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  • 1.
    Berrhazi, Badr-eddine
    et al.
    Ibn Tofail Univ, Morocco.
    El Fatini, Mohamed
    Ibn Tofail Univ, Morocco.
    Laaribi, Aziz
    Ibn Tofail Univ, Morocco.
    Pettersson, Roger
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    A stochastic viral infection model driven by Levy noise2018In: Chaos, Solitons & Fractals, ISSN 0960-0779, E-ISSN 1873-2887, Vol. 114, p. 446-452Article in journal (Refereed)
    Abstract [en]

    In this paper, we are interested in the study of a stochastic viral infection model with immune impairment driven by Levy noise. First we prove the existence of a unique global solution to the model. By means of the Lyapunov method we study the stability of the equilibria. We present sufficient conditions for the extinction and persistence in mean. Furthermore, we present some numerical results to support the theoretical work.

  • 2.
    Berrhazi, Badr-eddine
    et al.
    Ibn Tofail Univ, Morocco.
    El Fatini, Mohamed
    Ibn Tofail Univ, Morocco.
    Laaribi, Aziz
    Hassan II Univ, Morocco.
    Pettersson, Roger
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Taki, Regragui
    Ibn Tofail Univ, Morocco.
    A stochastic SIRS epidemic model incorporating media coverage and driven by Levy noise2017In: Chaos, Solitons & Fractals, ISSN 0960-0779, E-ISSN 1873-2887, Vol. 105, p. 60-68Article in journal (Refereed)
    Abstract [en]

    In this paper, we establish the existence of a unique global positive solution for a stochastic epidemic model, incorporating media coverage and driven by Levy noise. We also investigate the dynamic properties of the solution around both disease-free and endemic equilibria points of the deterministic model. Furthermore, we present some numerical results to support the theoretical work. (C) 2017 Elsevier Ltd. All rights reserved.

  • 3. Conte, Elio
    et al.
    Khrennikov, Andrei
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Federici, Antonio
    Zbilut, Joseph P.
    Fractal fluctuations and quantum-like chaos in the brain by analysis of variability of brain waves: A new method based on a fractal variance function and random matrix theory: A link with El Naschie fractal Cantorian space–time and V. Weiss and H. Weiss golden ratio in brain2009In: Chaos, Solitons & Fractals, ISSN 0960-0779, E-ISSN 1873-2887, Vol. 41, no 5, p. 2790-2800Article in journal (Refereed)
    Abstract [en]

    We develop a new method for analysis of fundamental brain waves as recorded by the EEG. To this purpose we introduce a Fractal Variance Function that is based on the calculation of the variogram. The method is completed by using Random Matrix Theory. Some examples are given. We also discuss the link of such formulation with H. Weiss and V. Weiss golden ratio found in the brain, and with El Naschie fractal Cantorian space–time theory.

  • 4.
    Khrennikov, Andrei
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Gene expression from polynomial dynamics in the2-adic information space2009In: Chaos, Solitons & Fractals, ISSN 0960-0779, E-ISSN 1873-2887, Vol. 42, no 1, p. 341-347Article in journal (Refereed)
    Abstract [en]

    We perform geometrization of genetics by representing genetic information by points of the 4-adic information space. By well known theorem of number theory this space can also be represented as the 2-adic space. The process of DNA-reproduction is described by the action of a 4-adic (or equivalently 2-adic) dynamical system. As we know, the genes contain information for production of proteins. The genetic code is a degenerate map of codons to proteins. We model this map as functioning of a polynomial dynamical system. The purely mathematical problem under consideration is to find a dynamical system reproducing the degenerate structure of the genetic code. We present one of possible solutions of this problem.

  • 5.
    Khrennikov, Andrei
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Yurova, Ekaterina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Criteria of ergodicity for p-adic dynamical systems in terms of coordinate functions2014In: Chaos, Solitons & Fractals, ISSN 0960-0779, E-ISSN 1873-2887, Vol. 60, p. 11-30Article in journal (Refereed)
    Abstract [en]

    This paper is devoted to the problem of ergodicity of p-adic dynamical systems. We solved the problem of characterization of ergodicity and measure preserving for (discrete) p-adic dynamical systems for arbitrary prime p for iterations based on 1-Lipschitz functions. This problem was open since long time and only the case p = 2 was investigated in details. We formulated the criteria of ergodicity and measure preserving in terms of coordinate functions corresponding to digits in the canonical expansion of p-adic numbers. (The coordinate representation can be useful, e.g., for applications to cryptography.) Moreover, by using this representation we can consider non-smooth p-adic transformations. The basic technical tools are van der Put series and usage of algebraic structure (permutations) induced by coordinate functions with partially frozen variables. We illustrate the basic theorems by presenting concrete classes of ergodic functions. As is well known, p-adic spaces have the fractal (although very special) structure. Hence, our study covers a large class of dynamical systems on fractals. Dynamical systems under investigation combine simplicity of the algebraic dynamical structure with very high complexity of behavior.

  • 6.
    Lindström, Torsten
    University of Kalmar, School of Pure and Applied Natural Sciences.
    Detecting chaos requires careful analysis of nearly periodic data2009In: Chaos, Solitons & Fractals, ISSN 0960-0779, E-ISSN 1873-2887, Vol. 42, no 1, p. 212-223Article in journal (Refereed)
    Abstract [en]

    We show that models fitted to data in many cases fit unstable periodic solutions in attracting periodic solutions of the 'true model' that generated the data. An attracting solution containing the neighborhood of the fitted unstable solution in its domain of attraction may possess entirely different dynamical properties. Thus, an attracting chaotic solution with positive Lyapunov exponent may describe periodic solutions with negative Lyapunov exponents and vice versa. These problems can in principle be remedied, if the fitted models would be allowed to contain an arbitrary complexity and if an infinite amount of data would be available. We claim that we stay far from such limits in ecology, for instance. Therefore, we think our approach is essential to bear in mind when making data-based predictions concerning dynamical behavior. Our general conclusion is that less data is required in nearly periodic cases than in chaotic cases for rejecting models not allowing complex behavior.

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