ScholarBank@NUShttps://scholarbank.nus.edu.sgThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Tue, 27 Sep 2022 21:10:16 GMT2022-09-27T21:10:16Z5071- The bifurcation characteristics of the generalized Lorenz equationshttps://scholarbank.nus.edu.sg/handle/10635/98247Title: The bifurcation characteristics of the generalized Lorenz equations
Authors: Yu, M.Y.; Zhou, C.T.; Lai, C.H.
Abstract: A graphical overview of the bifurcation characteristics of the generalized Lorenz equations obtained by Stenflo [Physica Scripta 53, 83 (1996)] for nonlinear acoustic gravity waves in a rotational system is presented.
Tue, 01 Oct 1996 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/982471996-10-01T00:00:00Z
- Pseudorecurrence and chaos of cubic-quintic nonlinear Schrödinger equationhttps://scholarbank.nus.edu.sg/handle/10635/97647Title: Pseudorecurrence and chaos of cubic-quintic nonlinear Schrödinger equation
Authors: Zhou, C.; Lai, C.H.
Abstract: Recurrence, pseudorecurrence, and chaotic solutions for a continuum Hamiltonian system in which there exist spatial patterns of solitary wave structures are investigated using the nonlinear Schrödinger equation (NSE) with cubic and quintic terms. The theoretical analyses indicate that there may exist Birkhoff's recurrence for the arbitrary parameter values. The numerical experiments show that there may be Fermi-Pasta-Ulam (FPU) recurrence, pseudorecurrence, and chaos when different initial conditions are chosen. The fact that the system energy is effectively shared by finite Fourier modes suggests that it may be possible to describe the continuum system in terms of some effective degrees of freedom.
Sun, 01 Dec 1996 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/976471996-12-01T00:00:00Z
- Chaos, bifurcations and periodic orbits of the Lorenz-Stenflo systemhttps://scholarbank.nus.edu.sg/handle/10635/95947Title: Chaos, bifurcations and periodic orbits of the Lorenz-Stenflo system
Authors: Zhou, C.; Lai, C.H.; Yu, M.Y.
Abstract: Chaos, bifurcation structures, and periodic orbits of the generalized Lorenz system obtained by Stenflo [Physical Scripta 53, 83 (1996)] for describing nonlinear low-frequency short-wavelength acoustic-gravity waves are investigated. It is shown that both saddle-node and period-doubling bifurcations exist in the domain of Hopf instability, and that forward and backward bifurcations may appear respectively in the rotation and Rayleigh number spaces, but both appear in the Prandtl-number space. Interactive empirical formulas for predicting the higher periodic windows are developed, and orbit characteristics in typical periodic windows are discussed.
Tue, 01 Apr 1997 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/959471997-04-01T00:00:00Z
- Bifurcation behavior of the generalized Lorenz equations at large rotation numbershttps://scholarbank.nus.edu.sg/handle/10635/95867Title: Bifurcation behavior of the generalized Lorenz equations at large rotation numbers
Authors: Zhou, C.; Lai, C.H.; Yu, M.Y.
Abstract: The bifurcation structure and periodic orbits of the Lorenz-Stenflo equations at large rotation numbers are given. It is shown that rotation can lead to a much richer dynamical behavior than that of the original Lorenz system and can be used to control or modify the latter's chaos behavior. Orbits with new topology arising from the merging and splitting of different periodic windows are observed. Abrupt changes in the one-dimensional map are pointed out and studied in terms of the interaction of the interior and exterior boundaries. © 1997 American Institute of Physics.
Wed, 01 Oct 1997 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/958671997-10-01T00:00:00Z
- Bifurcation structure and periodic orbits of the Lorenz equations in the Prandtl number spacehttps://scholarbank.nus.edu.sg/handle/10635/95870Title: Bifurcation structure and periodic orbits of the Lorenz equations in the Prandtl number space
Authors: Lai, C.H.; Zhou, C.T.; Yu, M.Y.
Abstract: The bifurcation structure and periodic orbits of the Lorenz system with the Prandtl number as the control parameter are investigated. It is shown that new bifurcation phenomena, both positive (forward) and inverse (backward) bifurcations, which do not appear together in the Rayleigh number space, can appear. The orbit characteristics in typical periodic windows are also studied. © World Scientific Publishing Company.
Fri, 20 Dec 1996 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/958701996-12-20T00:00:00Z
- Nonlinear properties of relativistically intense laser in plasmashttps://scholarbank.nus.edu.sg/handle/10635/111447Title: Nonlinear properties of relativistically intense laser in plasmas
Authors: Qiao, B.; Lai, C.H.; Zhou, C.T.; He, X.T.; Wang, X.G.; Yu, M.Y.
Abstract: Nonlinear characteristics including spatial chaos and patterns associated with relativistically intense laser-plasma interaction are studied theoretically and numerically using a model relativistic nonlinear Schrödinger equation. It is shown that in the phase space irregular homoclinic orbit crossings exist. The latter are verified and investigated numerically. The spatial chaos and complex patterns of the laser wave field can be attributed to the relativistic electron mass variation as well as the ponderomotive-force driven electron-density modulation. The formation of complex patterns results from stochastic partition of energy in the Fourier modes. © 2007 American Institute of Physics.
Mon, 01 Jan 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1114472007-01-01T00:00:00Z
- Model-based detector and extraction of weak signal frequencies from chaotic datahttps://scholarbank.nus.edu.sg/handle/10635/111436Title: Model-based detector and extraction of weak signal frequencies from chaotic data
Authors: Zhou, C.; Cai, T.; Heng Lai, C.; Wang, X.; Lai, Y.-C.
Abstract: Detecting a weak signal from chaotic time series is of general interest in science and engineering. In this work we introduce and investigate a signal detection algorithm for which chaos theory, nonlinear dynamical reconstruction techniques, neural networks, and time-frequency analysis are put together in a synergistic manner. By applying the scheme to numerical simulation and different experimental measurement data sets (H́non map, chaotic circuit, and NH3 laser data sets), we demonstrate that weak signals hidden beneath the noise floor can be detected by using a model-based detector. Particularly, the signal frequencies can be extracted accurately in the time-frequency space. By comparing the model-based method with the standard denoising wavelet technique as well as supervised principal components analysis detector, we further show that the nonlinear dynamics and neural network-based approach performs better in extracting frequencies of weak signals hidden in chaotic time series. © 2008 American Institute of Physics.
Tue, 01 Jan 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1114362008-01-01T00:00:00Z