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J C Sprott - One of the best experts on this subject based on the ideXlab platform.

  • megastability coexistence of a countable infinity of nested Attractors in a periodically forced oscillator with spatially periodic damping
    European Physical Journal-special Topics, 2017
    Co-Authors: J C Sprott, Sajad Jafari, Abdul Jalil M Khalaf, Tomasz Kapitaniak
    Abstract:

    In this paper, we describe a periodically-forced oscillator with spatially-periodic damping. This system has an infinite number of coexisting nested Attractors, including limit cycles, attracting tori, and Strange Attractors. We are aware of no similar example in the literature.

  • multistability in symmetric chaotic systems
    European Physical Journal-special Topics, 2015
    Co-Authors: J C Sprott, X Wang
    Abstract:

    Chaotic dynamical systems that are symmetric provide the possibility of multistability as well as an independent amplitude control parameter.The Rossler system is used as a candidate for demonstrating the symmetry construction since it is an asymmetric system with a single-scroll attractor. Through the design of symmetric Rossler systems, a symmetric pair of coexisting Strange Attractors are produced, along with the desired partial or total amplitude control.

  • multistability in the lorenz system a broken butterfly
    International Journal of Bifurcation and Chaos, 2014
    Co-Authors: Chunbiao Li, J C Sprott
    Abstract:

    In this paper, the dynamical behavior of the Lorenz system is examined in a previously unexplored region of parameter space, in particular, where r is zero and b is negative. For certain values of the parameters, the classic butterfly attractor is broken into a symmetric pair of Strange Attractors, or it shrinks into a small attractor basin intermingled with the basins of a symmetric pair of limit cycles, which means that the system is bistable or tristable under certain conditions. Although the resulting system is no longer a plausible model of fluid convection, it may have application to other physical systems.

  • bistability in a hyperchaotic system with a line equilibrium
    Journal of Experimental and Theoretical Physics, 2014
    Co-Authors: Chunbiao Li, J C Sprott, Wesley Thio
    Abstract:

    A hyperchaotic system with an infinite line of equilibrium points is described. A criterion is proposed for quantifying the hyperchaos, and the position in the three-dimensional parameter space where the hyperchaos is largest is determined. In the vicinity of this point, different dynamics are observed including periodicity, quasi-periodicity, chaos, and hyperchaos. Under some conditions, the system has a unique bistable behavior, characterized by a symmetric pair of coexisting limit cycles that undergo period doubling, forming a symmetric pair of Strange Attractors that merge into a single symmetric chaotic attractor that then becomes hyperchaotic. The system was implemented as an electronic circuit whose behavior confirms the numerical predictions.

  • multistability in a butterfly flow
    International Journal of Bifurcation and Chaos, 2013
    Co-Authors: Chunbiao Li, J C Sprott
    Abstract:

    A dynamical system with four quadratic nonlinearities is found to display a butterfly Strange attractor. In a relatively large region of parameter space the system has coexisting point Attractors and limit cycles. At some special parameter combinations, there are five coexisting Attractors, where a limit cycle coexists with two equilibrium points and two Strange Attractors in different attractor basins. The basin boundaries have a symmetric fractal structure. In addition, the system has other multistable regimes where a pair of point Attractors coexist with a single limit cycle or a symmetric pair of limit cycles and where a symmetric pair of limit cycles coexist without any stable equilibria.

G Pfister - One of the best experts on this subject based on the ideXlab platform.

Th Buzug - One of the best experts on this subject based on the ideXlab platform.

Musatenko I. - One of the best experts on this subject based on the ideXlab platform.

  • A mathematical model of the metabolism of a cell. Self-organization and chaos
    2018
    Co-Authors: Grytsay V., Musatenko I.
    Abstract:

    Using the classical tools of nonlinear dynamics, we study the process of self-organization and the appearance of the chaos in the metabolic process in a cell with the help of a mathematical model of the transformation of steroids by a cell Arthrobacter globiformis. We constructed the phase-parametric diagrams obtained under a variation of the dissipation of the kinetic membrane potential. The oscillatory modes obtained are classified as regular and Strange Attractors. We calculated the bifurcations, by which the self-organization and the chaos occur in the system, and the transitions "chaos-order", "order-chaos", "order-order", and "chaos-chaos" arise. Feigenbaum's scenarios and the intermittences are found. For some selected modes, the projections of the phase portraits of Attractors, Poincar\'e sections, and Poincar\'e maps are constructed. The total spectra of Lyapunov indices for the modes under study are calculated. The structural stability of the Attractors is demonstrated. A general scenario of the formation of regular and Strange Attractors in the given metabolic process in a cell is found. The physical nature of their appearance in the metabolic process is studied.Comment: 11 pages, 9 figure

  • Self-organization and chaos in the metabolism of a cell
    'Institute of Molecular Biology and Genetics (NAS Ukraine)', 2018
    Co-Authors: Grytsay V., Musatenko I.
    Abstract:

    Aim. To study the dynamics of auto-oscillations arising at the level of enzyme-substrate interaction in a cell and to find the conditions for the self-organization and the formation of chaos in the metabolic process. Methods. A mathematical model of the metabolic process of steroids transformation in Arthrobacter globiformis. The mathematical apparatus of nonlinear dynamics. Results. The bifurcations resulting in the appearance of Strange Attractors in the metabolic process are determined. The projections of the phase portraits of Attractors are constructed for some chosen modes. The total spectra of Lyapunov's indices are calculated. The structural stability of the Attractors obtained is studied. By the general scenario of formation of regular and Strange Attractors, the structural-functional connections in the metabolic process in the cell are found. Their physical nature is investigated. Conclusions. The presented model explains the mechanism of formation of auto-oscillations observed in the A. globiformis cells and demonstrates a possibility of the mathematical modeling of metabolic processes for the physical explanation of the self-organization of a cell and its vital activity.Comment: 10 pages, 5 figure

  • The structure of a chaos of Strange Attractors within a mathematical model of the metabolism of a cell
    2017
    Co-Authors: Grytsay V., Musatenko I.
    Abstract:

    This work continues the study of the earlier constructed mathematical model of the metabolic process running in a cell. We will consider auto-oscillations arising on the level of enzyme-substrate interactions in the nutrient and respiratory chains, which leads to the self-organization in autocatalysis of the integral metabolic process in cells. The auto-oscillations organize themselves in the total metabolic process of cells at autocatalysis. The behavior of the phase-parametric characteristic under the high dissipation of a kinetic membrane potentialis analyzed. All possible oscillatory modes of the system and the scenario of formation and destruction of regular and Strange Attractors are studied. The bifurcations of the transitions "order-chaos", "chaos-order", "chaos-chaos" and "order-order" are calculated. The total spectra of Lyapunov indices and the divergences for all types of Attractors on a part of the phase-parametric characteristic under consideration are determined. For various types of Strange Attractors, their Lyapunov dimensions, KS-entropies, and "predictability horizons" are calculated. Some conclusions about the structure of the chaos of Strange Attractors and its influence on the stability of the metabolic process in a cell are drawn.Comment: 10 pages, 5 figure

Grytsay V. - One of the best experts on this subject based on the ideXlab platform.

  • Self-organization and chaos in the metabolism of a cell
    'Institute of Molecular Biology and Genetics (NAS Ukraine)', 2018
    Co-Authors: Grytsay V., Musatenko I.
    Abstract:

    Aim. To study the dynamics of auto-oscillations arising at the level of enzyme-substrate interaction in a cell and to find the conditions for the self-organization and the formation of chaos in the metabolic process. Methods. A mathematical model of the metabolic process of steroids transformation in Arthrobacter globiformis. The mathematical apparatus of nonlinear dynamics. Results. The bifurcations resulting in the appearance of Strange Attractors in the metabolic process are determined. The projections of the phase portraits of Attractors are constructed for some chosen modes. The total spectra of Lyapunov's indices are calculated. The structural stability of the Attractors obtained is studied. By the general scenario of formation of regular and Strange Attractors, the structural-functional connections in the metabolic process in the cell are found. Their physical nature is investigated. Conclusions. The presented model explains the mechanism of formation of auto-oscillations observed in the A. globiformis cells and demonstrates a possibility of the mathematical modeling of metabolic processes for the physical explanation of the self-organization of a cell and its vital activity.Comment: 10 pages, 5 figure

  • A mathematical model of the metabolism of a cell. Self-organization and chaos
    2018
    Co-Authors: Grytsay V., Musatenko I.
    Abstract:

    Using the classical tools of nonlinear dynamics, we study the process of self-organization and the appearance of the chaos in the metabolic process in a cell with the help of a mathematical model of the transformation of steroids by a cell Arthrobacter globiformis. We constructed the phase-parametric diagrams obtained under a variation of the dissipation of the kinetic membrane potential. The oscillatory modes obtained are classified as regular and Strange Attractors. We calculated the bifurcations, by which the self-organization and the chaos occur in the system, and the transitions "chaos-order", "order-chaos", "order-order", and "chaos-chaos" arise. Feigenbaum's scenarios and the intermittences are found. For some selected modes, the projections of the phase portraits of Attractors, Poincar\'e sections, and Poincar\'e maps are constructed. The total spectra of Lyapunov indices for the modes under study are calculated. The structural stability of the Attractors is demonstrated. A general scenario of the formation of regular and Strange Attractors in the given metabolic process in a cell is found. The physical nature of their appearance in the metabolic process is studied.Comment: 11 pages, 9 figure

  • The structure of a chaos of Strange Attractors within a mathematical model of the metabolism of a cell
    2017
    Co-Authors: Grytsay V., Musatenko I.
    Abstract:

    This work continues the study of the earlier constructed mathematical model of the metabolic process running in a cell. We will consider auto-oscillations arising on the level of enzyme-substrate interactions in the nutrient and respiratory chains, which leads to the self-organization in autocatalysis of the integral metabolic process in cells. The auto-oscillations organize themselves in the total metabolic process of cells at autocatalysis. The behavior of the phase-parametric characteristic under the high dissipation of a kinetic membrane potentialis analyzed. All possible oscillatory modes of the system and the scenario of formation and destruction of regular and Strange Attractors are studied. The bifurcations of the transitions "order-chaos", "chaos-order", "chaos-chaos" and "order-order" are calculated. The total spectra of Lyapunov indices and the divergences for all types of Attractors on a part of the phase-parametric characteristic under consideration are determined. For various types of Strange Attractors, their Lyapunov dimensions, KS-entropies, and "predictability horizons" are calculated. Some conclusions about the structure of the chaos of Strange Attractors and its influence on the stability of the metabolic process in a cell are drawn.Comment: 10 pages, 5 figure

  • Self-Organization and Fractality in the Metabolic Process of Glycolysis
    'National Academy of Sciences of Ukraine (Co. LTD Ukrinformnauka)', 2017
    Co-Authors: Grytsay V.
    Abstract:

    Within a mathematical model, the metabolic process of glycolysis is studied. The general scheme of glycolysis is considered as a natural result of the biochemical evolution. By using the theory of dissipative structures, the conditions of self-organization of the given process are sought. The autocatalytic processes resulting in the conservation of cyclicity in the dynamics of the process are determined. The conditions of breaking of the synchronization of the process, increase in the multiplicity of a cyclicity, and appearance of chaotic modes are studied. The phase-parametric diagrams of a cascade of bifurcations, which characterize the transition to chaotic modes according to the Feigenbaum scenario and the intermittence, are constructed. The Strange Attractors formed as a result of the funnel effect are found. The complete spectra of Lyapunov indices and divergences for the obtained modes are calculated. The values of KS-entropy, horizons of predictability, and Lyapunov dimensions of Strange Attractors are determined. Some conclusions concerning the structural-functional connections in glycolysis and their influence on the stability of the metabolic process in a cell are presented.Comment: 13 pages, 5 figure