Bifurcation and Chaos in a Periodically Driven Quartic Oscillator at Relativistic Energies

1997 ◽  
Vol 07 (04) ◽  
pp. 945-949
Author(s):  
Sang Wook Kim ◽  
Hai-Woong Lee
Keyword(s):  
Chaotic Behavior ◽  
Relativistic Effects ◽  
Critical Value ◽  
Nonrelativistic Limit ◽  
Classical Dynamics ◽  
Bifurcation Diagrams ◽  
Bifurcation And Chaos ◽  
Force Amplitude ◽  
Regular Motion ◽  
Periodically Driven

The classical dynamics of a damped quartic oscillator driven by a sinusoidal force is investigated, with particular attention to the effects that arise when the motion of the oscillator becomes relativistic. Bifurcation diagrams constructed numerically indicate that, as relativistic effects become strong, chaotic behavior exhibited by the oscillator in the nonrelativistic limit at large force amplitude is replaced by a period-1 regular motion. At relativistic energies, therefore, a transition from chaos to a regular motion occurs as the force amplitude is increased beyond a critical value. The transition is seen to occur abruptly with a slight increase of the force amplitude from below to above the critical value. The sudden destruction of the chaotic attractor is probably triggered by the mechanism of crisis.

scholarly journals Bifurcation and Chaotic Behavior of a Discrete-Time SIS Model

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Junhong Li ◽  
Ning Cui
Keyword(s):  
Hopf Bifurcation ◽  
Discrete Time ◽  
Chaotic Behavior ◽  
Euler Method ◽  
Flip Bifurcation ◽  
Bifurcation Diagrams ◽  
Bifurcation And Chaos ◽  
Sis Model ◽  
Dynamical Behaviors ◽  
The Rich

The discrete-time epidemic model is investigated, which is obtained using the Euler method. It is verified that there exist some dynamical behaviors in this model, such as transcritical bifurcation, flip bifurcation, Hopf bifurcation, and chaos. The numerical simulations, including bifurcation diagrams and computation of Lyapunov exponents, not only show the consistence with the theoretical analysis but also exhibit the rich and complex dynamical behaviors.

Chaos in a 4D dissipative nonlinear fermionic model

2015 ◽  
Vol 26 (07) ◽  
pp. 1550083 ◽  
Author(s):  
Fatma Aydogmus
Keyword(s):  
Chaotic Behavior ◽  
Nonlinear Differential Equations ◽  
Classical Field ◽  
Bifurcation Diagrams ◽  
Field Equations ◽  
Bifurcation And Chaos ◽  
Fermionic Model ◽  
Conformally Invariant ◽  
Nonlinear Generalization ◽  
Dynamical Nature

Gursey Model is the only possible 4D conformally invariant pure fermionic model with a nonlinear self-coupled spinor term. It has been assumed to be similar to the Heisenberg's nonlinear generalization of Dirac's equation, as a possible basis for a unitary description of elementary particles. Gursey Model admits particle-like solutions for the derived classical field equations and these solutions are instantonic in character. In this paper, the dynamical nature of damped and forced Gursey Nonlinear Differential Equations System (GNDES) are studied in order to get more information on spinor type instantons. Bifurcation and chaos in the system are observed by constructing the bifurcation diagrams and Poincaré sections. Lyapunov exponent and power spectrum graphs of GNDES are also constructed to characterize the chaotic behavior.

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

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.

Quasi-Periodicity, Chaos and Coexistence in the Time Delay Controlled Two-Cell DC–DC Buck Converter

2014 ◽  
Vol 24 (10) ◽  
pp. 1450124 ◽  
Author(s):  
Karama Koubaâ ◽  
Moez Feki
Keyword(s):  
Numerical Simulation ◽  
Time Delay ◽  
Chaotic Attractor ◽  
Chaotic Behavior ◽  
Buck Converter ◽  
Design Parameters ◽  
Bifurcation And Chaos ◽  
Different Types ◽  
2D Torus ◽  
Discrete Map

In addition to border collision bifurcation, the time delay controlled two-cell DC/DC buck converter is shown to exhibit a chaotic behavior as well. The time delay controller adds new design parameters to the system and therefore the variation of a parameter may lead to different types of bifurcation. In this work, we present a thorough analysis of different scenarios leading to bifurcation and chaos. We show that the time delay controlled two-cell DC/DC buck converter may also exhibit a Neimark–Sacker bifurcation which for some parameter set may lead to a 2D torus that may then break yielding a chaotic behavior. Besides, the saturation of the controller can also lead to the coexistence of a stable focus and a chaotic attractor. The results are presented using numerical simulation of a discrete map of the two-cell DC/DC buck converter obtained by expressing successive crossings of Poincaré section in terms of each other.

Quantum versus classical dynamics in a periodically driven anharmonic oscillator

1992 ◽  
Vol 46 (3) ◽  
pp. 1669-1672 ◽  
Author(s):  
N. Ben-Tal ◽  
N. Moiseyev ◽  
H. J. Korsch
Keyword(s):  
Anharmonic Oscillator ◽  
Classical Dynamics ◽  
Periodically Driven

CLASSICAL DYNAMICS OF ESCAPE IN A PERIODICALLY DRIVEN UNBOUND HAMILTONIAN SYSTEM: INITIAL PHASE EFFECTS

2011 ◽  
Vol 21 (09) ◽  
pp. 2587-2596 ◽  
Author(s):  
LEONIDAS KONSTANTINIDIS ◽  
VASSILIOS CONSTANTOUDIS ◽  
CLEANTHES A. NICOLAIDES
Keyword(s):  
External Field ◽  
Initial Phase ◽  
Field Amplitude ◽  
Classical Dynamics ◽  
Morse Oscillator ◽  
Molecular Dissociation ◽  
Escape Probability ◽  
Periodic Field ◽  
Periodically Driven ◽  
Energy Exchanges

We consider the problem of a classical Morse oscillator driven by an external periodic field of controllable characteristics and study systematically the effects of the initial phase of the external field on the probability of escape upon molecular dissociation at the end of the interaction time. First, it is shown that such effects indeed exist and may become important depending on the field amplitude and frequency. Then, an explanation is given in terms of the energy exchanges between the basic periodic orbits and the external field and of the associated modifications of the shape of regular islands in phase space. Finally, we exploit this explanation in order to make predictions regarding the behavior of the escape probability as a function of the initial phase and frequency of the external field.

Subharmonic Bifurcations and Transition to Chaos in a Pipe Conveying Fluid under Harmonic Excitation

2013 ◽  
Vol 444-445 ◽  
pp. 791-795
Author(s):  
Yi Xiang Geng ◽  
Han Ze Liu
Keyword(s):  
Chaotic Behavior ◽  
Melnikov Method ◽  
Harmonic Excitation ◽  
Phase Portraits ◽  
Pipe Conveying Fluid ◽  
Bifurcation Diagrams ◽  
Dynamical Behaviors ◽  
Transition To Chaos ◽  
Subharmonic Bifurcations ◽  
Conveying Fluid

The subharmonic and chaotic behavior of a two end-fixed fluid conveying pipe whose base is subjected to a harmonic excitation are investigated. Melnikov method is applied for the system, and Melnikov criterions for subharmonic and homoclinic bifurcations are obtained analytically. The numerical simulations (including bifurcation diagrams, maximal Lyapunov exponents, phase portraits and Poincare map) confirm the analytical predictions and exhibit the complicated dynamical behaviors.

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.

CONTROLLING BIFURCATION AND CHAOS IN INTERNET CONGESTION CONTROL MODEL

2004 ◽  
Vol 14 (05) ◽  
pp. 1863-1876 ◽  
Author(s):  
LIANG CHEN ◽  
XIAO FAN WANG ◽  
ZHENG ZHI HAN
Keyword(s):  
Congestion Control ◽  
Chaotic Behavior ◽  
Control Strategies ◽  
Parameter Tuning ◽  
Delayed Feedback Control ◽  
Bifurcation And Chaos ◽  
Adaptive Parameter ◽  
Discrete Time Dynamical System ◽  
Basic Features ◽  
Time Delayed Feedback

The TCP end-to-end congestion control plus RED router queue management can be modeled as a discrete-time dynamical system, which can create complex bifurcating and chaotic behavior. Based on the basic features of the TCP-RED model, we investigate the possibility of controlling bifurcation and chaos in the system via several time-delayed feedback control strategies. Two adaptive parameter-tuning algorithms are proposed and evaluated.

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