- Department of Chemical Engineering, Technion, 32000 Technion City, Haifa, Israel
| | | |
Collapse
|
5
|
Monine M, Pismen L, Bär M, Or-Guil M. Modeling triangular titration fronts in the O2+H2 reaction on a catalytic Rh(111) surface. J Chem Phys 2002. [DOI: 10.1063/1.1496481] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|