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Journal ArticleDOI

Chemical hysteresis, a new type of behavior in the Belousov-Zhabotinskii reaction

22 Mar 1976-Physics Letters A (Elsevier)-Vol. 56, Iss: 3, pp 155-157
TL;DR: In this paper, chemical hysteresis is predicted for the transition between two stable homogeneous states, one stationary and the other oscillatory, based on studies of a reduced model for the Belousov-Zhabotinskii reaction.
About: This article is published in Physics Letters A.The article was published on 1976-03-22. It has received 9 citations till now. The article focuses on the topics: Hysteresis.
Citations
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Book ChapterDOI
A.T. Winfree1
01 Jan 1978

63 citations

Journal ArticleDOI
TL;DR: In this article, a modified version of the oregonator model of the Belousov-Zhabotinsky reaction is used to simulate composite double oscillation in which nearly identical bursts of oscillation are separated by regular periods of quiescence.
Abstract: A number of nonmonotonic behaviors appear when the Belousov–Zhabotinsky reaction is run in a flow system (CSTR) which are not observed when the reaction is run in a closed system. Among these behaviors is composite double oscillation in which nearly identical bursts of oscillation are separated by regular periods of quiescence. Here we use a modified version of the oregonator model of the Belousov–Zhabotinsky reaction to simulate composite double oscillation. Our modification involves the addition of a new variable which is related to the amount of brominated organic material present in the system. This new variable changes slowly on the time scale of the oscillations and controls the value of f, the stoichiometric factor of step 5 in the oregonator. Thus the behavior of the modified oregonator in CSTR mode when flowrates are moderate can be rationalized in terms of the properties of the unmodified oregonator in a closed system. We show that composite double oscillation is a hysteresis phenomenon occurrin...

44 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that the chemical entropy in the reversible Oregonator changes discontinuously at critical values of the concentration parameter at which points a limit cycle bifurcates out of an unstable steady state.
Abstract: We show that the chemical entropy production in the reversible Oregonator changes discontinuously at critical values of the concentration parameter at which points a limit cycle bifurcates out of an unstable steady state. The discontinuities in the entropy production are reminiscent of the behavior of the entropy change accompanying a first order phase transition in thermodynamics. They appear to be an example of dynamic phase transitions. For this model, by using Poore’s algorithm, we show that in the case of f=1 the limit cycle is orbitally asymptotically unstable and the bifurcation is subcritical, but in the case of f=0.5 the limit cycle bifurcation at the higher critical concentration of P is subcritical whereas the one at the lower critical concentration of P is supercritical. Therefore, a discontinuous change in chemical entropy production accompanies subcritical Hopf bifurcations and possibly a supercritical Hopf bifurcation. It is conjectured that if a bifurcation is subcritical, attractors of different topological dimensions have different characteristic entropy productions in the same manner as two different states of aggregation of matter have different entropies associated with them.

9 citations

Book ChapterDOI
01 Jan 1978

6 citations

References
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Journal ArticleDOI
TL;DR: In this paper, the authors extended the five-step Oregonator model by taking into account the reversibility of the various steps and found that there is a critical distance from equilibrium which must be exceeded before the steady state becomes unstable.
Abstract: The five‐step Oregonator model of the oscillatory Belousov–Zhabotinskii reaction has been expanded by taking into account the reversibility of the various steps. Forward and reverse rate constants have been assigned to four of the five steps by direct analogy to the detailed Field, Koros, and Noyes model of the Belousov–Zhabotinskii reaction. The rate constants and stoichiometry of the fifth step were parametrized and the stability of the steady state was investigated as a function of both of these parameters and the over‐all distance of the system from equilibrium. It was found that there is a critical distance from equilibrium which must be exceeded before the steady state becomes unstable. Numerical integration of the differential equations resulting from the model indicated that the system executes apparent limit cycle oscillations when the steady state is unstable. Introduction of reversibility into the Oregonator leads to a striking change in the range of values of the fifth step stoichiometric parameter over which oscillations will occur. This change is discussed in terms of the chemistry of the Belousov–Zhabotinskii reaction. Under some conditions the reversible Oregonator shows excitability such that a small finite perturbation of an infinitesimally stable steady state may be greatly amplified before the system returns to rest. An apparently analogous phenomenon appears in the Belousov–Zhabotinskii reaction itself.

80 citations