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
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.
Temperature-Induced Bifurcations in the Cu(II)-Catalyzed and Catalyst-Free Hydrogen Peroxide-Thiosulfate Oscillating Reaction. Yuan L, Gao Q, Zhao Y, Tang X, Epstein IR. J Phys Chem A. 2010 Jun 10. [abstract]
Oxygen-sulfur species distribution and kinetic analysis in the hydrogen peroxide-thiosulfate system.Lu Y, Gao Q, Xu L, Zhao Y, Epstein IR. Inorg Chem. 2010 Jul 5;49(13):6026-34. [abstract]
Quaternary cross-diffusion in water-in-oil microemulsions loaded with a component of the Belousov-Zhabotinsky reaction. Rossi F, Vanag VK, Tiezzi E, Epstein IR. J Phys Chem B. 2010 Jun 24;114(24):8140-6. [abstract]
Instabilities of a three-dimensional localized spot. Leda M, Vanag VK, Epstein IR. Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Dec;80(6 Pt 2):066204. Epub 2009 Dec 10. [abstract]
Patterns in the Belousov-Zhabotinsky reaction in water-in-oil microemulsion induced by a temperature gradient. Carballido-Landeira J, Vanag VK, Epstein IR. Phys Chem Chem Phys. 2010 Apr 21;12(15):3656-65. [abstract]
Oscillatory concentration pulses of some divalent metal ions induced by a redox oscillator. Horváth V, Kurin-Csörgei K, Epstein IR, Orbán M. Phys Chem Chem Phys. 2010 Feb 14;12(6):1248-52. [abstract]
Precipitation patterns with polygonal boundaries between electrolytes. Pan C, Gao Q, Xie J, Xia Y, Epstein IR. Phys Chem Chem Phys. 2009 Dec 14;11(46):11033-9. Epub 2009 Oct 13. [abstract]
Spiral instabilities in media supporting complex oscillations under periodic forcing. Gao Q, Li J, Zhang K, Epstein IR. Chaos. 2009 Sep;19(3):033134.[abstract]
Chemistry. Emergent or just complex? Balazs AC, Epstein IR. Science. 2009 Sep 25;325(5948):1632-4.
Pattern formation mechanisms in reaction-diffusion systems. Vanag VK, Epstein IR. Int J Dev Biol. 2009;53(5-6):673-81.[abstract]
High-frequency oscillations in the Belousov-Zhabotinsky reaction. Bánsági T Jr, Leda M, Toiya M, Zhabotinsky AM, Epstein IR. J Phys Chem A. 2009 May 14;113(19):5644-8. [abstract]
Temperature control of pattern formation in the Ru(bpy)(3)(2+)-catalyzed BZ-AOT system. McIlwaine R, Vanag VK, Epstein IR. Phys Chem Chem Phys. 2009 Mar 14;11(10):1581-7. [abstract]
Cross-diffusion and pattern formation in reaction-diffusion systems. Vanag VK, Epstein IR. Phys Chem Chem Phys. 2009 Feb 14;11(6):897-912.
Oscillations and mechanistic analysis of the chlorite-sulfide reaction in a continuous-flow stirred tank reactor. Mao S, Gao Q, Wang H, Zheng J, Epstein IR. J Phys Chem A. 2009 Feb 19;113(7):1231-4.
Small-amplitude and mixed-mode pH oscillations in the bromate-sulfite-ferrocyanide-aluminum(III) system. Kovacs K, Leda M, Vanag VK, Epstein IR. J Phys Chem A. 2009 Jan 8;113(1):146-56.
Breathing spiral waves in the chlorine dioxide-iodine-malonic acid reaction-diffusion system. Berenstein I, Muñuzuri AP, Yang L, Dolnik M, Zhabotinsky AM, Epstein IR. Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Aug;78(2 Pt 2):025101.
Diffusively coupled chemical oscillators in a microfluidic assembly. Toiya M, Vanag VK, Epstein IR. Angew Chem Int Ed Engl. 2008;47(40):7753-5.
Cross-diffusion in a water-in-oil microemulsion loaded with malonic acid or ferroin. Taylor dispersion method for four-component systems. Vanag VK, Rossi F, Cherkashin A, Epstein IR. J Phys Chem B. 2008 Jul 31;112(30):9058-70. Epub 2008 Jul 9.
Design and control of patterns in reaction-diffusion systems.Vanag VK, Epstein IR. Chaos. 2008 Jun;18(2):026107.
Oscillations in the concentration of fluoride ions induced by a pH oscillator. Horvath V, Kurin-Csörgei K, Epstein IR, Orban M. J Phys Chem A. 2008 May 8;112(18):4271-6.
Coupled and forced patterns in reaction-diffusion systems. Epstein IR, Berenstein IB, Dolnik M, Vanag VK, Yang L, Zhabotinsky AM. Philos Transact A Math Phys Eng Sci. 2008 Feb 13;366(1864):397-408.
Localized patterns in reaction-diffusion systems. Vanag VK, Epstein IR. Chaos. 2007 Sep;17(3):037110.
Fronts and pulses in an enzymatic reaction catalyzed by glucose oxidase. Míguez DG, Vanag VK, Epstein IR. Proc Natl Acad Sci U S A. 2007 Apr 24;104(17):6992-7.
Designing an enzymatic oscillator: bistability and feedback controlled oscillations with glucose oxidase in a continuous flow stirred tank reactor.Vanag VK, Míguez DG, Epstein IR. J Chem Phys. 2006 Nov 21;125(19):194515.
Yang L, Zhabotinsky AM, Epstein IR. (2006) Jumping solitary waves in an autonomous reaction-diffusion system with subcritical wave instability. Phys Chem Chem Phys. 2006 Oct 28;8(40):4647-51.
Predicting complex biology with simple chemistry.Epstein IR. Proc Natl Acad Sci U S A. 2006 Oct 24;103(43):15727-8. Epub 2006 Oct 16.
Turing patterns beyond hexagons and stripes.Yang L, Dolnik M, Zhabotinsky AM, Epstein IR. Chaos. 2006 Sep;16(3):037114.
Role of the neurogranin concentrated in spines in the induction
of long-term potentiation.Zhabotinsky AM, Camp RN, Epstein IR, Lisman JE. J Neurosci. 2006 Jul 12;26(28):7337-47.
of calcium ions in a chemical system.Kurin-Csorgei K, Epstein IR, Orban M. J Phys Chem A Mol
Spectrosc Kinet Environ Gen Theory. 2006 Jun 22;110(24):7588-92.
memory device. Kaminaga A, Vanag VK, Epstein IR. Angew Chem Int Ed Engl. 2006 May 5;45(19):3087-9.
patterns beyond hexagons and stripes.Yang L, Dolnik M, Zhabotinsky AM, Epstein IR. Chaos. 2006
Predicting complex biology with simple
chemistry.Epstein IR. Proc Natl Acad Sci U S A. 2006 Oct 24;103(43):15727-8.
waves in an autonomous reaction-diffusion system with subcritical
wave instability.Yang L, Zhabotinsky AM, Epstein IR. Phys Chem Chem Phys. 2006 Oct 28;8(40):4647-51.
Epub 2006 Sep 11.[abstract]
Designing an enzymatic
oscillator: bistability and feedback controlled oscillations
with glucose oxidase in a continuous flow stirred tank reactor. Vanag VK, Miguez DG, Epstein IR. J Chem Phys. 2006 Nov 21;125(19):194515. [abstract]
Complex patterns in reactive
microemulsions: self-organized nanostructures? Epstein IR, Vanag VK. Chaos.
2005 Dec;15(4):047510. [abstract]
Out-of-phase oscillatory Turing
patterns in a bistable reaction-diffusion system.Vanag VK, Epstein IR. Phys
Rev E Stat Nonlin Soft Matter Phys. 2005 Jun;71(6 Pt
2):066212. Epub 2005 Jun 23. [abstract]
in a surfactant-rich Belousov-Zhabotinsky reaction dispersed
in a water-in-oil microemulsion system. Kaminaga A, Vanag VK, Epstein IR. J Chem Phys. 2005 May 1;122(17):174706. [abstract]
Dynamic mechanism of photochemical induction
of turing superlattices in the chlorine dioxide-iodine-malonic
acid reaction-diffusion system. Berenstein I, Yang L, Dolnik M, Zhabotinsky AM, Epstein
IR. J Phys Chem A Mol Spectrosc
Kinet Environ Gen Theory. 2005 Jun 23;109(24):5382-7.
Design of Chemical Oscillators Using Complexation and Precipitation
Equilibria. K. Kurin-Csörgei, M. Orbán and I. R. Epstein. Nature 433, 139-142 (2005). [abstract]
Response of Complex Networks
to Stimuli. Y. Bar-Yam and I.R. Epstein. Proc. Natl. Acad. Sci. 101, 4341-4345
Translational and nontranslational
motion of perturbed Turing patterns.Vanag VK, Epstein IR. Phys Rev E Stat
Nonlin Soft Matter Phys. 2003 Jun;67(6 Pt 2):066219.
Segmented Spiral Waves in
a Reaction-Diffusion System. V.K. Vanag and I.R. Epstein. Proc. Nat. Acad. Sci. USA 100, 14635-14638 (2003) (cover article). [abstract]
Superlattice Turing Structures in a Photosensitive
Reaction-Diffusion System. I. Berenstein, L. Yang, M. Dolnik, A.M. Zhabotinsky and
I.R. Epstein. Phys. Rev. Lett. 91,
058302-1-4 (2003). [abstract]
Oscillatory Turing Patterns
in Reaction-Diffusion Systems with Two Coupled Layers. L. Yang and I.R. Epstein. Phys. Rev. Lett. 90, 178303-1-4 (2003). [abstract]
of Robustness and Connectivity in Complex Networks. B. Shargel, H. Sayama, I. R. Epstein and Y. Bar-Yam. Phys.
Rev. Lett. 90, 068701-1-4 (2003).
Search PubMed for Publications: Irving
Last review: July 7, 2010