共查询到20条相似文献,搜索用时 15 毫秒
1.
One-dimensional maps have proved to be useful models for understanding the transition to turbulence. We investigate a smooth perturbation of the well-known logistic system in order to examine numerically the change in the bifurcation behavior which is observed, when the Schwarzian derivative is allowed to become positive. We find coexistence of a fixed point attractor and a periodic or chaotic two-band-attractor. The chaotic two-band attractor can disappear by yielding a preturbulent state which will asymptotically settle down to a fixed-point. The chaotic behavior of some systems can be destroyed by arbitrarily small amounts of external noise. The concept of (ε, δ)-diffusions is used to describe the sensitivity of attractors against external noise. We also observe a direct transition from a fixed-point to a chaotic one-band attractor. This can be interpreted as type-III-intermittency of Pomeau and Manneville but with an almost linear scaling behavior of the Lyapunov exponent. 相似文献
2.
《Physics letters. A》2001,284(6):266-274
We present a reduction of the anti-self-dual Yang–Mills (ASDYM) equations to a system of partial differential equations (PDEs) introduced recently by Nijhoff et al. (Phys. Lett. A 267 (2000) 147). An auto-Bäcklund transformation of the reduced system is also presented. The system under consideration is related to a fourth-order nonlinear PDE of the Schwarzian type. The symmetry group of the latter equation is calculated and similarity reductions to the Schwarzian equation and the full Painlevé III, V and VI are presented. 相似文献
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Experimental evidence is presented for chaotic type nonperiodic motions of a parametrically forced pendulum. A bifurcation diagram is measured directly, showing successive subharmonic bifurcations to ?/4, onset of a periodic motion and the appearance of periodic motions via intermittency. The experimentally determined threshold values of the amplitude of the driving force for the first period doublings and the onset of a periodic motion are found to be in good agreement with the theoretical predictions. 相似文献
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A.T. Bernardes J.-G. Moreira A. Castro-e-Silva 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,1(3):393-396
In the time evolution of populations, many attractors can be found: fixed points, limit cycles and chaotic regimes. Usually,
chaotic behaviour is observed in species which have well defined breeding seasons and a high fertility rate. Different mathematical
models have been used in order to simulate those regimes. In this paper, we use the bitstring model introduced to simulate
the evolution of age-structured populations -- the Penna Model -- to simulate a sort of cyclic and chaotic behaviours. In
comparison with the standard logistic map, our results show a time changing parameter.
Received: 5 August 1997 / Revised: 8 November 1997 / Accepted: 13 November 1997 相似文献
6.
Approximation-error-ADP-based optimal tracking control for chaotic systems with convergence proof
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In this paper, an optimal tracking control scheme is proposed for a class of discrete-time chaotic systems using the approximation-error-based adaptive dynamic programming (ADP) algorithm. Via the system transformation, the optimal tracking problem is transformed into an optimal regulation problem, and then the novel optimal tracking control method is proposed. It is shown that for the iterative ADP algorithm with finite approximation error, the iterative performance index functions can converge to a finite neighborhood of the greatest lower bound of all performance index functions under some convergence conditions. Two examples are given to demonstrate the validity of the proposed optimal tracking control scheme for chaotic systems. 相似文献
7.
《Physics letters. [Part B]》1987,195(1):31-35
The problem of chaotic behaviour in multidimensional mixmaster models is discussed. We show that the chaotic regime disappears in the full class of homogeneous arbitrarily dimensional cosmological models if the dimension of space is n≠3. 相似文献
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This paper is concerned with the dynamic system nonlinear behaviour encountered in classical thermo-acoustic instability. The Poincaré map is adopted to analyse the stability of a simple non-autonomous system considering a harmonic oscillation behaviour for the combustion environment. The bifurcation diagram of a one-mode model is obtained where the analysis reveals a variety of chaotic behaviours for some select ranges of the bifurcation parameter. The bifurcation parameter and the corresponding period of a two-mode dynamic model are calculated using both analytical and numerical methods. The results computed by different methods are in good agreement. In addition, the dependence of the bifurcation parameter and the period on all the relevant coefficients in the model is investigated in depth. 相似文献
9.
David J. Jefferies 《Physics letters. A》1982,90(6):316-318
Experimental observations show that the frequencies of piezoelectrically active vibrational resonances of Rochelle salt can be tuned over a 2 : 1 range by an applied voltage. At high driving amplitudes, subharmonics of the driving frequency occur, accompanied by regions of chaotic behaviour, due to the non-linear nature of the resonant system. 相似文献
10.
For the Ising model on a Cayley tree with competing nearest neighbour coupling J and next nearest neighbour coupling J′, we find in addition to the expected paramagnetic, ferromagnetic and antiferromagnetic phases, an intermediate range of J′/J < 0 values where the local magnetization has chaotic oscillatory glass-like behaviour. 相似文献
11.
V. A. Buts A. G. Nerukh N. N. Ruzhytska D. A. Nerukh 《Optical and Quantum Electronics》2008,40(8):587-601
It is shown that regimes with dynamical chaos are inherent not only to nonlinear system but they can be generated by initially
linear systems and the requirements for chaotic dynamics and characteristics need further elaboration. Three simplest physical
models are considered as examples. In the first, dynamic chaos in the interaction of three linear oscillators is investigated.
Analogous process is shown in the second model of electromagnetic wave scattering in a double periodical inhomogeneous medium
occupying half-space. The third model is a linear parametric problem for the electromagnetic field in homogeneous dielectric
medium which permittivity is modulated in time. 相似文献
12.
The build-up of multimode gas laser spectra is studied on the basis of the full system of Lamb's equations of motion. Comparison is made with the results of the phase-averaged equations that constitute the so-called free-running approximation. It turns out that the range of validity of the latter is approximately given byr?0.5 wherer is the ratio of the homogeneous linewidth and the mode spacing (provided the former is mainly due to the decay of both the upper and the lower level). However, forr?2, the free-running approximation which generally predicts a steady-state spectrum to occur, breaks down. Actually, in this case multimode oscillation of a chaotic character takes place, and no steady-state regime is attained. 相似文献
13.
Virendra Singh 《Pramana》1985,24(1-2):31-37
We propose an analytic perturbative approach for the determination of the Feigenbaum-Cvitanović function and the universal
parameterα occurring in the Feigenbaum scenario of period doubling for approach to chaotic behaviour. We apply the method to the caseZ=2 whereZ is the order of the unique local maximum of the nonlinear map. Our third order approximation givesα=2.5000 as compared to “exact” numerical valueα=2.5029 ... We also obtain a reasonably accurate value of the Feigenbaum-Cvitanović function. 相似文献
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We give an explicit construction of the -cocycles of the group of contactomorphisms on the supercircle for , with coefficients in the space of differential operators acting on -tensor densities. We show that they satisfy properties similar to those of the super-Schwarzian derivative. 相似文献
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Temporal chaotic character of vortex motion in systems where defects are arranged in periodic arrays has been investigated by computer simulation. Due to the high nonlinearity of the vortex–defect interaction, the temporal evolution of the vortex motion is chaotic with a power spectrum similar to what have been observed in the experiments. It is found that the strength of both the vortex–vortex and vortex–defect interactions have no significant effects on the chaotic motion of the vortices, however, the mismatch between these two interactions causes attractor crisis of the system. Different from them, the Lorentz force is not the origin of the attractor crisis, but it causes a divergent motion of the vortex (i.e., the flux flow). 相似文献
19.
Integrability and chaotic behaviour in a two-coupled Duffing oscillators are studied. The coupling is nonlinear. Painlevé
test is performed to identify integrable cases of damped- and force-free system. Exact analytical solutions are given for
the integrable cases. Effect of external periodic forces for (i) single well with infinite height potential, (ii) potential
with a hump at the centre and (iii) single well with finite height hump potential are numerically investigated. Occurrence
of multiple attractors and period doubling cascades of coexisting attractors is presented. 相似文献
20.
《Solid State Communications》1984,52(5):551-554
Based on the theory of a previous letter [2], the possibility of period-doubling bifurcations and chaotic behaviour appearing in superconducting film under high quasiparticle injection and applied periodic field is argued. The complicated behaviour of system and the corresponding region of parameter are given. 相似文献