Difference scheme with instant transition "from order to chaos"

Difference scheme with instant transition "from order to chaos"

The one-dimensional nonlinear difference equation of the first order depending on a parameter is constructed on the infinite interval. Its exact solutions have semi-group properties and demonstrate regular or chaotic behavior for various regions of parameter changing. There is a parameter value that...

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Bibliographische Detailangaben
Hauptverfasser: Goloubentsev, A.F., Anikin, V.M., Barulina, Y.A.
Format: Tagungsbericht
Sprache:eng
Schlagworte:
Bifurcation
Chaos
Difference equations
Eigenvalues and eigenfunctions
Multidimensional systems
Nonlinear equations
Oscillators
Partial differential equations
Physics computing
Trajectory
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Beschreibung
Zusammenfassung:The one-dimensional nonlinear difference equation of the first order depending on a parameter is constructed on the infinite interval. Its exact solutions have semi-group properties and demonstrate regular or chaotic behavior for various regions of parameter changing. There is a parameter value that "provides" an instant transition "from order to chaos". The chaotic regime is characterized by having the invariant density in the form of the Cauchy distribution and the positive Lyapunov exponent In2. The eigenfunction and eigenvalues of the Perron-Frobenius operator for constructed map are found.
DOI:10.1109/PHYCON.2003.1236864