Narrow Results

In this paper, the dynamical behavior of a non-symmetric double potential well in a tilted magnetic field is studied. The classical Poincare section is given to exhibit the chaotic behavior of the system, and non-linear resonant lead to chaos. The paper has also given the energy spectral statistics which satisfies Brody's distribution, tunnelling effect develops quantum chaos and also holds back the development of chaos.

For linearly coupled double-well oscillators the regularity–partial chaos–regularity transition is found. First, an incomplete KAM scenario develops with increasing energy, from integrable pattern comprising in-phase and out-of-phase small elliptic orbits towards a partial chaos, with a deformed regular island immersed in a chaotic sea. At a critical energy a new deformed island appears as a mirror image. Above the critical energy the inverse KAM scenario leads to gradual destruction of partial chaos and to the appearance of large elliptic orbits which correspond to the large-amplitude limit governed by uncoupled oscillators with cubic anharmonicities.

In this paper, we present a study of the dynamical behavior in a Kelvin type gyrostat satellite. We firstly obtain the Hamiltonian equations of our model by using Cardan angles as generalized coordinates. Then, we make this Hamiltonian dimensionless and calculate motion equations for this dimensionless system. The study of the Poincare's sections of this system shows us that chaotic motion regimes are present for specific parameter values. The main goal of this work is the finding of stabilizing orbits by using a control technique, the fuzzy control of Poincare map method, so that it can be applied to stabilize special periodic orbits in this system. Finally, we expect that the technique can be useful for a better understanding of control theory and their applications in gyrostat problems.

One of the principal problems in identifying chaos using nonlinear time-series analysis of real-world data is additive noise. A straightforward procedure in traditional phase-space is introduced that can be used to identify data sets amenable to nonlinear projective noise reduction. This methodology can be used both as a tool for identifying candidates for noise reduction and, with some adaptation, for zeroth order noise quantification. Results for simulation data are compared with that for a quasiperiodic measured time series to illustrate when series can benefit most from nonlinear projective noise reduction.

Established the unsteady oil-film force with rub-impact fault of rotor-stator-bearing system mechanical models by using Lagrange equation, The numerical analysis method is used to study system with mass eccentricity of the time-domain waveform and orbit trace and Poincare section, revealing the system into chaos and bifurcation characteristic ways. The results show that when the mass eccentric cities as the only control parameters, system showing a complex nonlinear dynamics behavior, the results for the follow-up study of large rotating machinery fault diagnosis provides a theoretical basis.