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Comment on“Time-averaged properties of unstable periodic orbits and chaotic orbits in ordinary differential equation systems”
Time-averaged properties chaotic orbits unstable periodic orbits
2010/4/7
The recent paper claims that mean characteristics of chaotic orbits differ from the corresponding values averaged over the set of unstable periodic orbits, embedded in the chaotic attractor. We demons...
Unstable periodic orbits and attractor of the barotropic ocean model
Unstable periodic orbits barotropic ocean model
2009/11/13
A numerical method for detection of unstable periodic orbits on attractors of nonlinear models is proposed. The method requires similar techniques to data assimilation. This fact facilitates its imp...
Sensitivity of the attractor of the barotropic ocean model to external influences:approach by unstable periodic orbits
barotropic ocean model external influences unstable periodic orbits
2009/11/12
A description of a deterministic chaotic system in terms of unstable periodic orbits (UPO) is used to develop a method of an a priori estimate of the sensitivity of statistical averages of the solutio...
Numerical detection of unstable periodic orbits in continuous-time dynamical systems with chaotic behaviors
Numerical detection unstable periodic orbits continuous-time dynamical systems chaotic behaviors
2009/11/3
An infinite number of unstable periodic orbits (UPOs) are embedded in a chaotic system which models some complex phenomenon. Several algorithms which extract UPOs numerically from continuous-time chao...
Chaos in driven Alfvén systems:unstable periodic orbits and chaotic saddles
Chaos Alfvén systems unstable periodic orbits chaotic saddles
2009/11/2
The chaotic dynamics of Alfvén waves in space plasmas governed by the derivative nonlinear Schrödinger equation, in the low-dimensional limit described by stationary spatial solutions, is studied...
Time averaged properties along unstable periodic orbits and chaotic orbits in two map systems
Time averaged properties unstable periodic orbits chaotic orbits map systems
2009/11/2
Unstable periodic orbit (UPO) recently has become a keyword in analyzing complex phenomena in geophysical fluid dynamics and space physics. In this paper, sets of UPOs in low dimensional maps are theo...