A fast method to simulate travelling waves in nonhomogeneous chemical or biological media

Journal of Mathematical Chemistry

Volumn 34, Issue 3-4, 2003, Pages 163-176

  Kály Kullai, Kristóf ^a  

^a BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

Author keywords

Excitable medium; Geometric theory of waves; Involute

Indexed keywords

ANALYTIC METHOD; ARTICLE; CHEMICAL PARAMETERS; CHEMICAL PROCEDURES; CHEMICAL REACTION; CULTURE MEDIUM; GEOMETRY; MATHEMATICAL MODEL; PHYSICAL CHEMISTRY; REACTION ANALYSIS; THEORETICAL STUDY; WAVEFORM;

EID: 3542992733     PISSN: 02599791     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:JOMC.0000004066.71858.06     Document Type: Article

References (19)

1. J.A. Sethian, Level Set Methods - Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision, and Materials Science (Cambridge University Press, Cambridge, 1996).
2. R.J. Field and M. Burger (eds.), Oscillations and Traveling Waves in Chemical Systems (Wiley, New York, 1985).
3. S.K. Scott, Oscillations, Waves and Chaos in Chemical Kinetics (Oxford University Press, Oxford, 1994).
4. R. Kapral and K. Showalter (eds.), Chemical Waves and Patterns (Kluwer, Dordrecht, 1995).
5. A.S. Mikhailov, Distributed Active Systems, Foundations of Synergetics I (Springer, Heidelberg, 1990).
6. D. Barkley, A model for fast computer simulation of waves in excitable media, Physica D 49 (1991) 61-70.
7. V.I. Arnold, Singularities of Caustics and Wave Fronts (Kluwer Academic, Dordrecht, 1990).
8. P.L. Simon and H. Farkas, Geometric theory of trigger waves. A dynamical system approach, J. Math. Chem. 19 (1996) 301-315.
9. S. Sieniutycz and H. Farkas, Chemical waves in confined regions by Hamilton-Jacobi-Bellman theory, Chemical Engineering Science 52(17) (1997) 2927-2945.
10. J. Sainhas and R. Dilao, Wave optics in reaction-diffusion systems, Phys. Rev. Letters 80 (1998) 5216-5219.
11. N. Wiener and A. Rosenblueth, The mathematical formulation of the problem of conduction of impulses in a network of connected excitable elements, specifically in cardiac muscle, Arch. Inst. Cardiol. Mexico 16 (1946) 205-265.
12. A. Lázár, Z. Noszticzius, H. Farkas and H.D. Försterling, Involutes: the geometry of chemical waves rotating in annular membranes, Chaos 5 (1995) 443-447.
13. A. Lázár, H.D. Försterling, H. Farkas, P.L. Simon, A. Volford and Z. Noszticzius, Waves of excitations on nonuniform membrane rings, caustics, and reverse involutes, Chaos 7 (1997) 731-737.
14. A. Volford, P.L. Simon and H. Farkas, Waves of excitation in heterogeneous annular region, asymmetric arrangement, in: Geometry and Topology of Caustics - Caustics'98, eds. S. Janeczko and V.M. Zakhalyukin (Banach Center publications, Warszava, 1999) pp. 305-320.
15. A. Volford, P.L. Simon, H. Farkas and Z. Noszticzius, Rotating chemical waves: theory and experiments, Physica A 274 (1999) 30-49.
16. P.K. Brazhnik, V.A. Davydov, V.S. Zykov and A.S. Mikhailov, Zh. Eksper. Teoret. Fiz. 93 (1987) 1725-1736.
17. J.J. Tyson and J.P. Keener, Physica D 32 (1988) 327.
18. A. Volford, private communication (experimental figures).
19. J.A. Nelder and R. Mead, A simplex method for function minimization, Computer Journal 7 (1965) 308-313.