Chaos in Chemistry and Biochemistry

Field, Richard J.; Györgyi, László

doi:10.1142/1706

Cited by 104 publications

(55 citation statements)

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“…Bifurcations are familiar phenomena routinely used nowadays as sensitive indicators of drastic changes in dynamical behaviors in physics and related sciences [1][2][3][4][5]. In fact, the past two decades witnessed extensive efforts to describe how bifurcations between periodic and chaotic oscillations unfold in all sorts of systems.…”

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confidence: 99%

“…They are ubiquitous features supported by all theoretical descriptions, based on models ranging from ''simple'' discrete-time mappings to sophisticated continuous-time multidimensional flows ruled by sets of differential equations. Bifurcation phenomena involving the variation of just a single parameter, referred to as codimension-one bifurcations, are now reasonably well understood [1][2][3][4][5]. In contrast, fragmentary information is available about much more realistic situations requiring the simultaneous variation of at least two independent parameters (codimension two).…”

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confidence: 99%

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Periodicity Hub and Nested Spirals in the Phase Diagram of a Simple Resistive Circuit

2008

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We report the discovery of a remarkable ''periodicity hub'' inside the chaotic phase of an electronic circuit containing two diodes as a nonlinear resistance. The hub is a focal point from where an infinite hierarchy of nested spirals emanates. By suitably tuning two reactances simultaneously, both current and voltage may have their periodicity increased continuously without bound and without ever crossing the surrounding chaotic phase. Familiar period-adding current and voltage cascades are shown to be just restricted one-parameter slices of an exceptionally intricate and very regular onionlike parameter surface centered at the focal hub which organizes all the dynamics.

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confidence: 99%

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Periodicity Hub and Nested Spirals in the Phase Diagram of a Simple Resistive Circuit

2008

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“…As evidenced by not only fundamental research undertaken but also tutorials both inside and outside of the classic chemistry literature [35,36], as well as texts describing fractals and chaos in a manner useful to practicing chemists [37][38][39], interest in chaos theory and fractal dimensionality continued throughout the late 1980s and the 1990s in general. For example, 1991 saw a review article in the chemometrics literature by Hibbert [40] regarding the intersection of fractal and chemical analyses, including synergistic applications in the experimental areas of electrochemical deposition (which produces nonlinearly uneven surfaces) and size exclusion, affinity and ion chromatography techniques as well as the evaluation of reaction kinetics on differing uneven surfaces.…”

Section: Chaos In Chemsitrymentioning

confidence: 99%

Chaos theory in chemistry and chemometrics: a review

Cramer

Booksh

2006

Journal of Chemometrics

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Since the initial development of chaos theory and corollary concepts such as the strange attractor and fractal dimensionality, there has been a nontrivial effort to apply these concepts to the quantification of material and data structures. There exists within chaos theory modeling concepts that allow for thorough complexity analyses not available through alternate paradigms. The purpose of this paper is to review the main body of work that has been pursued in both experimental chemistry research and related data analysis development with respect to chaos theory and derivative ideas.

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“…Since then, chaos has been observed in many systems, such as population growth in ecology [20], weather and climate [19] and in laboratory, in a great number of systems, such as electrical circuits [21], chemical reactions [23], lasers [22], fluid dynamics [24] and mechanical systems as well as magneto-mechanical devices [25]. So, chaos can explain various phenomena not only in nature, but also in laboratory and many chaotic dynamical systems can be used in different scientific fields.…”

Section: Introductionmentioning

confidence: 99%

Analysis, adaptive control and circuit simulation of a novel finance system with dissaving

Tacha¹,

Volos²,

Stouboulos³

et al. 2016

Archives of Control Sciences

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Analysis, adaptive control and circuit simulation of a novel finance system with dissaving OURANIA I. TACHA, CHRISTOS K. VOLOS, IOANNIS N. STOUBOULOS and IOANNIS M. KYPRIANIDISIn this paper a novel 3-D nonlinear finance chaotic system consisting of two nonlinearities with negative saving term, which is called 'dissaving' is presented. The dynamical analysis of the proposed system confirms its complex dynamic behavior, which is studied by using wellknown simulation tools of nonlinear theory, such as the bifurcation diagram, Lyapunov exponents and phase portraits. Also, some interesting phenomena related with nonlinear theory are observed, such as route to chaos through a period doubling sequence and crisis phenomena. In addition, an interesting scheme of adaptive control of finance system's behavior is presented. Furthermore, the novel nonlinear finance system is emulated by an electronic circuit and its dynamical behavior is studied by using the electronic simulation package Cadence OrCAD in order to confirm the feasibility of the theoretical model.

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Chaos in Chemistry and Biochemistry

Cited by 104 publications

References 0 publications

Periodicity Hub and Nested Spirals in the Phase Diagram of a Simple Resistive Circuit

Periodicity Hub and Nested Spirals in the Phase Diagram of a Simple Resistive Circuit

Chaos theory in chemistry and chemometrics: a review

Analysis, adaptive control and circuit simulation of a novel finance system with dissaving

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