Review and overview articles


  • Nicolis, G. & Portnow, J., Chemical oscillations. Chem. Rev. 95, 365-384 (1973). (DOI)


  • Noyes, R. M. & Field, R. J., Oscillatory Chemical Reactions. Annual Review of Physical Chemistry 25, 95-119 (1974). (DOI)
    • Good review of curvature effect on propagating fronts and spirals.


  • Franck, U. F., Chemical oscillations. Angewandte Chemie International Edition in English 17, 1-15 (1978). (DOI)
  • Leff, D., The strange world of chemical oscillations. Mosaic 9, 32-41 (1978).


  • Vidal, C. & Pacault, A., Spatial chemical structures, chemical waves. A review. In Haken, H. (ed.) Evolution of Order and Chaos in Physics, Chemistry, and Biology (Proceedings of the International Symposium on Synergetics at Schloss Elmau, Bavaria, April 26-May 1, 1982), 74-99 (Springer-Verlag, 1982). (DOI)
    • Short review with explanations of the various wave types and behaviors. Tables with component concentrations for experiments and equation for analytical and numerical models.


  • Gurel, D. & Gurel, O., Recent developments in chemical oscillations. In Oscillations in Chemical Reactions, book series Topics in Current Chemistry - Vol. 118 (Springer-Verlag, 1983), 75-118 (Springer-Verlag, 1983). (DOI)
  • Gurel, O. & Gurel, d., Types of oscillations in chemical reactions. In Oscillations in Chemical Reactions, book series Topics in Current Chemistry - Vol. 118 (Springer-Verlag, 1983), 1-73 (Springer-Verlag, 1983). (DOI)


  • Epstein, I. R., Patterns in time and space - generated by chemistry. Chem. Eng. News 65, 24-36 (1987). (DOI)


  • Ross, J., Müller, S. C. & Vidal, C., Chemical waves. Science 240, 460-465 (1988). (DOI)


  • Meron, E., Pattern formation in excitable media. Phys. Rep. 218, 1-66 (1992). (DOI)


  • Cross, M. C. & Hohenberg, P. C., Pattern formation outside of equilibrium. Rev. Mod. Phys. 65, 851-1112 (1993). (DOI)
    • A comprehensive (270 page) review of spatiotemporal pattern formation in systems driven away from equilibrium is presented, with emphasis on comparisons between theory and quantitative experiments. Examples include patterns in hydrodynamic systems such as thermal convection in pure fluids and binary mixtures, Taylor-Couette flow, parametric-wave instabilities, as well as patterns in solidification fronts, nonlinear optics, oscillatory chemical reactions and excitable biological media.


  • Koch, A. J. & Meinhardt, H., Biological pattern formation: From basic mechanisms to complex structures. Rev. Mod. Phys. 66, 1481-1507 (1994). (DOI)


  • Epstein, I. R. & Showalter, K., Nonlinear chemical dynamics: Oscillations, patterns, and chaos. J. Phys. Chem. 100 (1996). (DOI)
    • Short introduction for a special issue of Chaos.


  • Fast, V. G. & Kléber, A. G., Role of wavefront curvature in propagation of cardiac impulse. Cardiovascular Research 33, 258-271 (1997). (DOI)
  • Hess, B., Periodic patterns in biochemical reactions. Q. Rev. Biophys. 30, 121-176 (1997). (DOI)
    • A very complete overview about nonlinear biochemical systems.


  • Gollub, J. P. & Langer, J. S., Pattern formation in nonequilibrium physics. Rev. Mod. Phys. 71, S396-S403 (1999). (DOI)
  • Merzhanov, A. G. & Rumanov, E. N., Physics of reaction waves. Rev. Mod. Phys. 71, 1173-1211 (1999). (DOI)
    • Mainly about combustion waves but with a section about spiral fronts.


  • Ben-Jacob, E., Cohen, I. & Levine, H., Cooperative self-organization of microorganism. Adv. in Phys. 49, 395-554 (2000). (DOI)
  • Hess, B., Periodic patterns in biology. Naturwissenschaften 87, 199-211 (2000). (DOI)


  • Shanks, N., Modeling biological systems: The Belousov-Zhabotinsky reaction. Found. Chem. 3, 33-53 (2001). (DOI)


  • Taylor, A. F., Mechanism and phenomenology of an oscillating chemical reaction. Prog. Reac. Kin. Mech. 27, 247-325 (2002). (DOI)


  • Sagués, F. & Epstein, I. R., Nonlinear chemical dynamics. Dalton Trans. 7, 1201-1217 (2003). (DOI)
    • A review with an extensive bibliography.


  • Miura, T. & Maini, P. K., Periodic pattern formation in reaction-diffusion systems: An introduction for numerical simulation. Anat. Sci. Int. 79, 112-123 (2004). (DOI)
    • A very comprehensive review of Turing-type stationary reaction-diffusion systems with many sketches and detailed explanations of the used equations. Examples are presented using Excel and Mathematica.
  • Panja, D., Effects of fluctuations on propagating fronts. Phys. Rep. 393, 87-174 (2004). (DOI)


  • Biosa, G., Bastianoni, S. & Rustici, M., Chemical Waves. Chemistry - A European Journal 12, 3430-3437 (2006). (DOI)
  • Epstein, I. R., Pojman, J. A. & Steinbock, O.Introduction: Self-organization in nonequilibrium chemical systems. Chaos 16, 037101 (2006). (DOI)
  • Mikhailov, A. S. & Showalter, K., Control of waves, patterns and turbulence in chemical systems. Phys. Rep. 425 (2006). (DOI)
    • A detailed review of experimental and theoretical studies on the design and control of spatiotemporal behavior in chemical systems with many figures and references.
  • Rabinovich, M. I., Varona, P., Selverston, A. I. & Abarbanel, H. D. I. Dynamical principles in neuroscience. Rev. Mod. Phys. 78, 1213-1265 (2006). (DOI)
  • Tóth, R. & Taylor, A.The Tris(2,2'-Bipyridyl)Ruthenium-Catalysed Belousov-Zhabotinsky reaction. Progress in Reaction Kinetics and Mechanism 31, 59-115 (2006).(DOI)
    • A very good and complete review about this light-sensitive BZ reaction.


  • Goldbeter, A., Dissipative structures and biological rhythms. In Rice, S. A. (ed.) Special Volume in Memory of Ilya Prigogine: Advances in Chemical Physics, Volume 135, 253-295 (John Wiley & Sons, Inc., 2007). (DOI)
    • As the title describes: review on biological systems. Part of the Chaos focus issue to celebrate Ilya Prigogine's 100th birthday.
  • Jaeger, H. & Liu, A. J., What Happens Far from Equilibrium and Why? (2007). (link)
    • Explanation of 'far from equilibrium' but more towards granular media.
  • Sagués, F., Sancho, J. M. & García-Ojalvo, J., Spatiotemporal order out of noise. Rev. Mod. Phys. 79, 829-882 (2007). (DOI)


  • Volpert, V. & Petrovskii, S., Reaction-diffusion waves in biology. Physics of Life Reviews 6, 267 - 310 (2009). (DOI)
  • Vanag, V. K. & Epstein, I. R., Pattern formation mechanisms in reaction-diffusion systems. Int. J. Dev. Biol. 53, 673-681 (2009). (DOI)


  • Jaeger, H. & Liu, A. J., Far-From-Equilibrium Physics: An Overview (2010). (Arxiv)
    • This is an overview of the field designed for non-experts that was included in the CMMP2010 decadal study report. Reworked version of the 2007 article with a long publication list.


  • Roth, S., Mathematics and biology: A Kantian view on the history of pattern formation theory. Dev. Genes Evol. 221, 255-279 (2011). (DOI)
    • An interesting different approach to the history of pattern formation.


  • Qu, Z., Hu, G., Garfinkel, A. & Weiss, J., Nonlinear and stochastic dynamics of the heart. Phys. Rep. 543, 61-162 (2014). (DOI)


  • Field, R. J., Chaos in the Belousov-Zhabotinsky reaction. Modern Physics Letters B 29, 1530015 (2015). (DOI)
    • Short history and detailed explanation of the Brusselator, Oregonator, and the FKN mechanism.
  • Glass, L., Dynamical disease: Challenges for nonlinear dynamics and medicine,  Chaos 25, 097603 (2015). (DOI)
    • Includes an overview about physiological systems with complex dynamics as the heart or the nervous system.
  • Hohenberg, P. C. & Krekhov, A. P., An introduction to the Ginzburg-Landau theory of phase transitions and nonequilibrium patterns. Phys. Rep. 572, 1-42 (2015). (DOI)
  • Jacobs, D. T., Self-organizing physics. Am. J. Phys. 83, 680-687 (2015). (DOI)
    • A Resource Letter from the \textit{American Journal of Physics} of the AAPT with an introduction into several self-organizing physical systems.


  • Boiangiu, C. A., Morosan, A. G. & Stan, M., A fractal world: Building visually-rich and fully realistic natural environments. Int. J. Math. Comp. Sci. 10, 100-111 (2016).
    • Overview about fractal structures with some unusual references.


  • Ashkenasy, G., Hermans, T. M., Otto, S. & Taylor, A. F., Systems chemistry. Chem. Soc. Rev. 46, 2543-2554 (2017). (DOI)
  • Budroni, M. A. & Wit, A. D. , Dissipative structures: From reaction-diffusion to chemohydrodynamic patterns. Chaos: An Interdisciplinary Journal of Nonlinear Science 27, 104617 (2017). (DOI)
    • As the title describes. Part of the Chaos focus issue to celebrate \textsc{Ilya Prigogine}'s 100th birthday.
  • Goldbeter, A., Dissipative structures and biological rhythms. Chaos: An Interdisciplinary Journal of Nonlinear Science 27, 104612 (2017). (DOI)
  • Nagel, S. R., Experimental soft-matter science. Rev. Mod. Phys. 89, 025002 (2017). (DOI)
  • Orlik, M., Introduction to the dynamic self-organization of chemical systems: Part I: Basic concepts and techniques of nonlinear dynamics in chemistry and Part II: Dynamic instabilities in selected chemical systems. ChemTexts. 3, 11 and 12 (2017). (Part I DOI, Part II DOI)


  • Zykov, V. S. & Bodenschatz, E., Wave propagation in inhomogeneous excitable media. Annual Review of Condensed Matter Physics 9, 435-461 (2018). (DOI
  • Zykov, V. S., Spiral wave initiation in excitable media. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 376 (2018). (DOI)


    • De Wit, A.Chemo-Hydrodynamic Patterns and Instabilities, Annual Review of Fluid Mechanics, Vol. 52:531-555 (2020) (DOI)


    • Taylor, A. F.From Clocks to Synchrony: The Design of Bioinspired Self-Regulation in Chemical Systems, In Giuseppone, N. and Walther, A. (eds.) Out‐of‐Equilibrium (Supra)molecular Systems and Materials, 61-90 (John Wiley & Sons, Inc., 2021 (DOI)


    • Field, R. J., Mazo, R. M., & Manz, N.Science, serendipity, coincidence, and the Oregonator at the University of Oregon, 1969-1974, Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 32:052101 (2022) (DOI)

    • Pribus, M., Orlik, M., & Valent, I.From classical metal‑catalyzed homogeneous oscillators to an uncatalyzed version of the Belousov–Zhabotinsky reaction: a review, Reaction Kinetics, Mechanisms and Catalysis, Vol. 135:1 (2022) (DOI)

    • Tyson, J. J.From the Belousov–Zhabotinsky reaction to biochemical clocks, traveling waves and cell cycle regulation, Biochemical Journal, Vol. 479:185–206 (2022) (DOI)

    Review and overview articles