scholarly journals A periodic vibrational resonance in the fractional-order bistable system

2018 ◽  
Vol 67 (5) ◽  
pp. 054501
Author(s):  
Yang Jian-Hua ◽  
Ma Qiang ◽  
Wu Cheng-Jin ◽  
Liu Hou-Guang
Keyword(s):  
Fractional Order ◽  
Bistable System ◽  
Vibrational Resonance

Amplification of the LFM signal by using piecewise vibrational methods

2018 ◽  
Vol 25 (1) ◽  
pp. 141-150 ◽  
Author(s):  
Pengxiang Jia ◽  
Jianhua Yang ◽  
Chengjin Wu ◽  
Miguel A.F. Sanjuán
Keyword(s):  
Fractional Order ◽  
Bistable System ◽  
Optimal Model ◽  
Vibrational Resonance ◽  
Linear Frequency

We propose the piecewise re-scaled vibrational resonance (VR) method and the piecewise twice sampling VR method to amplify the weak linear frequency-modulated (LFM) signal. The system used to amplify the weak LFM signal is a typical bistable system with fractional-order deflection nonlinearity. The concrete procedures of both the piecewise re-scaled VR method and the piecewise twice sampling VR method are explained in detail. Through studying the effect of the factional-order exponent on VR, we find that the traditional bistable system is not the optimal model to improve the weak LFM signal. By investigating different parameters on the VR phenomenon, we verify the effectiveness of the two proposed methods.

Vibrational Resonance in an Overdamped System with a Fractional Order Potential Nonlinearity

2018 ◽  
Vol 28 (07) ◽  
pp. 1850082 ◽  
Author(s):  
Jianhua Yang ◽  
Dawen Huang ◽  
Miguel A. F. Sanjuán ◽  
Houguang Liu
Keyword(s):  
Numerical Simulation ◽  
Nonlinear System ◽  
Theoretical Analysis ◽  
Fractional Order ◽  
Low Frequency ◽  
Response Amplitude ◽  
Resonance Phenomenon ◽  
Vibrational Resonance ◽  
Frequency Excitation ◽  
Overdamped System

We investigate the vibrational resonance by the numerical simulation and theoretical analysis in an overdamped system with fractional order potential nonlinearities. The nonlinearity is a fractional power function with deflection, in which the response amplitude presents vibrational resonance phenomenon for any value of the fractional exponent. The response amplitude of vibrational resonance at low-frequency is deduced by the method of direct separation of slow and fast motions. The results derived from the theoretical analysis are in good agreement with those of numerical simulation. The response amplitude decreases with the increase of the fractional exponent for weak excitations. The amplitude of the high-frequency excitation can induce the vibrational resonance to achieve the optimal response amplitude. For the overdamped systems, the nonlinearity is the crucial and necessary condition to induce vibrational resonance. The response amplitude in the nonlinear system is usually not larger than that in the corresponding linear system. Hence, the nonlinearity is not a sufficient factor to amplify the response to the low-frequency excitation. Furthermore, the resonance may be also induced by only a single excitation acting on the nonlinear system. The theoretical analysis further proves the correctness of the numerical simulation. The results might be valuable in weak signal processing.

Saddle-Node Bifurcation and Vibrational Resonance in a Fractional System with an Asymmetric Bistable Potential

2015 ◽  
Vol 25 (02) ◽  
pp. 1550023 ◽  
Author(s):  
J. H. Yang ◽  
Miguel A. F. Sanjuán ◽  
F. Tian ◽  
H. F. Yang
Keyword(s):  
Potential Function ◽  
Fractional Order ◽  
Nonlinear Dynamical Systems ◽  
Technical Problem ◽  
Vibrational Resonance ◽  
High Frequency Signal ◽  
Saddle Node Bifurcation ◽  
Saddle Node ◽  
Bistable Potential ◽  
Fractional System

We investigate the saddle-node bifurcation and vibrational resonance in a fractional system that has an asymmetric bistable potential. Due to the asymmetric nature of the potential function, the response and its amplitude closely depend on the potential well where the motion takes place. And consequently for numerical simulations, the initial condition is a key and important factor. To overcome this technical problem, a method is proposed to calculate the bifurcation and response amplitude numerically. The numerical results are in good agreement with the analytical predictions, indicating the validity of the numerical and theoretical analysis. The results show that the fractional-order of the fractional system induces one saddle-node bifurcation, while the asymmetric parameter associated to the asymmetric nature of the potential function induces two saddle-node bifurcations. When the asymmetric parameter vanishes, the saddle-node bifurcation turns into a pitchfork bifurcation. There are three kinds of vibrational resonance existing in the system. The first one is induced by the high-frequency signal. The second one is induced by the fractional-order. The third one is induced by the asymmetric parameter. We believe that the method and the results shown in this paper might be helpful for the analysis of the response problem of nonlinear dynamical systems.

Effects of Different Fast Periodic Excitations on the Pitchfork Bifurcation and Vibrational Resonance

2020 ◽  
Vol 30 (06) ◽  
pp. 2050092
Author(s):  
Jiaqi Zhang ◽  
Jianhua Yang ◽  
Zhencai Zhu ◽  
Gang Shen ◽  
Miguel A. F. Sanjuán
Keyword(s):  
Initial Conditions ◽  
Pitchfork Bifurcation ◽  
Harmonic Excitation ◽  
Bistable System ◽  
Periodic Excitation ◽  
Vibrational Resonance ◽  
Key Factor ◽  
Fast Excitation ◽  
Relationship Of ◽  
The Relationship

We investigate the effects on the pitchfork bifurcation and the vibrational resonance of an overdamped bistable system subjected to both a slow harmonic excitation and a fast periodic excitation with different waveforms. We use numerical simulations along with theoretical explanations to analyze some interesting phenomena. The bifurcation configuration depends closely on the form of the fast excitation. As a result, we have found that the key factor to influence the bifurcation configuration is the symmetry property of the fast excitation. Further, due to the relationship of the vibrational resonance with the pitchfork bifurcation, the vibrational resonance also depends closely on the form of the fast periodic excitation. Moreover, for anharmonic fast excitations, if it is asymmetric, the vibrational resonance usually depends closely on the initial conditions.

Different fast excitations on the improvement of stochastic resonance in bounded noise excited system

2020 ◽  
Vol 34 (26) ◽  
pp. 2050238
Author(s):  
Huayu Liu ◽  
Jianhua Yang ◽  
Houguang Liu ◽  
Shuai Shi
Keyword(s):  
Stochastic Resonance ◽  
Circuit Simulation ◽  
Bistable System ◽  
Key Factors ◽  
Vibrational Resonance ◽  
Bounded Noise ◽  
High Frequency Signal ◽  
Excited System ◽  
Improvement Effect ◽  
Fast Excitation

Stochastic resonance is significant for signal detection. In this paper, a method to improve the stochastic resonance performance in a bistable system excited by bounded noise is studied. Specifically, we add a high-frequency signal to the system as an auxiliary excitation to induce vibrational resonance and focus on the influence of the auxiliary excitation waveform on the improvement effect. We investigate the stochastic resonance performance improved by a fast excitation in different waveforms through numerical simulations. The results show that, the improvement effect of the stochastic resonance depends on the waveform of the fast excitation closely. The symmetry property and constant component of the fast excitation are two key factors. Further, we accomplish the circuit simulation by constructing a circuit to generate bounded noise and the circuit of the bistable system.

Pitchfork bifurcation and vibrational resonance in a fractional-order Duffing oscillator

Pramana ◽  
2013 ◽  
Vol 81 (6) ◽  
pp. 943-957 ◽  
Author(s):  
J H YANG ◽  
M A F SANJUÁN ◽  
W XIANG ◽  
H ZHU
Keyword(s):  
Fractional Order ◽  
Duffing Oscillator ◽  
Pitchfork Bifurcation ◽  
Vibrational Resonance
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