Control of chemical wave propagation

Using the Schl\"{o}gl model as a paradigmatic example of a bistable reaction-diffusion system, we discuss some physically feasible options of open and closed loop spatio-temporal control of chemical wave propagation.

[1]  Stefania Residori,et al.  Patterns, fronts and structures in a Liquid-Crystal-Light-Valve with optical feedback , 2005 .

[2]  E. Schöll.  Pattern Formation and Time Delayed Feedback Control at the Nanoscale , 2010 .

[3]  H Engel,et al.  Global control of spiral wave dynamics in an excitable domain of circular and elliptical shape. , 2004, Physical review letters.

[4]  B. Malomed,et al.  Pulled fronts in the Cahn–Hilliard equation , 2002 .

[5]  P. Colet,et al.  Formation of localized structures in bistable systems through nonlocal spatial coupling. II. The nonlocal Ginzburg-Landau equation. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Kenneth Showalter,et al.  Chemical waves and patterns , 1995 .

[7]  Breathing current domains in globally coupled electrochemical systems: a comparison with a semiconductor model. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Yoshiki Kuramoto,et al.  Rotating spiral waves with phase-randomized core in nonlocally coupled oscillators. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Kenneth Showalter,et al.  Control of waves, patterns and turbulence in chemical systems , 2006 .

[10]  H. Sompolinsky,et al.  Mexican hats and pinwheels in visual cortex , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[11]  M. Or-Guil,et al.  Drifting pattern domains in a reaction-diffusion system with nonlocal coupling. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Philipp Hövel,et al.  Stabilization of complex spatio-temporal dynamics near a subcritical Hopf bifurcation by time-delayed feedback , 2009 .

[13]  Kenneth Showalter,et al.  Feedback stabilization of unstable propagating waves. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  P. Colet,et al.  Formation of localized structures in bistable systems through nonlocal spatial coupling. I. General framework. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Alexander S. Mikhailov,et al.  Controlling Chemical Turbulence by Global Delayed Feedback: Pattern Formation in Catalytic CO Oxidation on Pt(110) , 2001, Science.

[16]  Dirk Lebiedz,et al.  Manipulation of self-aggregation patterns and waves in a reaction-diffusion system by optimal boundary control strategies. , 2003, Physical review letters.

[17]  Péter Érdi,et al.  Mathematical Models of Chemical Reactions: Theory and Applications of Deterministic and Stochastic Models , 1989 .

[18]  H. Engel,et al.  Controlling the position of traveling waves in reaction-diffusion systems. , 2013, Physical review letters.

[19]  Harald Engel,et al.  Feedback-mediated control of spiral waves , 2004 .

[20]  G. Ertl,et al.  Reaction fronts and pulses in the CO oxidation on Pt: theoretical analysis , 1992 .

[21]  Friedrich Schl gl.  Chemical Reaction Models for Non-Equilibrium Phase Transitions , 2005 .

[22]  S. Alonso,et al.  Wave propagation in heterogeneous bistable and excitable media , 2010 .

[23]  A R Bishop,et al.  Targeted transfer of solitons in continua and lattices. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Harm Hinrich Rotermund,et al.  Reaction diffusion patterns in the catalytic CO‐oxidation on Pt(110): Front propagation and spiral waves , 1993 .

[25]  H. Engel,et al.  Efficient control of spiral wave location in an excitable medium with localized heterogeneities , 2008 .

[26]  Eckehard Schöll,et al.  Nonlinear Spatio-Temporal Dynamics and Chaos in Semiconductors , 2001 .

[27]  Kenneth Showalter,et al.  Bistability in the iodate oxidation of arsenous acid , 1981 .

[28]  Eckehard Schöll,et al.  Lateral current density fronts in globally coupled bistable semiconductors with S- or Z-shaped current voltage characteristics , 2000 .

[29]  R. Berry,et al.  Fluctuations in the interface between two phases , 1983 .

[30]  M. Bode,et al.  Front-bifurcations in reaction-diffusion systems with inhomogeneous parameter distributions , 1997 .

[31]  Eckehard Schöll,et al.  Dynamics of reaction-diffusion patterns controlled by asymmetric nonlocal coupling as a limiting case of differential advection. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  E Schöll,et al.  Stabilization of unstable rigid rotation of spiral waves in excitable media. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  Irving R Epstein,et al.  Design and control of patterns in reaction-diffusion systems. , 2008, Chaos.

[34]  Fredi Tröltzsch,et al.  On the optimal control of the Schlögl-model , 2013, Comput. Optim. Appl..

[35]  Yoshiki Kuramoto,et al.  Chemical Oscillations, Waves, and Turbulence , 1984, Springer Series in Synergetics.

[36]  Kenneth Showalter,et al.  Detailed studies of propagating fronts in the iodate oxidation of arsenous acid , 1982 .

[37]  Mathias Bode,et al.  ON THE INFLUENCE OF INHOMOGENEITIES IN A REACTION-DIFFUSION SYSTEM , 1995 .

[38]  I. Kevrekidis,et al.  Dragging bistable fronts , 2004 .

[39]  Werner Ebeling,et al.  Interaction of moving interfaces with obstacles , 1987 .

[40]  K B Blyuss,et al.  Control of spatiotemporal patterns in the Gray-Scott model. , 2009, Chaos.

[41]  Eckehard Schöll,et al.  Controlling the onset of traveling pulses in excitable media by nonlocal spatial coupling and time-delayed feedback. , 2008, Chaos.

[42]  F. Schlögl.  Chemical reaction models for non-equilibrium phase transitions , 1972 .

[43]  Eckehard Schöll,et al.  Nonequilibrium phase transitions in semiconductors , 1987 .

[44]  Influence of boundaries on dissipative structures in the Schlögl model , 1987 .

[45]  A. Engel.  Noise-induced front propagation in a bistable system , 1985 .

[46]  Kestutis Pyragas.  Continuous control of chaos by self-controlling feedback , 1992 .

[47]  M G Clerc,et al.  Driven front propagation in 1D spatially periodic media. , 2009, Physical review letters.

[48]  F. Tröltzsch.  Optimal Control of Partial Differential Equations: Theory, Methods and Applications , 2010 .

[49]  M A Katsoulakis,et al.  Wave initiation through spatiotemporally controllable perturbations. , 2003, Physical review letters.

[50]  Kenneth Showalter,et al.  Design and Control of Wave Propagation Patterns in Excitable Media , 2002, Science.

[51]  A. Sekiguchi,et al.  Tomography of Reaction-Diffusion Microemulsions Reveals Three-Dimensional Turing Patterns , 2022 .

[52]  Eckehard Schöll,et al.  Handbook of Chaos Control , 2007 .

[53]  Gentle dragging of reaction waves. , 2003, Physical review letters.

[54]  Z. Rácz.  Nonequilibrium Phase Transitions , 2002, cond-mat/0210435.

[55]  S. Residori,et al.  Front dynamics and pinning-depinning phenomenon in spatially periodic media. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[56]  A G Papathanasiou,et al.  Spatiotemporal Addressing of Surface Activity , 2001, Science.

[57]  J. Kurths,et al.  Analysis and control of complex nonlinear processes in physics, chemistry and biology , 2007 .

[58]  Eckehard Schöll,et al.  Failure of feedback as a putative common mechanism of spreading depolarizations in migraine and stroke. , 2008, Chaos.

[59]  Werner Ebeling,et al.  Effect of Fluctuation on Plane Front Propagation in Bistable Nonequilibrium Systems , 1983 .

[60]  A. Mikhailov.  Foundations of Synergetics I: Distributed Active Systems , 1991 .

[61]  M. Bär,et al.  Front propagation in one-dimensional spatially periodic bistable media. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.