共查询到10条相似文献,搜索用时 93 毫秒
1.
We apply time-delayed feedback control to stabilise unstable periodic orbits of an amplitude-phase oscillator. The control acts on both, the amplitude and the frequency of the oscillator, and we show how the phase of the control signal influences the dynamics of the oscillator. A comprehensive bifurcation analysis in terms of the control phase and the control strength reveals large stability regions of the target periodic orbit, as well as an increasing number of unstable periodic orbits caused by the time delay of the feedback loop. Our results provide insight into the global features of time-delayed control schemes. 相似文献
2.
We demonstrate experimental control of long-period orbits and arbitrary chaotic trajectories using a new chaos control technique called dynamic limiting. Based on limiter control, dynamic limiting uses a predetermined sequence of limiter levels applied to the chaotic system to stabilize natural states of the system. The limiter sequence is clocked by the natural return time of the chaotic system such that the oscillator sees a new limiter level for each peak return. We demonstrate control of period-8 and period-34 unstable periodic orbits in a low-frequency circuit and provide evidence that the control perturbations are minimal. We also demonstrate control of an arbitrary waveform by replaying a sequence captured from the uncontrolled oscillator, achieving a form of delayed self-synchronization. Finally, we discuss the use of dynamic limiting for high-frequency chaos communications. (c) 2002 American Institute of Physics. 相似文献
3.
FANG Jian-Shu 《理论物理通讯》2003,39(5)
We have obtained a general unstable chaotic solution of a typical nonlinear oscillator in a double potential trap with weak periodic perturbations by using the direct perturbation method. Theoretical analysis reveals that the stable periodic orbits are embedded in the Melnikov chaotic attractors. The corresponding chaotic region and orbits in parameter space are described by numerical simulations. 相似文献
4.
The unstable periodic orbits of a chaotic system provide an important skeleton of the dynamics in a chaotic system, but they can be difficult to find from an observed time series. We present a global method for finding periodic orbits based on their symbolic dynamics, which is made possible by several recent methods to find good partitions for symbolic dynamics from observed time series. The symbolic dynamics are approximated by a Markov chain estimated from the sequence using information-theoretical concepts. The chain has a probabilistic graph representation, and the cycles of the graph may be exhaustively enumerated with a classical deterministic algorithm, providing a global, comprehensive list of symbolic names for its periodic orbits. Once the symbolic codes of the periodic orbits are found, the partition is used to localize the orbits back in the original state space. Using the periodic orbits found, we can estimate several quantities of the attractor such as the Lyapunov exponent and topological entropy. 相似文献
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A. ALGABAF. FERNÁNDEZ-SÁNCHEZ E. FREIREE. GAMERO A.J. RODRÍGUEZ-LUIS 《Journal of sound and vibration》2002,249(5):899-907
Some periodic behaviour exhibited by a modified van der Pol-Duffing electronic oscillator near a degenerate Hopf-pitchfork bifurcation have been studied. Numerical continuation of these periodic orbits leads to the appearance of interesting phenomena. After varying one of the characteristics of the oscillator, oscillation-sliding between two periodic régimes is detected. In the region where oscillation-sliding is present, quasiperiodic oscillations (invariant torus), breakdown of the torus and the corresponding resonant periodic orbits are also found. 相似文献
7.
Continuous control of chaos by self-controlling feedback 总被引:127,自引:0,他引:127
K. Pyragas 《Physics letters. A》1992,170(6):421-428
Two methods of chaos control with a small time continuous perturbation are proposed. The stabilization of unstable periodic orbits of a chaotic system is achieved either by combined feedback with the use of a specially designed external oscillator, or by delayed self-controlling feedback without using of any external force. Both methods do not require an a priori analytical knowledge of the system dynamics and are applicable to experiment. The delayed feedback control does not require any computer analyses of the system and can be particularly convenient for an experimental application. 相似文献
8.
G. Contopoulos M. Harsoula C. Efthymiopoulos 《The European physical journal. Special topics》2016,225(6-7):1053-1070
We summarize various cases where chaotic orbits can be described analytically. First we consider the case of a magnetic bottle where we have non-resonant and resonant ordered and chaotic orbits. In the sequence we consider the hyperbolic Hénon map, where chaos appears mainly around the origin, which is an unstable periodic orbit. In this case the chaotic orbits around the origin are represented by analytic series (Moser series). We find the domain of convergence of these Moser series and of similar series around other unstable periodic orbits. The asymptotic manifolds from the various unstable periodic orbits intersect at homoclinic and heteroclinic orbits that are given analytically. Then we consider some Hamiltonian systems and we find their homoclinic orbits by using a new method of analytic prolongation. An application of astronomical interest is the domain of convergence of the analytical series that determine the spiral structure of barred-spiral galaxies. 相似文献
9.
从Berry–Tabor求迹公式出发,导出了二维可积系统周期轨道作用量的半经典量子化条件.利用此量子化条件,考虑周期轨道满足的周期条件,得到了二维无关联四次振子系统周期轨道作用量的半经典量子化条件,并给出了半经典能级公式.对能级与周期轨道的对应关系做了分析. 相似文献