A Route to Chaos

作者: Wolfgang Metzler

DOI: 10.1007/978-1-4684-6389-7_4

关键词:

摘要: The route to chaos of the coupled logistic map is studied. We observe a flip bifurcation from stable fixed point period-2 orbit which followed by Hopf bifurcation, quasiperiodic behaviour and periodic orbits. At end iteration scheme tends fascinating strange attractor looking like Eiffel tower.

参考文章(14)
H. O. Peitgen, The Beauty of Fractals ,(1986)
Pierre Collet, Jean Pierre Eckmann, Iterated maps on the interval as dynamical systems ,(1980)
Predrag Cvitanović, Universality in Chaos ,(1989)
Wolfgang Beau, Walter H. Hehl, Wolfgang Metzler, Computerbilder als Hilfsmittel zur Analyse chaoserzeugender Abbildungen Inform. Forsch. Entwickl.. ,vol. 2, pp. 122- 130 ,(1987)
Sidnie Dresher Feit, Characteristic exponents and strange attractors Communications in Mathematical Physics. ,vol. 61, pp. 249- 260 ,(1978) , 10.1007/BF01940767
Irene Waller, Raymond Kapral, Spatial and temporal structure in systems of coupled nonlinear oscillators Physical Review A. ,vol. 30, pp. 2047- 2055 ,(1984) , 10.1103/PHYSREVA.30.2047
W. Metzler, W. Beau, W. Frees, A. Ueberla, Symmetry and self-similarity with coupled logistic maps Zeitschrift für Naturforschung A. ,vol. 42, pp. 310- 318 ,(1987) , 10.1515/ZNA-1987-0320
Tien-Yien Li, James A. Yorke, Period Three Implies Chaos The Theory of Chaotic Attractors. ,vol. 82, pp. 77- 84 ,(2004) , 10.1007/978-0-387-21830-4_6
Benoit B. Mandelbrot, The Fractal Geometry of Nature ,(1982)