NUMERICAL AND EXPERIMENTAL STUDIES OF SELF-SYNCHRONIZATION AND SYNCHRONIZED CHAOS

1992 ◽  
Vol 02 (03) ◽  
pp. 645-657 ◽  
Author(s):  
M. DE SOUSA VIEIRA ◽  
P. KHOURY ◽  
A. J. LICHTENBERG ◽  
M. A. LIEBERMAN ◽  
W. WONCHOBA ◽  
...  
Keyword(s):  
Chaotic Behavior ◽  
Experimental Studies ◽  
Chaotic Signal ◽  
Chaotic Synchronization ◽  
Parameter Variation ◽  
Phase Locked Loops ◽  
Bifurcation Diagrams ◽  
Digital Phase Locked Loops ◽  
Chaotic Carrier ◽  
Good Agreement

We study self-synchronization of digital phase-locked loops (DPLL's) and the chaotic synchronization of DPLL's in a communication system which consists of three or more coupled DPLL's. Triangular wave signals, convenient for experiments, are employed. Numerical and experimental studies of two loops are in good agreement, giving bifurcation diagrams that show quasiperiodic, locked, and chaotic behavior. The approach to chaos does not show the full bifurcation sequence of sinusoidal signals. For studying synchronization to a chaotic signal, the chaotic carrier is generated in a subsystem of two or more self-synchronized DPLL's where one of the loops is stable and the other is unstable. The receiver consists of a stable loop. We verified numerically and experimentally that the receiver may synchronize with the transmitter if the stable loop in the transmitter and receiver are nearly identical and the synchronization degrades with noise and parameter variation. We studied the phase space where synchronization occurs, and quantify the deviation from synchronization using the concept of mutual information.

NONLINEAR DYNAMICS OF DIGITAL PHASE-LOCKED LOOPS WITH DELAY

1994 ◽  
Vol 04 (03) ◽  
pp. 715-726 ◽  
Author(s):  
MARIA DE SOUSA VIEIRA ◽  
ALLAN J. LICHTENBERG ◽  
MICHAEL A. LIEBERMAN
Keyword(s):  
Nonlinear Dynamics ◽  
Chaotic Behavior ◽  
Nonlinear Oscillators ◽  
Coupled Systems ◽  
Phase Locked Loops ◽  
Bifurcation Diagrams ◽  
Digital Phase ◽  
Coupled Nonlinear Oscillators ◽  
Digital Phase Locked Loops ◽  
The Stability

We investigate numerically and analytically the nonlinear dynamics of a system consisting of two self-synchronizing pulse-coupled nonlinear oscillators with delay. The particular system considered consists of connected digital phase-locked loops. We find mapping equations that govern the system and determine the synchronization properties. We study the bifurcation diagrams, which show regions of periodic, quasiperiodic and chaotic behavior, with unusual bifurcation diagrams, depending on the delay. We show that depending on the parameter that is varied, the delay will have a synchronizing or desynchronizing effect on the locked state. The stability of the system is studied by determining the Liapunov exponents, indicating marked differences compared to coupled systems without delay.

NONLINEAR DYNAMICS OF SELF-SYNCHRONIZING SYSTEMS

1991 ◽  
Vol 01 (03) ◽  
pp. 691-699 ◽  
Author(s):  
M. DE SOUSA VIEIRA ◽  
A. J. LICHTENBERG ◽  
M. A. LIEBERMAN
Keyword(s):  
Nonlinear Dynamics ◽  
Nonlinear Systems ◽  
Universality Class ◽  
Chaotic Signal ◽  
The Self ◽  
Phase Locked Loops ◽  
Secure Communications ◽  
Circle Map ◽  
One Dimensional ◽  
Digital Phase Locked Loops

We investigate the self-synchronization of nonlinear systems. The particular system considered is two-coupled, digital phase-locked loops. It is shown that the overall dynamics is far more complicated than that of a single loop, which is governed by a one-dimensional circle map. In the case of two-coupled loops, we observe that the dynamics is governed by explicit mapping equations only for certain regions of the parameter space. In the regions for which mapping equations can be derived, we find the universality class of the coupled loops. Using such a two loop system as a transmitter of a chaotic signal, it is shown how a third loop can synchronize with this signal. Our results may provide one possible solution to the problem of secure communications.

scholarly journals Study of a Fractional-Order Chaotic System Represented by the Caputo Operator

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Ndolane Sene
Keyword(s):  
Fractional Derivative ◽  
Lyapunov Exponents ◽  
Fractional Order ◽  
Chaotic System ◽  
Caputo Fractional Derivative ◽  
Numerical Scheme ◽  
Chaotic Behavior ◽  
Bifurcation Diagrams ◽  
Numerical Discretization ◽  
Good Agreement

This paper is presented on the theory and applications of the fractional-order chaotic system described by the Caputo fractional derivative. Considering the new fractional model, it is important to establish the presence or absence of chaotic behaviors. The Lyapunov exponents in the fractional context will be our fundamental tool to arrive at our conclusions. The variations of the model’s parameters will generate chaotic behavior, in general, which will be established using the Lyapunov exponents and bifurcation diagrams. For the system’s phase portrait, we will present and apply an interesting fractional numerical discretization. For confirmation of the results provided in this paper, the circuit schematic is drawn and simulated. As it will be observed, the results obtained after the simulation of the numerical scheme and with the Multisim are in good agreement.

scholarly journals Experimental studies on the transformation from firn to ice in the wet-snow zone of temperate glaciers

1997 ◽  
Vol 24 ◽  
pp. 181-185 ◽  
Author(s):  
Katsuhisa Kawashima ◽  
Tomomi Yamada
Keyword(s):  
Experimental Studies ◽  
Ice Formation ◽  
Compression Tests ◽  
Densification Rate ◽  
Overburden Pressure ◽  
Proportionality Constant ◽  
Wet Snow ◽  
Water Saturated ◽  
The Relationship ◽  
Good Agreement

The densification of water-saturated firn, which had formed just above the firn-ice transition in the wet-snow zone of temperate glaciers, was investigated by compression tests under pressures ranging from 0.036 to 0.173 MPa, with special reference to the relationship between densification rate, time and pressure. At each test, the logarithm of the densification rate was proportional to the logarithm of the time, and its proportionality constant increased exponentially with increasing pressure. The time necessary for ice formation in the firn aquifer was calculated using the empirical formula obtained from the tests. Consequently, the necessary time decreased exponentially as the pressure increased, which shows that the transformation from firn in ice can be completed within the period when the firn aquifer exists, if the overburden pressure acting on the water-saturated firn is above 0.12–0.14 MPa. This critical value of pressure was in good agreement with the overburden pressure obtained from depth–density curves of temperate glaciers. It was concluded that the depth of firn–ice transition was self-balanced by the overburden pressure to result in the concentration between 20 and 30 m.

scholarly journals Period-doubling bifurcation analysis and chaos control for load torque using FLC

2021 ◽  
Author(s):  
Eman Moustafa ◽  
Abdel-Azem Sobaih ◽  
Belal Abozalam ◽  
Amged Sayed A. Mahmoud
Keyword(s):  
Floquet Theory ◽  
Chaos Control ◽  
Fuzzy Logic Controller ◽  
Chaotic Behavior ◽  
Period Doubling ◽  
Parameter Variation ◽  
Period Doubling Bifurcation ◽  
Load Torque ◽  
Nonlinear Behaviors ◽  
Scientific Fields

AbstractChaotic phenomena are observed in several practical and scientific fields; however, the chaos is harmful to systems as they can lead them to be unstable. Consequently, the purpose of this study is to analyze the bifurcation of permanent magnet direct current (PMDC) motor and develop a controller that can suppress chaotic behavior resulted from parameter variation such as the loading effect. The nonlinear behaviors of PMDC motors were investigated by time-domain waveform, phase portrait, and Floquet theory. By varying the load torque, a period-doubling bifurcation appeared which in turn led to chaotic behavior in the system. So, a fuzzy logic controller and developing the Floquet theory techniques are applied to eliminate the bifurcation and the chaos effects. The controller is used to enhance the performance of the system by getting a faster response without overshoot or oscillation, moreover, tends to reduce the steady-state error while maintaining its stability. The simulation results emphasize that fuzzy control provides better performance than that obtained from the other controller.

scholarly journals Chaotic Behavior in Gear System. Adaptation of Bifurcation Diagrams and Method of Statistical Mechanics.

1995 ◽  
Vol 61 (587) ◽  
pp. 3108-3115
Author(s):  
Keijin Sato ◽  
Sumio Yamamoto ◽  
Kazutaka Yokota ◽  
Toshihiro Aoki ◽  
Shu Karube
Keyword(s):  
Statistical Mechanics ◽  
Chaotic Behavior ◽  
Gear System ◽  
Bifurcation Diagrams ◽  
System Adaptation

Effect of Boundary Layer Suction on Aerodynamic Performance of High-Turning Compressor Cascade

2013 ◽  
Author(s):  
Longxin Zhang ◽  
Shaowen Chen ◽  
Hao Xu ◽  
Jun Ding ◽  
Songtao Wang
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Experimental Studies ◽  
Aerodynamic Performance ◽  
Parameter Distribution ◽  
Compressor Cascade ◽  
Boundary Layer Suction ◽  
End Wall ◽  
Low Speed Wind Tunnel ◽  
Good Agreement

Compared with suction slots, suction holes are (1) flexible in distribution; (2) alterable in size; (3) easy to fabricate and (4) high in strength. In this paper, the numerical and experimental studies for a high turning compressor cascade with suction air removed by using suction holes in the end-wall at a low Mach numbers are carried out. The main objective of the investigation is to study the influence of different suction distributions on the aerodynamic performance of the compressor cascade and to find a better compound suction scheme. A numerical model was first made and validated by comparing with the experimental results. The computed flow visualization and exit parameter distribution showed a good agreement with experimental data. Second, the model was then used to simulate the influence of different suction distributions on the aerodynamic performance of the compressor cascade. A better compound suction scheme was obtained by summarizing numerical results and tested in a low speed wind tunnel. As a result, the compound suction scheme can be used to significantly improve the performance of the compressor cascade because the corner separation gets further suppressed.

Analytical and Experimental Simulation of Loose Pedestal Dynamic Effects on a Rotating Machine Vibrational Response

1991 ◽  
Author(s):  
Pavel Goldman ◽  
Agnes Muszynska
Keyword(s):  
Excitation Frequency ◽  
Experimental Studies ◽  
Experimental Simulation ◽  
Physical Parameters ◽  
Vibrational Response ◽  
Rotating Machine ◽  
Qualitative Pattern ◽  
The Impact ◽  
Good Agreement ◽  
Periodic Changes

Abstract This report presents experimental, analytical, and numerical results describing vibrational phenomena in a rotating machine with one loose pedestal. The loose-pedestal machine rotor vibrations represent unbalance-related excited vibrations of synchronous and fractional subsynchronous regimes. In this study the loose-pedestal machine is first simulated by a simple vibrating beam excited by a shaker mounted on it. The shaker simulates an unbalanced machine rotor. The beam occasionally enters in contact with the foundation. The excited vibrations are modified by impacting occurrences, and by periodic changes in system stiffness. A new model of the impact has been developed. The results of analytical and experimental studies stand in a good agreement. They illustrate the existence of the synchronous regime and several subsynchronous fractional regimes in various excitation frequency ranges. The analysis adequately predicts the occurrence of these regimes and determines the physical parameters affecting them. The analytical and experimental results are then compared with the responses of experimental rotor rig with one bearing pedestal looseness. They show the same qualitative pattern.

Analyzing Bifurcation, Stability and Chaos for a Passive Walking Biped Model with a Sole Foot

2018 ◽  
Vol 28 (09) ◽  
pp. 1850113 ◽  
Author(s):  
Maysam Fathizadeh ◽  
Sajjad Taghvaei ◽  
Hossein Mohammadi
Keyword(s):  
Dynamic Models ◽  
Chaotic Behavior ◽  
Bifurcation Diagrams ◽  
Behavior Simulation ◽  
Passive Walking ◽  
Low Energy Consumption ◽  
Nonlinear Dynamic Models ◽  
Soles Of The Feet ◽  
The Stability ◽  
Intrinsic Characteristic

Human walking is an action with low energy consumption. Passive walking models (PWMs) can present this intrinsic characteristic. Simplicity in the biped helps to decrease the energy loss of the system. On the other hand, sufficient parts should be considered to increase the similarity of the model’s behavior to the original action. In this paper, the dynamic model for passive walking biped with unidirectional fixed flat soles of the feet is presented, which consists of two inverted pendulums with L-shaped bodies. This model can capture the effects of sole foot in walking. By adding the sole foot, the number of phases of a gait increases to two. The nonlinear dynamic models for each phase and the transition rules are determined, and the stable and unstable periodic motions are calculated. The stability situations are obtained for different conditions of walking. Finally, the bifurcation diagrams are presented for studying the effects of the sole foot. Poincaré section, Lyapunov exponents, and bifurcation diagrams are used to analyze stability and chaotic behavior. Simulation results indicate that the sole foot has such a significant impression on the dynamic behavior of the system that it should be considered in the simple PWMs.

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