Our group pioneered the systematic design and mechanistic study of oscillating chemical reactions. We continue to be interested in developing new reactions that have particularly desirable features, e.g., producing specific types of patterns or being photosensitive. We also carry out studies to elucidate the mechanisms of reactions that display complex dynamical behavior.

• F. Sagués and I. R. Epstein, “Nonlinear Chemical Dynamics,” Dalton Trans. 1201-1217 (2003) (cover article).


• I. Szalai, K. Kurin-Csörgei, I. R. Epstein and M. Orbán, “Dynamics and Mechanism of Bromate Oscillators with 1,4-Cyclohexanedione,” J. Phys. Chem. A 107, 10074-10081 (2003).


• A. K. Horváth, I. Nagypál, G. Peintler and I. R. Epstein, “Autocatalysis and Selfinhibition: Coupled Kinetic Phenomena in the Chlorite-Tetrathionate Reaction,” J. Am. Chem. Soc. 126, 6246-6247 (2004).


• I. Berenstein, L. Yang, M. Dolnik, A. M. Zhabotinsky and I. R. Epstein, “Dynamic mechanism of photochemical induction of Turing superlattices in the chlorine dioxide-iodine-malonic acid reaction-diffusion system,” J. Phys. Chem. A 109, 5382-5387 (2005).


• V. K. Vanag and I. R. Epstein, “Resonance-Induced Oscillons in a Reaction-Diffusion System,” Phys. Rev. E 73, 016201-1-7 (2006).


• K. Kovács, M. Leda, V. K. Vanag and I. R. Epstein, “Small amplitude and mixed mode pH oscillations in the bromate-sulfite-ferrocyanide-aluminum(III) system,” J. Phys. Chem. A 113, 146–156 (2009).

Pattern formation in uncatalyzed bromate oscillatory system visualized by various indicators

• M. Orbán, K. Kurin-Csörgei, A. M. Zhabotinsky, and I. R. Epstein, “A New Chemical System for Studying Pattern Formation: Bromate - Hypophosphite - Acetone - Dual Catalyst,” Faraday Disc. 120, 11-19 (2001).


• A. K. Horváth, I. Nagypál and I. R. Epstein, “Oscillatory Photochemical Decomposition of Tetrathionate Ion,” J. Am. Chem. Soc. 124, 10956-10957 (2002).


• K. Kurin-Csörgei, M. Orbán and I. R. Epstein, “Systematic Design of Chemical Oscillators Using Complexation  and Precipitation Equilibria,” Nature 433, 139-142 (2005).


• K. Kurin-Csörgei, I. R. Epstein and M. Orbán, “Periodic Pulses of Calcium Ions in a Chemical System,” J. Phys. Chem. A. 110, 7588-7592 (2006).

One of the most visually striking occurrences in chemical systems is the formation of spatial patterns and waves. These phenomena are thought to be of importance in a variety of pattern formation phenomena in living systems. We are studying the dynamical origin of pattern formation, attempting to design new kinds of patterns, and investigating how introducing feedback can induce or alter pattern formation


Pattern Formation Associated with the Wave Instability: Standing wave patterns on a disc - pattern with C6 symmetry (top), pattern with C9 symmetry (bottom)

• M. Dolnik, A. B. Rovinsky, A. M. Zhabotinsky and I. R. Epstein, "Standing Waves in a Two-Dimensional Reaction-Diffusion Model with the Short-Wave Instability," J. Phys. Chem. A 103, 38-45 (1999).


• M. Dolnik, A. M. Zhabotinsky, A. B. Rovinsky, I. R. Epstein, "Spatio-temporal patterns in a reaction-diffusion system with wave instability", Chem. Eng. Sci. 55, 223-231 (2000).


• V. K. Vanag and I. R. Epstein, “Subcritical Wave Instability in Reaction-Diffusion Systems,” J. Chem. Phys. 121, 890-894 (2004).

Pattern Formation Associated with the Wave Instability: Standing wave patterns on a disc - pattern with C6 symmetry (top), pattern with C9 symmetry (bottom)

• V. K. Vanag, L. Yang, M. Dolnik, A. M. Zhabotinsky and I. R. Epstein, " Oscillatory cluster patterns in a homogeneous chemical system with global feedback",Nature 406,389-391 (2000).


• V. K. Vanag, A. M. Zhabotinsky and I. R. Epstein " Pattern formation in the Belousov-Zhabotinsky reaction with photochemical global feedback", J.Phys. Chem 104A, 11566-11577 (2000).


• H. G. Rotstein, N. Kopell, A. Zhabotinsky and I. R. Epstein, “A Canard Mechanism for Localization in Systems of Globally Coupled Oscillators,” SIAM J. Appl. Math. 63, 1998-2019 (2003).


• H. G. Rotstein, N. Kopell, A. M. Zhabotinsky and I. R. Epstein, “Canard Phenomenon and Localization of Oscillations in the Belousov-Zhabotinsky Reaction with Global Feedback,” J. Chem. Phys. 119, 8824-8832 (2003).

When an oscillator is driven by an external force, a variety of phenomena, including resonance, may arise. When two or more chemical oscillators are coupled to one another, they can exhibit a much richer range of behavior than the individual component oscillators. We are seeking to understand what happens when systems that oscillate not only in time but also in space (pattern formation) are forced and/or coupled. Biological examples include organisms under the periodic forcing resulting from circadian oscillations in light intensity.

• Temporally Periodic Forcing


• V. K. Vanag, A. M. Zhabotinsky and I. R. Epstein,"Oscillatory Clusters in the Periodically Illuminated, Spatially Extended Belousov-Zhabotinsky Reaction", Phys. Rev. Lett. 86, 552-555 (2001).


• M. Dolnik, I. Berenstein, A. M. Zhabotinsky and I. R. Epstein, “Spatial Periodic Forcing of Turing Structures,” Phys. Rev. Lett. 87, 238301-1-4 (2001).


• Spatiotemporal Forcing of Turing Structures:


Modulation of Turing structures in CDIMA reaction with spatial periodic forcing (PRL 87,238301,2001)

• M. Dolnik, A. M. Zhabotinsky and I. R. Epstein,"Resonant Suppression of Turing Patterns by Periodic Illumination", Phys. Rev. E 63, 026101-1-10 (2001).


• A. Sanz-Anchelergues, A. M. Zhabotinsky, I. R. Epstein and A. P. Muñuzuri, "Turing Pattern Formation Induced by Spatially Correlated Noise", Phys. Rev. E 63, 056124-1-4 (2001).


• M. Dolnik, I. Berenstein, A. M. Zhabotinsky and I. R. Epstein, "Spatial Periodic Forcing of Turing Structures", Phys. Rev. Lett. 87, 238301-1-4(2001).


• I. Berenstein, M. Dolnik, A. M. Zhabotinsky and I. R. Epstein, “Spatial Periodic Perturbation of Turing Pattern Development Using a Striped Mask,” J. Phys. Chem. A 107, 4428-4435 (2003).


• I. Berenstein, L. Yang, M. Dolnik, A. M. Zhabotinsky and I. R. Epstein, “Superlattice Turing Structures in a Photosensitive Reaction-Diffusion System,” Phys. Rev. Lett. 91, 058302-1-4 (2003).


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Most studies of patterns and waves in chemical systems assume or attempt to create uniform, homogeneous media. Real reaction-diffusion systems, particularly those of biological or industrial importance, involve media that are not homogeneous.We are seeking to understand how the structure of the medium affects the behavior of such systems. Recent work has focused on a microemulsion, a mixture of oil, water and a surfactant, where we are able to “tune” the structure of the medium, and hence the behavior of the system, by varying the composition.


Fully developed inwardly moving spirals and target patterns in BZ-AOT microemulsion.

• Microemulsion Systems


• V. K. Vanag and I. R. Epstein, “Inwardly Rotating Spiral Waves in a Reaction-Diffusion System,” Science 294, 835-837 (2001).              

• V. K. Vanag and I. R. Epstein, “Dash-waves in a Reaction Diffusion System,” Phys. Rev. Lett. 90, 098301-1-4 (2003).

• V. K. Vanag and I. R. Epstein, “Segmented Spiral Waves in a Reaction-Diffusion System,” Proc. Nat. Acad. Sci. USA 100, 14635-14638 (2003) (cover article).

• A. Kaminaga, V. K. Vanag, and I. R. Epstein “`Black spots’ in a surfactant-rich Belousov-Zhabotinsky reaction dispersed in a water-in-oil microemulsion system,” J. Chem. Phys. 122, 174706-1-11 (2005).

• A. Kaminaga, V. K. Vanag, and I. R. Epstein, “A reaction-diffusion memory device,” Angew. Chem. Int. Ed. 45, 3087-3089 (2006).

• Coupled Patterns


• L. Yang and I. R. Epstein, “Oscillatory Turing Patterns in Reaction-Diffusion Systems with Two Coupled Layers,” Phys. Rev. Lett. 90, 178303-1-4 (2003).  

• L. Yang and I. R. Epstein, “Symmetric, Asymmetric and Antiphase Turing Patterns in a Model System with Two Identical Coupled Layers,” Phys. Rev. E 69, 026211-1-6 (2004).

• I. Berenstein, M. Dolnik, L. Yang, A. M. Zhabotinsky and I. R. Epstein, “Turing Pattern Formation in a Two-Layer System: Superposition and Superlattice Patterns,” Phys. Rev. E  70, 046219-1-5 (2004).

We are always interested in applying insights and techniques from our studies of chemical systems to systems of significance in other areas, particularly biology. Although theseprojects primarily involve mathematical modeling, we also collaborate with experimentalists working on the relevant biological systems


Synaptic Memory: Schematic of the first two steps of autophosporylation of CaMKII holoenzyme and hysteresis loop in the system with the Ca2+ independent protein phosphatase in vitro

• A. M. Zhabotinsky, "Bistability in the Ca2+/calmodulin-dependent protein kinase-phosphatase system" Biophys. J. 79, 2211-2221 (2000).


• J. E. Lisman and A. M. Zhabotinsky,"A Model of Synaptic Memory: A CaMKII/PP1 Switch that Potentiates Transmission by Organizing an AMPA Receptor Anchoring Assembly", Neuron 31, 191-201 (2001).


• A. M. Zhabotinsky, R. N. Camp, I. R. Epstein and J. E. Lisman, “Role of the Neurogranin Concentrated in Spines in the Induction of Long-term Potentiation,” J. Neurosci. 26, 7337-7447 (2006).


• I. R. Epstein “Predicting complex biology with simple chemistry,” Proc. Nat. Acad. Sci. USA 103, 15727-15728 (2006).

Gene Expression Networks: Synthetic gene network for entraining and amplifying cellular oscillations

• J.Hasty, J. Pradines, M. Dolnik, J. J. Collins,"Noise-based switches and amplifiers for gene expression" Proc. Nat. Acad. Sci. 97, 2075-2080 (2000).


• J.Hasty, F. Isaacs, M. Dolnik, D. McMillen, J.J. Collins, “Designer gene networks: Towards fundamental cellular control” Chaos 11, 207-220 (2001).

A significant portion of our work involves the development and analysis of mathematical models for a variety of systems in chemistry, biology and other areas that exhibit interesting behavior in time and/or space.  Wherever possible, this theoretical work is closely coupled to our experimental studies.


Synaptic Memory: Schematic of the first two steps of autophosporylation of CaMKII holoenzyme and hysteresis loop in the system with the Ca2+ independent protein phosphatase in vitro

• Reaction-Diffusion Systems
• L. Yang, M. Dolnik, A. M. Zhabotinsky and I. R. Epstein, “Spatial Resonances and Superposition Patterns in a Reaction-Diffusion Model with Interacting Turing Modes,” Phys. Rev. Lett. 88, 208303-1-4 (2002). (more ... | )


• V. K. Vanag and I. R. Epstein, “Stationary and Oscillatory Localized Patterns, and Subcritical Bifurcations,” Phys. Rev. Lett. 92, 128301-1-4 (2004). ( | )


• L. Yang, A. M. Zhabotinsky and I. R. Epstein, “Stable Squares and other Oscillatory Turing Patterns in a Reaction-Diffusion Model,” Phys. Rev. Lett. 92, 198303-1-4 (2004).


• L. Yang, A. M. Zhabotinsky and I. R. Epstein, “Jumping solitary waves in an autonomous reaction-diffusion system with subcritical wave instability,” PhysChemChemPhys. 8, 4647 - 4651 (2006) (cover article).


• Networks
• B. Shargel, H. Sayama, I. R. Epstein and Y. Bar-Yam, “Optimization of Robustness and Connectivity in Complex Networks,” Phys. Rev. Lett. 90, 068701-1-4 (2003).


• Y. Bar-Yam and I. R. Epstein, “Response of Complex Networks to Stimuli,” Proc. Natl. Acad. Sci. 101, 4341-4345 (2004). ( | )


• M.A. M. de Aguiar, I. R. Epstein and Y. Bar-Yam, “Analytically Solvable Model of Probabilistic Network Dynamics,” Phys. Rev. E 72, 067102-1-4 (2005).