Статті КІТ

Permanent URI for this collection

http://crust.ust.edu.ua/handle/123456789/694
ENG: Articles

Browse

Browsing Статті КІТ by Subject "1D дискретна карта"

Now showing 1 - 3 of 3
  • Thumbnail Image
    Item
    Generating Chaos in 3D Systems Of Quadratic Differential Equations With 1D Exponential Maps
    (World Scientific Publishing Company, 2013) Belozyorov, Vasiliy Ye.; Chernyshenko, Sergey V.
    EN: New existence conditions of homoclinic orbits for some systems of ordinary quadratic differential equations with singular linear part are found. A realization of these conditions guarantees the existence of chaotic attractors at 3D autonomous quadratic systems. Examples of chaotic attractors are given.
  • Thumbnail Image
    Item
    A Novel Search Method of Chaotic Autonomous Quadratic Dynamical Systems without Equilibrium Points
    (Springer Netherlands, 2016) Belozyorov, Vasiliy Ye.
    EN: A wide class of autonomous real quadratic dynamic system without real (but with two complex conjugate or even imaginary) equilibrium points is considered. For any system of this class, a new idea of the uniquely definite degenerate autonomous real quadratic dynamic system having exactly one real double equilibrium point (there are no complex equilibrium points) is introduced. It is shown that if the degenerate system demonstrates the chaotic behavior, then for the original (not degenerate) system, a similar chaotic behavior also takes place. The idea of the degenerate system for researches of the real quadratic systems, for which number of complex conjugate equilibrium points more than two, is also used. The same idea can be adapted to research of any autonomous real quadratic system having at least one pair complex conjugate equilibrium points. An attempt to apply some derived results to a search problem of hidden chaotic attractors was undertaken. Examples are given.
  • Thumbnail Image
    Item
    Role of Logistic and Ricker’s Maps in Appearance of Chaos in Autonomous Quadratic Dynamical Systems
    (Springer Netherlands, 2016) Belozyorov, Vasiliy Ye.; Volkova, Svetlana A.
    EN: New existence conditions of a chaotic behavior for wide class of (n+1)-dimensional autonomous quadratic dynamical systems are suggested. It is shown that in all such systems the chaotic dynamics is generated by 1D discrete map by some combination of the logistic map f (x) = λx(1−x);λ> 0 and Ricker’s map g(x) = x exp(μ−x);μ>0.