Ordered and Chaotic Response of a Modulated or Driven NMR Laser

1986 ◽  
pp. 119-133
Author(s):  
E. Brun ◽  
B. Derighetti ◽  
M. Ravani ◽  
G. Broggi ◽  
P. Meier ◽  
...  
Keyword(s):  
Chaotic Response

Chaotic Response of Aerosurfaces with Structural Nonlinearities

1989 ◽  
Author(s):  
Anthony J. Hauenstein ◽  
Robert M. Laurenson
Keyword(s):  
Chaotic Response ◽  
Structural Nonlinearities

Chaotic response of a limit cycle

1979 ◽  
Vol 21 (1) ◽  
pp. 65-86 ◽  
Author(s):  
Kazuhisa Tomita ◽  
Tohru Kai
Keyword(s):  
Limit Cycle ◽  
Chaotic Response

A New Chaotic Jerk System with Double-Hump Nonlinearity

2020 ◽  
Vol 29 (14) ◽  
pp. 2050232
Author(s):  
Debabrata Biswas
Keyword(s):  
Chaotic Regime ◽  
Third Order ◽  
Parameter Mismatch ◽  
Chaotic Response ◽  
Variation Of Parameters ◽  
Electronic Hardware ◽  
Jerk System ◽  
Lyapunov Exponent Spectrum ◽  
Two Parameter ◽  
Good Analogy

In this paper, we report a new third-order chaotic jerk system with double-hump (bimodal) nonlinearity. The bimodal nonlinearity is of basic interest in biology, physics, etc. The proposed jerk system is able to exhibit chaotic response with proper choice of parameters. Importantly, the chaotic response is also obtained from the system by tuning the nonlinearity preserving its bimodal form. We analytically obtain the symmetry, dissipativity and stability of the system and find the Hopf bifurcation condition for the emergence of oscillation. Numerical investigations are carried out and different dynamics emerging from the system are identified through the calculation of eigenvalue spectrum, two-parameter and single parameter bifurcation diagrams, Lyapunov exponent spectrum and Kaplan–Yorke dimension. We identify that the form of the nonlinearity may bring the system to chaotic regime. Effect of variation of parameters that controls the form of the nonlinearity is studied. Finally, we design the proposed system in an electronic hardware level experiment and study its behavior in the presence of noise, fluctuations, parameter mismatch, etc. The experimental results are in good analogy with that of the analytical and numerical ones.

scholarly journals Research on Chaos Response of the Nonlinear Vibration System of Giant Magnetostrictive Actuator

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Hongbo Yan ◽  
Yu Niu ◽  
Hong Gao ◽  
Hongbo Hao
Keyword(s):  
Mathematical Model ◽  
Amplitude Spectrum ◽  
Experimental Simulation ◽  
System Response ◽  
Threshold Condition ◽  
Vibration System ◽  
Chaotic Response ◽  
Magnetostrictive Actuator ◽  
Excitation Force ◽  
The Mathematical Model

In the present study, the chaotic response of the nonlinear magnetostrictive actuator (GMA) vibration system is investigated. The mathematical model of the nonlinear GMA vibration system is established according to J-A hysteresis nonlinear model, quadratic domain rotation model, Newton’s third law, and principle of GMA structural dynamics by analyzing the working principle of GMA. Then, the Melnikov function method is applied to the threshold condition of the chaotic response of the system to obtain the sense of Smale horseshoe transformation. Furthermore, the mathematical model is solved to investigate the system response to the excitation force and frequency. Accordingly, the corresponding displacement waveform, phase plane trajectory, Poincaré map, and amplitude spectrum are obtained. The experimental simulation is verified using Adams software. The obtained results show that the vibration equation of the nonlinear GMA vibration system has nonlinear and complex motion characteristics with different motion patterns. It is found that the vibration characteristics of the system can be controlled through adjusting the excitation force and frequency.

Chaotic response of nonlinear oscillators

1982 ◽  
Vol 86 (3) ◽  
pp. 113-167 ◽  
Author(s):  
Kazuhisa Tomita
Keyword(s):  
Nonlinear Oscillators ◽  
Chaotic Response

Adaptive targeting of chaotic response in periodically stimulated neural systems

2006 ◽  
Vol 16 (2) ◽  
pp. 023116 ◽  
Author(s):  
Kopal Gupta ◽  
Harinder P. Singh ◽  
B. Biswal ◽  
R. Ramaswamy
Keyword(s):  
Neural Systems ◽  
Chaotic Response

Investigation of Rub-Impact Setup Supported on Flexible Multi-Bearing Rotor

2012 ◽  
Author(s):  
Abdulazim H. Falah ◽  
Emad A. Khorshid ◽  
Khalid A. Alhazza
Keyword(s):  
Nonlinear Dynamics ◽  
Mathematical Model ◽  
Ball Bearings ◽  
Vibration System ◽  
Test Rig ◽  
Chaotic Response ◽  
Impact Device ◽  
Modeling And Experiments ◽  
In The Beginning ◽  
The Mathematical Model

Vibration system investigation of the chaotic response of full annular rub impact rotor system supported on two ball bearings is investigated. Modeling and experiments of nonlinear dynamics on flexible multi-bearing rotor test rig is presented in this work. The test rig has two balancers that are assembled on rotor shaft, a rub impact device at the center, and ball bearings at both ends of the shaft. A 12-degree-of-freedom (DOF) linear model was developed for this test rig. The mathematical model was developed in the beginning without considering the rub impact part in order to validate the model with the experiment results. Then, then experimentally chaotic response and bifurcation diagram of the rub impact system were investigated.

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