Electronic Resource
Springer
Journal of statistical physics
26 (1981), S. 149-171
ISSN:
1572-9613
Keywords:
Dynamical system
;
chaos
;
bifurcations
;
attractor
;
Lyapunov exponents
;
fluctuations
;
Chapman-Kolmogorov equation
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract The behavior of the logistic system which is generated by the functionf(x =ax (1−x) changes in an interesting way if it is perturbed by external noise. It turns out that the chaotic behavior which was predicted by Li and Yorke for orbits of period 3, becomes visible and that a sequence of mergence transitions occurs at the critical parameter. The change of the invariant probability density and the Lyapunov exponents are examined numerically. The power spectrum for the period 3 orbit for different fluctuations is calculated and a recursion formula for the time evolution of the probability density is presented as a discrete-time analog of a Chapman-Kolmogorov equation.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01106791
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