Neurofuzzy adaptive modelling and construction of nonlinear dynamical processes

2011 ◽  
pp. 253-292 ◽  
Author(s):  
K. Bossley ◽  
M. Brown ◽  
C. Harris
Keyword(s):  
Dynamical Processes ◽  
Nonlinear Dynamical ◽  
Adaptive Modelling

scholarly journals Chaos in driven Alfvén systems: unstable periodic orbits and chaotic saddles

2007 ◽  
Vol 14 (1) ◽  
pp. 17-29 ◽  
Author(s):  
A. C.-L. Chian ◽  
W. M. Santana ◽  
E. L. Rempel ◽  
F. A. Borotto ◽  
T. Hada ◽  
...  
Keyword(s):  
Periodic Orbits ◽  
Chaotic Attractor ◽  
Unstable Periodic Orbits ◽  
Gap Filling ◽  
Intermittent Turbulence ◽  
Dynamical Processes ◽  
Nonlinear Dynamical ◽  
Derivative Nonlinear Schrödinger Equation ◽  
Low Dimensional ◽  
Chaotic Saddle

Abstract. 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. A bifurcation diagram is constructed, by varying the driver amplitude, to identify a number of nonlinear dynamical processes including saddle-node bifurcation, boundary crisis, and interior crisis. The roles played by unstable periodic orbits and chaotic saddles in these transitions are analyzed, and the conversion from a chaotic saddle to a chaotic attractor in these dynamical processes is demonstrated. In particular, the phenomenon of gap-filling in the chaotic transition from weak chaos to strong chaos via an interior crisis is investigated. A coupling unstable periodic orbit created by an explosion, within the gaps of the chaotic saddles embedded in a chaotic attractor following an interior crisis, is found numerically. The gap-filling unstable periodic orbits are responsible for coupling the banded chaotic saddle (BCS) to the surrounding chaotic saddle (SCS), leading to crisis-induced intermittency. The physical relevance of chaos for Alfvén intermittent turbulence observed in the solar wind is discussed.

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