Skip to main content

2019 | OriginalPaper | Buchkapitel

6. Dynamical Transitions in Chemistry and Biology

verfasst von : Tian Ma, Shouhong Wang

Erschienen in: Phase Transition Dynamics

Verlag: Springer International Publishing

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

This chapter studies dynamic transitions and pattern formations of a few typical nonequilibrium chemical and biological models. The main focus is on Belousov–Zhabotinsky models, the chemotactic model, and a population model.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
Zurück zum Zitat Bao, W. (2002). The random projection method for a model problem of combustion with stiff chemical reactions. Appl. Math. Comput. 130(2-3), 561–571.MathSciNetMATH Bao, W. (2002). The random projection method for a model problem of combustion with stiff chemical reactions. Appl. Math. Comput. 130(2-3), 561–571.MathSciNetMATH
Zurück zum Zitat Belousov, B. P. (1959). An oscillating reaction and its mechanism. Sborn. referat. radiat. med., 145. Belousov, B. P. (1959). An oscillating reaction and its mechanism. Sborn. referat. radiat. med., 145.
Zurück zum Zitat Brenner, M. P., L. S. Levitov, and E. O. Budrene (1998). Physical mechanisms for chemotactic pattern formation by bacteria. Biophysical Journal 74, 1677–1693.CrossRef Brenner, M. P., L. S. Levitov, and E. O. Budrene (1998). Physical mechanisms for chemotactic pattern formation by bacteria. Biophysical Journal 74, 1677–1693.CrossRef
Zurück zum Zitat Budrene, E. O. and H. C. Berg (1991). Complex patterns formed by motile cells of Escherichia coli. Nature 349, 630–633.CrossRef Budrene, E. O. and H. C. Berg (1991). Complex patterns formed by motile cells of Escherichia coli. Nature 349, 630–633.CrossRef
Zurück zum Zitat Budrene, E. O. and H. C. Berg (1995). Dynamics of formation of symmetric patterns of chemotactic bacteria. Nature 376, 49–53.CrossRef Budrene, E. O. and H. C. Berg (1995). Dynamics of formation of symmetric patterns of chemotactic bacteria. Nature 376, 49–53.CrossRef
Zurück zum Zitat Cross, M. and P. Hohenberg (1993). Pattern formation outside of equilibrium. Reviews of Modern Physics 65(3), 851–1112.CrossRef Cross, M. and P. Hohenberg (1993). Pattern formation outside of equilibrium. Reviews of Modern Physics 65(3), 851–1112.CrossRef
Zurück zum Zitat Desai, R. C. and R. Kapral (2009). Self-Organized and Self-Assembled Structures. Cambridge University Press.CrossRef Desai, R. C. and R. Kapral (2009). Self-Organized and Self-Assembled Structures. Cambridge University Press.CrossRef
Zurück zum Zitat Field, R. J., E. Körös, and R. M. Noyes (1972). Oscillations in chemical systems, Part 2. thorough analysis of temporal oscillations in the bromate-cerium-malonic acid system. J. Am Chem. Soc. 94, 8649–8664. Field, R. J., E. Körös, and R. M. Noyes (1972). Oscillations in chemical systems, Part 2. thorough analysis of temporal oscillations in the bromate-cerium-malonic acid system. J. Am Chem. Soc. 94, 8649–8664.
Zurück zum Zitat Field, R. J. and R. M. Noyes (1974). Oscillations in chemical systems, IV. limit cycle behavior in a model of a real chemical reaction. J. Chem. Physics. 60, 1877–1884. Field, R. J. and R. M. Noyes (1974). Oscillations in chemical systems, IV. limit cycle behavior in a model of a real chemical reaction. J. Chem. Physics. 60, 1877–1884.
Zurück zum Zitat Glansdorff, P. and I. Prigogine (1971). Structure, stability, and fluctuations. Wiley-Interscience, New York.MATH Glansdorff, P. and I. Prigogine (1971). Structure, stability, and fluctuations. Wiley-Interscience, New York.MATH
Zurück zum Zitat Guo, B. and Y. Han (2009). Attractor and spatial chaos for the Brusselator in R N. Nonlinear Anal. 70(11), 3917–3931.MathSciNetCrossRef Guo, B. and Y. Han (2009). Attractor and spatial chaos for the Brusselator in R N. Nonlinear Anal. 70(11), 3917–3931.MathSciNetCrossRef
Zurück zum Zitat Guo, Y. and H. J. Hwang (2010). Pattern formation (I): the Keller-Segel model. J. Differential Equations 249(7), 1519–1530.MathSciNetCrossRef Guo, Y. and H. J. Hwang (2010). Pattern formation (I): the Keller-Segel model. J. Differential Equations 249(7), 1519–1530.MathSciNetCrossRef
Zurück zum Zitat Hastings, S. P. and J. D. Murray (1975). The existence of oscillatory solutions in the Field-Noyes model for the Belousov-Zhabotinskii reaction. SIAM J. Appl. Math. 28, 678–688.MathSciNetCrossRef Hastings, S. P. and J. D. Murray (1975). The existence of oscillatory solutions in the Field-Noyes model for the Belousov-Zhabotinskii reaction. SIAM J. Appl. Math. 28, 678–688.MathSciNetCrossRef
Zurück zum Zitat Kaper, H. G. and T. J. Kaper (2002). Asymptotic analysis of two reduction methods for systems of chemical reactions. Phys. D 165(1-2), 66–93.MathSciNetCrossRef Kaper, H. G. and T. J. Kaper (2002). Asymptotic analysis of two reduction methods for systems of chemical reactions. Phys. D 165(1-2), 66–93.MathSciNetCrossRef
Zurück zum Zitat Kapral, R. and K. Showalter (1995). Chemical Waves and Patterns. Kluwer, Dordrecht.CrossRef Kapral, R. and K. Showalter (1995). Chemical Waves and Patterns. Kluwer, Dordrecht.CrossRef
Zurück zum Zitat Keller, E. F. and L. A. Segel (1970). Initiation of slime mold aggregation viewed as an instability. J. Theor. Biol. 26, 399–415.MathSciNetCrossRef Keller, E. F. and L. A. Segel (1970). Initiation of slime mold aggregation viewed as an instability. J. Theor. Biol. 26, 399–415.MathSciNetCrossRef
Zurück zum Zitat Lapidus, I. and R. Schiller (1976). Model for the chemotactic response of a bacterial population. Biophys J. 16(7), 779–789.CrossRef Lapidus, I. and R. Schiller (1976). Model for the chemotactic response of a bacterial population. Biophys J. 16(7), 779–789.CrossRef
Zurück zum Zitat Liu, H., T. Sengul, and S. Wang (2011). Dynamic transitions for quasilinear systems and Cahn-Hilliard equation with Onsager mobility. Journal of Mathematical Physics. Liu, H., T. Sengul, and S. Wang (2011). Dynamic transitions for quasilinear systems and Cahn-Hilliard equation with Onsager mobility. Journal of Mathematical Physics.
Zurück zum Zitat Ma, T. and S. Wang (2005b). Bifurcation theory and applications, Volume 53 of World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ. Ma, T. and S. Wang (2005b). Bifurcation theory and applications, Volume 53 of World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ.
Zurück zum Zitat Ma, T. and S. Wang (2007b). Stability and Bifurcation of Nonlinear Evolutions Equations. Science Press, Beijing. Ma, T. and S. Wang (2007b). Stability and Bifurcation of Nonlinear Evolutions Equations. Science Press, Beijing.
Zurück zum Zitat Ma, T. and S. Wang (2010b). Dynamic transition theory for thermohaline circulation. Phys. D 239(3-4), 167–189.MathSciNetCrossRef Ma, T. and S. Wang (2010b). Dynamic transition theory for thermohaline circulation. Phys. D 239(3-4), 167–189.MathSciNetCrossRef
Zurück zum Zitat Ma, T. and S. Wang (2011a). Dynamic transition and pattern formation for chemotactic systems. Ma, T. and S. Wang (2011a). Dynamic transition and pattern formation for chemotactic systems.
Zurück zum Zitat Ma, T. and S. Wang (2011c). Phase transitions for Belousov-Zhabotinsky reactions. Math. Methods Appl. Sci. 34(11), 1381–1397.MathSciNetCrossRef Ma, T. and S. Wang (2011c). Phase transitions for Belousov-Zhabotinsky reactions. Math. Methods Appl. Sci. 34(11), 1381–1397.MathSciNetCrossRef
Zurück zum Zitat Murray, J. (2002). Mathematical Biology, II. 3rd Ed. Springer-Verlag.CrossRef Murray, J. (2002). Mathematical Biology, II. 3rd Ed. Springer-Verlag.CrossRef
Zurück zum Zitat Nadin, G., B. Perthame, and L. Ryzhik (2008). Traveling waves for the Keller-Segel system with Fisher birth terms. Interfaces Free Bound. 10(4), 517–538.MathSciNetCrossRef Nadin, G., B. Perthame, and L. Ryzhik (2008). Traveling waves for the Keller-Segel system with Fisher birth terms. Interfaces Free Bound. 10(4), 517–538.MathSciNetCrossRef
Zurück zum Zitat Nicolis, G. and I. Prigogine (1977). Self-organization in nonequilibrium systems. Wiley-Interscience, New York.MATH Nicolis, G. and I. Prigogine (1977). Self-organization in nonequilibrium systems. Wiley-Interscience, New York.MATH
Zurück zum Zitat Perthame, B. and A.-L. Dalibard (2009). Existence of solutions of the hyperbolic Keller-Segel model. Trans. Amer. Math. Soc. 361(5), 2319–2335.MathSciNetCrossRef Perthame, B. and A.-L. Dalibard (2009). Existence of solutions of the hyperbolic Keller-Segel model. Trans. Amer. Math. Soc. 361(5), 2319–2335.MathSciNetCrossRef
Zurück zum Zitat Perthame, B., C. Schmeiser, M. Tang, and N. Vauchelet (2011). Travelling plateaus for a hyperbolic Keller-Segel system with attraction and repulsion: existence and branching instabilities. Nonlinearity 24(4), 1253–1270.MathSciNetCrossRef Perthame, B., C. Schmeiser, M. Tang, and N. Vauchelet (2011). Travelling plateaus for a hyperbolic Keller-Segel system with attraction and repulsion: existence and branching instabilities. Nonlinearity 24(4), 1253–1270.MathSciNetCrossRef
Zurück zum Zitat Pismen, L. M. (2006). Patterns and Interfaces in Dissipative Dynamics. Springer, Berlin.MATH Pismen, L. M. (2006). Patterns and Interfaces in Dissipative Dynamics. Springer, Berlin.MATH
Zurück zum Zitat Prigogine, I. and R. Lefever (1968). Symmetry breaking instabilities in dissipative systems. II. J. Chem. Phys. 48, 1695.CrossRef Prigogine, I. and R. Lefever (1968). Symmetry breaking instabilities in dissipative systems. II. J. Chem. Phys. 48, 1695.CrossRef
Zurück zum Zitat Reichl, L. E. (1998). A modern course in statistical physics (Second ed.). A Wiley-Interscience Publication. New York: John Wiley & Sons Inc.MATH Reichl, L. E. (1998). A modern course in statistical physics (Second ed.). A Wiley-Interscience Publication. New York: John Wiley & Sons Inc.MATH
Zurück zum Zitat Shi, J. (2009). Bifurcation in infinite dimensional spaces and applications in spatiotemporal biological and chemical models. Front. Math. China 4(3), 407–424.MathSciNetCrossRef Shi, J. (2009). Bifurcation in infinite dimensional spaces and applications in spatiotemporal biological and chemical models. Front. Math. China 4(3), 407–424.MathSciNetCrossRef
Zurück zum Zitat Smoller, J. (1983). Shock waves and reaction-diffusion equations, Volume 258 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science]. New York: Springer-Verlag.CrossRef Smoller, J. (1983). Shock waves and reaction-diffusion equations, Volume 258 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science]. New York: Springer-Verlag.CrossRef
Zurück zum Zitat Swinney, H. L., N. Kreisberg, W. D. McCormick, Z. Noszticzius, and G. Skinner (1990). Spatiotemporal patterns in reaction-diffusion systems. In Chaos (Woods Hole, MA, 1989), pp. 197–204. New York: Amer. Inst. Phys. Swinney, H. L., N. Kreisberg, W. D. McCormick, Z. Noszticzius, and G. Skinner (1990). Spatiotemporal patterns in reaction-diffusion systems. In Chaos (Woods Hole, MA, 1989), pp. 197–204. New York: Amer. Inst. Phys.
Zurück zum Zitat Temam, R. (1997). Infinite-dimensional dynamical systems in mechanics and physics (Second ed.), Volume 68 of Applied Mathematical Sciences. New York: Springer-Verlag. Temam, R. (1997). Infinite-dimensional dynamical systems in mechanics and physics (Second ed.), Volume 68 of Applied Mathematical Sciences. New York: Springer-Verlag.
Zurück zum Zitat Tzou, J. C., B. J. Matkowsky, and V. A. Volpert (2009). Interaction of Turing and Hopf modes in the superdiffusive Brusselator model. Appl. Math. Lett. 22(9), 1432–1437.MathSciNetCrossRef Tzou, J. C., B. J. Matkowsky, and V. A. Volpert (2009). Interaction of Turing and Hopf modes in the superdiffusive Brusselator model. Appl. Math. Lett. 22(9), 1432–1437.MathSciNetCrossRef
Zurück zum Zitat Zhabotinski, A. (1964). Periodic process of the oxidation of malonic acid in solution (study of the kinetics of Belousov’s reaction). Biofizika 9, 306–311. Zhabotinski, A. (1964). Periodic process of the oxidation of malonic acid in solution (study of the kinetics of Belousov’s reaction). Biofizika 9, 306–311.
Metadaten
Titel
Dynamical Transitions in Chemistry and Biology
verfasst von
Tian Ma
Shouhong Wang
Copyright-Jahr
2019
DOI
https://doi.org/10.1007/978-3-030-29260-7_6

Premium Partner