Papers by Keyword: Chaos

Abstract: Machined surface carries the inherent features of machining process. Investigation of surface topography generated by machining process is helpful to extract the features of surface development process. In the present study, roughness profiles measured on machined surface generated by EDM are considered as time series and used for extraction of inherent features of surface topography through phase space reconstruction. Presence of self-similarity in surface topography is assessed by estimating a second order fractal dimension, called as correlation dimension. Saturation of correlation exponents with the increase of embedding dimension indicates the presence of chaos in surface topography.

Abstract: This research reports a theoretical investigation on the role of filtered optical feedback (FOF) in the quantum dot light emitting diode (QD-LED). The underlying dynamics is affected by a sidle node, which returns to an elliptical shape when the wetting layer (WL) is neglected. Both filter width and time delay change the appearance of different dynamics (chaotic and mixed mode oscillations ,MMOs). The results agrees with the experimental observations. Here, the fixed point analysis for QDs was done for the first time. For QD-LED with FOF, the system transits from the coherence collapse (CC) case in conventional optical feedback (COF) to a coherent case with a filtered mode in FOF. It was found that the WL washes out the modes which is an unexpected result. This may attributed to the longer capture time of WL compared with that between QD states. Thus, WL reduces the chaotic behavior.

Abstract: Controlling chaotic dual-ring erbium-doped fiber laser and the produced dynamics are studied by modulating or shifting the laser loss while the control model is presented to pressure behavior of the laser to a periodic state or multi-periodic states by a periodic signal perturbing or shifting the loss. When the loss of one ring of the laser is modulated via a sinusoidal signal, chaotic behaviors of the dual-ring can be pressured in two single-periodic states while two rings emit cyclic pulses. It indicates that chaotic dual-ring erbium-doped fiber laser is effectively controlled. When another sinusoidal signal is taken to perform on the loss, the laser can be educe to present a period-2 or period-3 state. When the loss is shifted between two different levels, the dual-ring can be deduced to a period-4, a period-6 and other multi-periodic state. The results indicate that controlling chaotic dual-ring erbium-doped fiber laser can be realized via the chaos-control method.

Abstract: Aimed at the issue that predicable time scale is neglected about the current gas emission forecast method, the Lyapunov index method in the chaos theory is adopted to research the predicable time scales of gas emission. The measured data of gas emission about a fully mechanized mining face was investgated. The delay time of time series about gas emission was determined by Non-bias multiple autocorrelation method, and the embedding dimension was determined by G-P algorithm is taken to determine. Based on this, the maximal Lyapunov index of ime series was got and the maximal predicable time scale was got. It is avoided that the time scale is too large when making a prediction of gas emission. On the side, the chaotic time series prediction model can make the correct prediction of gas emission based on the calculation of Lyapunov index value.

Abstract: The magneto-rheological(MR) suspension system has been established, by employing the modified Bouc-wen force-velocity (F-v) model of magneto-rheological damper(MRD). The possibility of chaotic motions in MR suspension is discovered by employing nonlinear systems stability theory. With the bifurcation diagram and corresponding Lyapunov exponent spectrum diagrams detected through numerical calculation, we can observe the complex dynamical behaviors and oscillating mechanism of alternating periodic oscillations, quasi-periodic oscillations and chaotic oscillations with different profiles of road excitation, as well as the dynamical evolution to chaos by period-doubling bifurcations, saddle-node bifurcations and reverse period-doubling bifurcations.

Abstract: This article focuses on the complicated dynamics behavior of the nonlinear vibrations of the bistable cantilevered piezoelectric beam. The base excitation on the beam is the harmonic load. We studied the jump phenomenon of the system by sweeping the voltage and displacement, the experimental results show that the bistable piezoelectric cantilever beam reflects the obvious hard spring characteristics. In addition, the influence of the distance between the magnets and the thickness of the piezoelectric layer on the dynamic behavior also being studied. Experimental results show that the distance between the magnets is closely impact on the nonlinear dynamic responses of the system, there is an optimal distance between the magnets causes the most complex dynamic behavior in frequency domain. System appears period doubling bifurcation into chaos many times when the distance between magnets is appropriate.

Abstract: The chaos and nonlinear dynamic behaviors of porous air bearing system are studied by a hybrid numerical method combining the finite difference method (FDM) and differential transformation method (DTM). The numerical results are verified by two different schemes including hybrid method and FDM and the current analytical results are found to be in good agreement. Furthermore, the results reveal the changes which take place in the dynamic behavior of the bearing system as the rotor mass is increased. From the dynamic responses of the rotor center, they reveal complex dynamic behaviors including periodic, sub-harmonic motion and chaos. The results of this study provide an understanding of the nonlinear dynamic behavior of PAB systems characterized by different rotor masses. Specifically, the results have shown that system exists chaotic motion over the ranges of rotor mass 10.66≤ M_r<13.7kg. The proposed method and results provide an effective means of gaining insights into the porous air bearing systems.

Abstract: A water price-supply model is presented to describe the relationship between water price and water supplier's decision in a closed irrigation district. Then some nonlinear studies are implemented, such as Neimark-Sacker bifurcation , chaotic attractor, Lyapunov exponents and time series. It shows that the parameter of the water price can lead the price-supply system from stability into bifurcation and chaos.

Abstract: This paper derives bifurcation and chaos phenomena for the Boost converter under current-mode control. The precise discrete iterative mode is compiled in M file of MATLAB to obtain the bifurcation diagram, the Poincare mapping, the discrete value of output voltage and inductor current; The piecewise smooth switch model is built in Simulink of MATLAB to obtain the phase diagram and the time-domain chart. On the basis of two models, the bifurcation phenomena under variation of a range of circuit parameters including load resistance, have been investigated. Two kinds of model simulation results had the better consistency, which were proved the existence of bifurcation and chaos phenomena in the current-mode Boost converter.

Abstract: To overcome the shortcomings of realizing chaotic system by analog circuits, digital chaotic signal generation circuits based on DSP are designed. Computer simulation of chaotic system is performed firstly, and the discrete equations are obtained using discretization algorithm. On this basis, the design of hardware circuits based on DSP is made, and the corresponding C programs are constructed. Through the debugging of software and hardware, digital design of chaotic system based on DSP is achieved, and chaotic attractor is observed through an oscilloscope by digital-to-analog conversion circuit. The experimental results coincide with the simulation, proving the correctness of the design. The chaotic signal generation circuits can provide rich digital chaotic signals sources for the application of chaotic systems in engineering.