scholarly journals Route to chaos and some properties in the boundary crisis of a generalized logistic mapping

2017 ◽  
Vol 486 ◽  
pp. 674-680 ◽  
Author(s):  
Diogo Ricardo da Costa ◽  
Rene O. Medrano-T ◽  
Edson Denis Leonel
Keyword(s):  
Logistic Mapping ◽  
Route To Chaos ◽  
Boundary Crisis

MOLECULAR ORDERING VERSUS ELECTRONIC INSTABILITIES A ROUTE TO CHAOS ?

1983 ◽  
Vol 44 (C3) ◽  
pp. C3-1007-C3-1010 ◽  
Author(s):  
K. Carneiro ◽  
A. E. Underhill
Keyword(s):  
Molecular Ordering ◽  
Route To Chaos

Complex Route to Chaos in Velocity Driven Atoms

1990 ◽  
Author(s):  
Phouc X. Tran ◽  
D. W. Brenner ◽  
C. T. White
Keyword(s):  
Route To Chaos

A STUDY OF BIFURCATIONS IN A CIRCULAR REAL CELLULAR AUTOMATON

1993 ◽  
Vol 03 (02) ◽  
pp. 293-321 ◽  
Author(s):  
JÜRGEN WEITKÄMPER
Keyword(s):  
Hopf Bifurcation ◽  
Dynamical Systems ◽  
Cellular Automata ◽  
Cellular Automaton ◽  
Parallel Computers ◽  
Discrete Dynamical Systems ◽  
Two Dimensional ◽  
Bifurcation Structure ◽  
Logistic Mapping ◽  
Henon Mapping

Real cellular automata (RCA) are time-discrete dynamical systems on ℝN. Like cellular automata they can be obtained from discretizing partial differential equations. Due to their structure RCA are ideally suited to implementation on parallel computers with a large number of processors. In a way similar to the Hénon mapping, the system we consider here embeds the logistic mapping in a system on ℝN, N>1. But in contrast to the Hénon system an RCA in general is not invertible. We present some results about the bifurcation structure of such systems, mostly restricting ourselves, due to the complexity of the problem, to the two-dimensional case. Among others we observe cascades of cusp bifurcations forming generalized crossroad areas and crossroad areas with the flip curves replaced by Hopf bifurcation curves.

HIGHER ORDER COMPLEXITY OF TIME SERIES

2004 ◽  
Vol 14 (08) ◽  
pp. 2979-2990 ◽  
Author(s):  
FANJI GU ◽  
ENHUA SHEN ◽  
XIN MENG ◽  
YANG CAO ◽  
ZHIJIE CAI
Keyword(s):  
Time Series ◽  
Mental Arithmetic ◽  
Higher Order ◽  
Second Order ◽  
Stationary Time Series ◽  
Eeg Signals ◽  
Eyes Closed ◽  
Logistic Mapping ◽  
Original Time ◽  
Different Order

A concept of higher order complexity is proposed in this letter. If a randomness-finding complexity [Rapp & Schmah, 2000] is taken as the complexity measure, the first-order complexity is suggested to be a measure of randomness of the original time series, while the second-order complexity is a measure of its degree of nonstationarity. A different order is associated with each different aspect of complexity. Using logistic mapping repeatedly, some quasi-stationary time series were constructed, the nonstationarity degree of which could be expected theoretically. The estimation of the second-order complexity of these time series shows that the second-order complexities do reflect the degree of nonstationarity and thus can be considered as its indicator. It is also shown that the second-order complexities of the EEG signals from subjects doing mental arithmetic are significantly higher than those from subjects in deep sleep or resting with eyes closed.

Regulation of external harmonic frequency on the route to chaos

2009 ◽  
Author(s):  
Xuhong Chu ◽  
Yuejin Zhao ◽  
Liquan Dong ◽  
Lingqin Kong
Keyword(s):  
Harmonic Frequency ◽  
Route To Chaos

Transitions Through Period Doubling Route to Chaos

1991 ◽  
Author(s):  
R. M. Evan-lwanowski ◽  
Chu-Ho Lu
Keyword(s):  
Period Doubling ◽  
Mirror Image ◽  
Flip Flop ◽  
Physical Systems ◽  
Starting Conditions ◽  
Spatial System ◽  
Stationary Bifurcation ◽  
Extreme Sensitivity ◽  
Route To Chaos ◽  
Parameter Values

Abstract The Duffing driven, damped, “softening” oscillator has been analyzed for transition through period doubling route to chaos. The forcing frequency and amplitude have been varied in time (constant sweep). The stationary 2T, 4T… chaos regions have been determined and used as the starting conditions for nonstationary regimes, consisting of the transition along the Ω(t)=Ω0±α2t,f=const., Ω-line, and along the E-line: Ω(t)=Ω0±α2t;f(t)=f0∓α2t. The results are new, revealing, puzzling and complex. The nonstationary penetration phenomena (delay, memory) has been observed for a single and two-control nonstationary parameters. The rate of penetrations tends to zero with increasing sweeps, delaying thus the nonstationary chaos relative to the stationary chaos by a constant value. A bifurcation discontinuity has been uncovered at the stationary 2T bifurcation: the 2T bifurcation discontinuity drops from the upper branches of (a, Ω) or (a, f) curves to their lower branches. The bifurcation drops occur at the different control parameter values from the response x(t) discontinuities. The stationary bifurcation discontinuities are annihilated in the nonstationary bifurcation cascade to chaos — they reside entirely on the upper or lower nonstationary branches. A puzzling drop (jump) of the chaotic bifurcation bands has been observed for reversed sweeps. Extreme sensitivity of the nonstationary bifurcations to the starting conditions manifests itself in the flip-flop (mirror image) phenomena. The knowledge of the bifurcations allows for accurate reconstruction of the spatial system itself. The results obtained may model mathematically a number of engineering and physical systems.

Secure Medical Multimedia Data Using Symmetric Cipher Based Chaotic Logistic Mapping

2021 ◽  
Author(s):  
Harshitha M ◽  
Ch. Rupa ◽  
K. Pujitha Sai ◽  
A. Pravallika ◽  
V. Kusuma Sowmya
Keyword(s):  
Multimedia Data ◽  
Logistic Mapping ◽  
Medical Multimedia

Route to Chaos in a CO2 Laser with Injected Signal

1984 ◽  
pp. 1227-1231 ◽  
Author(s):  
F. T. Arecchi ◽  
G. L. Lippi ◽  
G. Puccioni ◽  
J. Tredicce
Keyword(s):  
Co2 Laser ◽  
Route To Chaos

scholarly journals Dynamic Behavior of Geared Rotors

1997 ◽  
Author(s):  
T. N. Shiau ◽  
J. S. Rao ◽  
J. R. Chang ◽  
Siu-Tong Choi
Keyword(s):  
Dynamic Behavior ◽  
Chaotic Behavior ◽  
Squeeze Film ◽  
Rotor Systems ◽  
Lateral Vibrations ◽  
Squeeze Film Dampers ◽  
Torsional Excitation ◽  
Route To Chaos

This paper is concerned with the dynamic behavior of geared rotor systems supported by squeeze film dampers, wherein coupled bending torsion vibrations occur. Considering the imbalance forces and gravity, it is shown that geared rotors exhibit chaotic behavior due to non linearity of damper forces. The route to chaos in such systems is established. In geared rotor systems, it is shown that torsional excitation can induce lateral vibrations. It is shown that squeeze film dampers can suppress large amplitudes of whirl arising out of torsional excitation.

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