Title :
Difference scheme with instant transition "from order to chaos"
Author :
Goloubentsev, Alexander F. ; Anikin, Valery M. ; Barulina, Yuliya A.
Author_Institution :
Dept. of comput. phys., Saratov State Univ., Russia
Abstract :
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.
Keywords :
chaos; eigenvalues and eigenfunctions; nonlinear differential equations; statistical distributions; Cauchy distribution; Perron-Frobenius operator; chaos; chaotic behavior; chaotic regime; eigenfunction; eigenvalues; first order differential equation; infinite interval; invariant density; map construction; one-dimensional nonlinear difference equations; positive Lyapunov exponent; semigroup properties; Bifurcation; Chaos; Difference equations; Eigenvalues and eigenfunctions; Multidimensional systems; Nonlinear equations; Oscillators; Partial differential equations; Physics computing; Trajectory;
Conference_Titel :
Physics and Control, 2003. Proceedings. 2003 International Conference
Print_ISBN :
0-7803-7939-X
DOI :
10.1109/PHYCON.2003.1236864
