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Statistical closure and the logistic map
Physical Review E, 1994We consider the chaotic logistic map with stochastic initial conditions. All initial conditions assume a Gaussian distribution centered in the unit interval with a small dispersion. We show that the system exhibits behavior characterized by three different regimes (called initial, transient, and final).
, Bauer, , Graziani
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Chaos, Solitons & Fractals, 1996
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Journal of Theoretical Probability, 2000
The paper studies iterations of i.i.d. random logistic maps, i.e. it studies the sequence \(X_{n+1}=C_{n+1}X_n(1-X_n)\) where \(C_n, n=1,2,\dots\), is a sequence of i.i.d. random variables with values in \([0,4].\) The authors show that \(X_n\) tends to zero a.s. if \(E\ln C_10\) and \(E|\ln(4-C_1)|
Athreya, K. B., Dai, Jack
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The paper studies iterations of i.i.d. random logistic maps, i.e. it studies the sequence \(X_{n+1}=C_{n+1}X_n(1-X_n)\) where \(C_n, n=1,2,\dots\), is a sequence of i.i.d. random variables with values in \([0,4].\) The authors show that \(X_n\) tends to zero a.s. if \(E\ln C_10\) and \(E|\ln(4-C_1)|
Athreya, K. B., Dai, Jack
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AIP Conference Proceedings, 2005
The Logistic Mapping is studied from a particular perspective. Firstly an identification is made of this mapping with the Newton iterating mapping to find the roots of a corresponding function. With this approach one identifies the fixed points and the periodic points of a stable cycle as zeros of that function, and the unstable fixed points and ...
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The Logistic Mapping is studied from a particular perspective. Firstly an identification is made of this mapping with the Newton iterating mapping to find the roots of a corresponding function. With this approach one identifies the fixed points and the periodic points of a stable cycle as zeros of that function, and the unstable fixed points and ...
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CHAOTIC CONTROL OF LOGISTIC MAP
Modern Physics Letters B, 2008With the occasional feedback method, the chaotic logistic map is stabilized at an unstable low-periodic orbit. In our method, the qualified feedback coefficient can be obtained through calculation instead of through simulation. Besides, the bifurcation control of the logistic map is studied, and a new scheme is proposed to change the parameter value of
Wang, Xingyuan, Wang, Mingjun
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An Image Encryption using Intertwining Logistic map and Enhanced Logistic Map
2020 5th International Conference on Communication and Electronics Systems (ICCES), 2020Chaos is used for encryption of data because of its characteristics such as sensitiveness to the initial conditions and high unpredictability. Even though some of the image encryption schemes based on chaos are having security issues. To overcome the limitation an encryption technique that uses the combination of 3D Intertwining Logistic Map (ILM) and ...
Bharath Kumar Nancharla, Mohit Dua
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Results for the discontinuous logistic map
Physical Review A, 1992It is known that inverse cascades arise in discontinuous logistic maps [de Sousa Viera and co-workers, Phys. Rev. A 35, 945 (1987); in Universalities in Condensed Matter, edited by R. Jullien, L. Peliti, R. Rammal, and N. Boccara (Springer, New York, 1988); in Disordered Systems and Biological Models, edited by L.
Chia, T.T., Tan, B.L.
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Computers & Graphics, 1997
Abstract The process of generating artistic logistic maps which form various kinds of colorful graphs using addition, subtraction, multiplication and division is described. These simple arithmetic operations help generate many complicated ‘landscapes’.
Haijian Sun, Lin Liu, Aike Guo
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Abstract The process of generating artistic logistic maps which form various kinds of colorful graphs using addition, subtraction, multiplication and division is described. These simple arithmetic operations help generate many complicated ‘landscapes’.
Haijian Sun, Lin Liu, Aike Guo
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Synchronization of Chains of Logistic Maps
We study the synchronisation dynamics of a chain of coupled chaotic maps arranged in a parent-children configuration, with each parent node connected to two children nodes, one of which is also the parent of the next node. We analyse two distinct phenomena: parent-child synchronisation, characterised by the vanishing distance between consecutive nodes,Franco Bagnoli +3 more
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Determinantal solution of the logistic map
Journal of Physics A: Mathematical and General, 1998The paper deals with the logistic (quadratic) map (shortly LM) which has a broad spectrum of applications in physics, biology, economy and fractal geometry. The author proves that the solution of the LM can be written in a closed form or equivalently it can be given as the characteristic polynomial of a simple matrix that is explicitly written down for
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