Robust feed-back control of travelling waves in a class of reaction–diffusion distributed biological systems

[1]  Dr. M. G. Worster Methods of Mathematical Physics , 1947, Nature.

[2]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1952, The Journal of physiology.

[3]  A. Turing The chemical basis of morphogenesis , 1952, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences.

[4]  R. FitzHugh Impulses and Physiological States in Theoretical Models of Nerve Membrane. , 1961, Biophysical journal.

[5]  S. Yoshizawa,et al.  An Active Pulse Transmission Line Simulating Nerve Axon , 1962, Proceedings of the IRE.

[6]  J Bures,et al.  Spiral waves of spreading depression in the isolated chicken retina. , 1983, Journal of neurobiology.

[7]  L. Sirovich Turbulence and the dynamics of coherent structures. I. Coherent structures , 1987 .

[8]  Topological considerations in the generation of scroll waves in excitable and cyclical media , 1994 .

[9]  P. Daoutidis,et al.  Finite-dimensional control of parabolic PDE systems using approximate inertial manifolds , 1997 .

[10]  Jonathan C. Mattingly,et al.  Low-dimensional models of coherent structures in turbulence , 1997 .

[11]  Markus Bär,et al.  Pulse bifurcation and transition to spatiotemporal chaos in an excitable reaction-diffusion model , 1997 .

[12]  S. Shvartsman,et al.  Nonlinear model reduction for control of distributed systems: A computer-assisted study , 1998 .

[13]  F. Fenton,et al.  Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: Filament instability and fibrillation. , 1998, Chaos.

[14]  J Jalife,et al.  Spiral waves in two-dimensional models of ventricular muscle: formation of a stationary core. , 1998, Biophysical journal.

[15]  L. J. Leon,et al.  Spatiotemporal evolution of ventricular fibrillation , 1998, Nature.

[16]  Flavio H. Fenton,et al.  SPATIOTEMPORAL CONTROL OF WAVE INSTABILITIES IN CARDIAC TISSUE , 1999 .

[17]  V. Krinsky,et al.  Unpinning of a rotating wave in cardiac muscle by an electric field. , 1999, Journal of theoretical biology.

[18]  M A Dahlem,et al.  Image processing techniques applied to excitation waves in the chicken retina. , 2000, Methods.

[19]  Constantinos Theodoropoulos,et al.  Order reduction for nonlinear dynamic models of distributed reacting systems , 2000 .

[20]  Antonio A. Alonso,et al.  Stabilization of distributed systems using irreversible thermodynamics , 2001, Autom..

[21]  I. Kevrekidis,et al.  ROBUST NONLINEAR CONTROL DESIGN OF DISTRIBUTED PROCESS SYSTEMS WITH INPUT CONSTRAINTS , 2002 .

[22]  Elizabeth M Cherry,et al.  Real-time computer simulations of excitable media: JAVA as a scientific language and as a wrapper for C and FORTRAN programs. , 2002, Bio Systems.

[23]  C. W. Gear,et al.  'Coarse' integration/bifurcation analysis via microscopic simulators: Micro-Galerkin methods , 2002 .

[24]  P. Christofides,et al.  Nonlinear and Robust Control of PDE Systems: Methods and Applications to Transport-Reaction Processes , 2002 .

[25]  Hans V Westerhoff,et al.  Control of spatially heterogeneous and time-varying cellular reaction networks: a new summation law. , 2002, Journal of theoretical biology.

[26]  H. Wio,et al.  Influence of boundary conditions on the dynamics of oscillatory media , 2003 .

[27]  W. Troy,et al.  On the bifurcation curve for an elliptic system of FitzHugh–Nagumo type , 2003 .

[28]  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.

[29]  James P Keener,et al.  The topology of defibrillation. , 2004, Journal of theoretical biology.

[30]  Julio R. Banga,et al.  Optimal sensor location and reduced order observer design for distributed process systems , 2004, Comput. Chem. Eng..

[31]  Julio R. Banga,et al.  Dissipative systems: from physics to robust nonlinear control , 2004 .

[32]  Antonio A. Alonso,et al.  Optimal sensor placement for state reconstruction of distributed process systems , 2004 .

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

[34]  J. Stelling,et al.  Robustness of Cellular Functions , 2004, Cell.

[35]  Jiuping Xu,et al.  Simulation of biological waves in single-species bacillus system governed by birth and death-diffusion dynamical equation , 2005, Math. Comput. Simul..

[36]  Stabilization of inhomogeneous patterns in a diffusion-reaction system under structural and parametric uncertainties. , 2006, Journal of theoretical biology.

[37]  Giles Auchmuty,et al.  Rotating wave solutions of the FitzHugh–Nagumo equations , 2006, Journal of mathematical biology.

[38]  Julio R. Banga,et al.  Robust Feed-back Control of Distributed Chemical Reaction Systems , 2007 .

[39]  O. Slaby,et al.  Targeting characteristic wave properties in reaction-diffusion systems by optimization of external forcing. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.