Effect of a Constant Bias on the Nonlinear Dynamics of a Biharmonically Driven Sinusoidal Potential System

2020 ◽  
Vol 30 (15) ◽  
pp. 2030046
Author(s):  
Ivan Skhem Sawkmie ◽  
Mangal C. Mahato
Keyword(s):  
Nonlinear Dynamics ◽  
Chaotic Motion ◽  
Small Amplitude ◽  
Frequency Component ◽  
Force Frequency ◽  
Constant Force ◽  
Regular Motion ◽  
Constant Bias ◽  
Additional Constant ◽  
Potential System

The nonlinear dynamics of an underdamped sinusoidal potential system is experimentally and numerically studied. The system shows regular (nonchaotic) periodic motion when driven by a small amplitude ([Formula: see text]) sinusoidal force (frequency [Formula: see text]). However, when the system is driven by a similarly small amplitude biharmonic force (frequencies [Formula: see text] and [Formula: see text] with amplitudes [Formula: see text] and [Formula: see text], respectively) chaotic motion appear as a function of amplitude ([Formula: see text]) of the [Formula: see text]-frequency component for a fixed [Formula: see text]. We investigate the effect of an additional constant force [Formula: see text] on the dynamics of the system in the ([Formula: see text]) space. We find that [Formula: see text] can cause chaotic motion to move to regular motion and regular motion can also become chaotic in certain ([Formula: see text]) domains.

scholarly journals Electron acoustic solitons in the Earth's magnetotail

2004 ◽  
Vol 11 (2) ◽  
pp. 215-218 ◽  
Author(s):  
S. G. Tagare ◽  
S. V. Singh ◽  
R. V. Reddy ◽  
G. S. Lakhina
Keyword(s):  
Electron Beam ◽  
Small Amplitude ◽  
Low Frequency ◽  
Frequency Component ◽  
Magnetized Plasma ◽  
Cold Electron ◽  
Ion Plasma ◽  
Electron Acoustic ◽  
Two Temperature ◽  
Perpendicular Polarization

Abstract. Small amplitude electron - acoustic solitons are studied in a magnetized plasma consisting of two types of electrons, namely cold electron beam and background plasma electrons and two temperature ion plasma. The analysis predicts rarefactive solitons. The model may provide a possible explanation for the perpendicular polarization of the low-frequency component of the broadband electrostatic noise observed in the Earth's magnetotail.

THE INTERPLAY BETWEEN REGULAR AND CHAOTIC MOTION IN NUCLEI

1987 ◽  
Vol 02 (04) ◽  
pp. 233-237 ◽  
Author(s):  
I. ROTTER
Keyword(s):  
Chaotic Motion ◽  
Level Density ◽  
Quantum Mechanical ◽  
Nuclear System ◽  
Dissipative Forces ◽  
Open Quantum ◽  
Low Level ◽  
Regular Motion ◽  
Regular And Chaotic Motion ◽  
High Level

The regular motion of nucleons in the low-lying nuclear states and the chaotic motion in the compound nuclei are shown to arise from the interplay of conservative and dissipative forces in the open quantum mechanical nuclear system. The regularity at low level density is caused by selforganization in a conservative field of force. At high level density, chaoticity appears since information on the environment is transferred into the system by means of dissipative forces.

Effect of bounded noise on chaotic motion of a triple-well potential system

2005 ◽  
Vol 25 (2) ◽  
pp. 415-424 ◽  
Author(s):  
Xiaoli Yang ◽  
Wei Xu ◽  
Zhongkui Sun ◽  
Tong Fang
Keyword(s):  
Chaotic Motion ◽  
Bounded Noise ◽  
Potential System

scholarly journals Remarks on the parallel propagation of small-amplitude dispersive Alfvénic waves

1999 ◽  
Vol 6 (3/4) ◽  
pp. 169-178 ◽  
Author(s):  
S. Champeaux ◽  
D. Laveder ◽  
T. Passot ◽  
P. L. Sulem
Keyword(s):  
Nonlinear Dynamics ◽  
Speed Of Sound ◽  
Small Amplitude ◽  
Modulational Instability ◽  
Wave Train ◽  
Nonlinear Effects ◽  
Mhd Equations ◽  
Alfven Wave ◽  
Expected Time ◽  
Hall Mhd

Abstract. The envelope formalism for the description of a small-amplitude parallel-propagating Alfvén wave train is tested against direct numerical simulations of the Hall-MHD equations in one space dimension where kinetic effects are neglected. It turns out that the magnetosonic-wave dynamics departs from the adiabatic approximation not only near the resonance between the speed of sound and the Alfvén wave group velocity, but also when the speed of sound lies between the group and phase velocities of the Alfvén wave. The modulational instability then does not anymore affect asymptotically large scales and strong nonlinear effects can develop even in the absence of the decay instability. When the Hall-MHD equations are considered in the long-wavelength limit, the weakly nonlinear dynamics is accurately reproduced by the derivative nonlinear Schrödinger equation on the expected time scale, provided no decay instabilities are present. The stronger nonlinear regime which develops at later time is captured by including the coupling to the nonlinear dynamics of the magnetosonic waves.

Chaotic Motions in Resonant Separatrix Zones of Periodically Forced, Axially Travelling, Thin Plates

2005 ◽  
Vol 219 (3) ◽  
pp. 237-247 ◽  
Author(s):  
A C J Luo
Keyword(s):  
Chaotic Motion ◽  
Small Amplitude ◽  
Geometrical Nonlinearity ◽  
Excitation Amplitude ◽  
Numerical Prediction ◽  
Energy Approach ◽  
Thin Plates ◽  
Kutta Method ◽  
Chaotic Motions ◽  
Runge Kutta Method

The analytical conditions for chaotic motions of axially travelling, thin plates are obtained from the incremental energy approach. A numerical prediction of chaotic motions from the scenario of the conservative energy varying with excitation amplitude is also presented through the symplectic Runge-Kutta method. The chaotic motions in the primary resonant and homoclinic separatrix zones of axially travelling plates are exhibited through Poincaré mapping sections. From this study, chaotic motion might occur in the small-amplitude oscillations of the axially travelling, thin plates once the geometrical nonlinearity is considered. The chaotic motions of post-buckled plates are much more easily observed than pre-buckled plates. Because the buckling of travelling plates is caused by high translation speeds, chaotic motions of thin plates travelling with high transport speeds can be easily observed.

Chaotic Motion of a Symmetric Gyro Subjected to a Harmonic Base Excitation

2001 ◽  
Vol 68 (4) ◽  
pp. 681-684 ◽  
Author(s):  
X. Tong ◽  
N. Mrad
Keyword(s):  
Numerical Integration ◽  
Chaotic Motion ◽  
Poincaré Map ◽  
Melnikov Method ◽  
Poincare Map ◽  
Base Excitation ◽  
Regular Motion

Chaotic motion of a symmetric gyro subjected to a harmonic base excitation is investigated in this note. The Melnikov method is applied to show that the system possesses a Smale horse when it is subjected to small excitation. The transition from regular motion to chaotic motion is investigated through numerical integration in conjunction with Poincare´ map. It is shown that as the spin velocity increases, the chaotic motion turns into a regular motion.

scholarly journals Nonlinear Dynamics of a Duffing-Like Negative Stiffness Oscillator: Modeling and Experimental Characterization

2020 ◽  
Vol 2020 ◽  
pp. 1-13 ◽  
Author(s):  
D. Anastasio ◽  
A. Fasana ◽  
L. Garibaldi ◽  
S. Marchesiello
Keyword(s):  
Nonlinear Dynamics ◽  
Chaotic Motion ◽  
Nonlinear Oscillations ◽  
Dynamical Behavior ◽  
Shaking Table ◽  
Negative Stiffness ◽  
Nonlinear Dynamical ◽  
Current Collection ◽  
Input Amplitude ◽  
Linear And Nonlinear

In this paper, a negative stiffness oscillator is modelled and tested to exploit its nonlinear dynamical characteristics. The oscillator is part of a device designed to improve the current collection quality in railway overhead contact lines, and it acts like an asymmetric double-well Duffing system. Thus, it exhibits two stable equilibrium positions plus an unstable one, and the oscillations can either be bounded around one stable point (small oscillations) or include all the three positions (large oscillations). Depending on the input amplitude, the oscillator can exhibit linear and nonlinear dynamics and chaotic motion as well. Furthermore, its design is asymmetrical, and this plays a key role in its dynamic response, as the two natural frequencies associated with the two stable positions differ from each other. The first purpose of this study is to understand the dynamical behavior of the system in the case of linear and nonlinear oscillations around the two stable points and in the case of large oscillations associated with a chaotic motion. To accomplish this task, the device is mounted on a shaking table and it is driven with several levels of excitations and with both harmonic and random inputs. Finally, the nonlinear coefficients associated with the nonlinearities of the system are identified from the measured data.

APPROACHING NONLINEAR DYNAMICS BY STUDYING THE MOTION OF A PENDULUM II: ANALYZING CHAOTIC MOTION

1994 ◽  
Vol 04 (04) ◽  
pp. 761-771 ◽  
Author(s):  
R. DOERNER ◽  
B. HÜBINGER ◽  
H. HENG ◽  
W. MARTIENSSEN
Keyword(s):  
Nonlinear Dynamics ◽  
Lyapunov Exponents ◽  
Time Scale ◽  
Chaotic Motion ◽  
Deterministic Chaos ◽  
Fractal Dimensions ◽  
Equation Of Motion ◽  
Unstable Periodic Orbits ◽  
Initial State ◽  
Sensitive Dependence

Using a driven damped pendulum as a demonstration model we illustrate some fundamental concepts of nonlinear dynamics. We find deterministic chaos in the motion of the pendulum by observing its sensitive dependence on the initial state. We calculate the corresponding Lyapunov exponents from the equation of motion. The largest exponent gives the average predictability time scale. We estimate fractal dimensions of the attractor by determining the Kaplan Yorke dimension. Further we investigate the organization of unstable periodic orbits embedded in the attractor of the pendulum.

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