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Irving R. Epstein


Henry F. Fischbach Professor of Chemistry and HHMI Professor
Ph.D., Harvard University
781-736-2503
epstein@brandeis.edu
group website

Research in our group covers oscillatory chemical reactions, spatial pattern formation, dynamical systems and neurobiology.


Many phenomena in living systems involve periodic changes. In the past decade, oscillating chemical reactions have blossomed from a curiosity studied by an obscure group of Russians to a major area of scientific research. We study these systems both experimentally and theoretically, from several points of view. We have achieved the first successful design of a new chemical oscillator. We have used our systematic design algorithm to expand the family of chemical oscillators from two accidentally discovered reactions to some two dozen deliberately constructed systems. While we continue the search for new types of oscillators, we probe by a variety of techniques, including spectrophotometry, potentiometry, rapid mixing and computer simulation, the mechanisms of those that have already been discovered.


Chemical oscillators can be "tweaked" to give a variety of related phenomena, some with suggestive connections to biological systems. We study spatial pattern formation, in which an initially homogeneous medium spontaneously gives rise to concentric rings, or spiral color patterns resembling those seen in embryonic development or the aggregation of slime molds, and chemical chaos, in which concentrations oscillate deterministically, but in an aperiodic and apparently irreproducible fashion that depends very sensitively on the initial conditions. We investigate, both experimentally and theoretically, Turing structures, patterns that arise from the interaction of reaction and diffusion, which have been suggested as the mechanism of spatial pattern formation in phenomena ranging from biological morphogenesis to geological stratification.

We are interested in the phenomena that can occur when two or more oscillators are coupled together, either physically, i.e., by diffusion or an electrical connection, or chemically, by having two oscillators share a common chemical species. Such systems can give rise to surprising phenomena, such as "oscillator death," the cessation of oscillation in two coupled oscillating systems, or the converse, "rhythmogenesis," in which coupling two systems at steady state causes them to start oscillating. Coupled chemical oscillators provide simple models for networks of oscillatory neurons. We have begun to apply some of the insights gained in our studies of coupled chemical oscillators to the modeling of small neural networks in conjunction with the Marder laboratory, to develop chemical analogs of neural oscillators and to coupling chemical and neural oscillators.

Click here for a complete list of publications

Recent Publications

I.R. Epstein, J.A. Pojman and Q. Tran-Cong-Miyata, “Nonlinear Dynamics and Polymeric Systems: An Overview,” in Nonlinear Dynamics in Polymeric Systems, ACS Symp. Ser. 869, J.A. Pojman and Q. Tran-Cong-Miyata, eds., Am. Chem. Soc., Washington, DC, pp 2-15 (2004).

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).

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

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).

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

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).

K. Kurin-Csörgei, I.R. Epstein and M. Orbán, “New Heterogeneous Chemical Oscillators: Reduction of Manganese Species by Hypophosphite on a Pt Surface,” J. Phys. Chem. B 108, 7352-7358 (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).

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

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).

L. Yang, I. Berenstein and I.R. Epstein, “Segmented Waves from a Spatiotemporal Transverse Wave Instability,” Phys. Rev. Lett. 95, 038303-1-4 (2005).

V.K. Vanag and I.R. Epstein, “Out-of-Phase Oscillatory Turing Patterns in a Bistable Reaction-Diffusion System,” Phys. Rev. E 71, 066212-1-7 (2005).

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. 109, 5382-5387 (2005).

A. Kaminaga, V.K. Vanag, and I.R. Epstein, “Wavelength Halving in a Standing Wave–Traveling Wave Transition,” Phys. Rev. Lett.  95, 058302-1-7 (2005).