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991.
State diagrams of two model systems involving three variables are constructed. The parameter dependence of different forms of complex nonperiodic behavior, and particularly of homoclinic orbits, is analyzed. It is shown that the onset of homoclinicity is reflected by deep changes in the qualitative behavior of the system. 相似文献
992.
993.
We test the applicability of the Gallavotti–Cohen fluctuation formula on a nonequilibrium version of the periodic Ehrenfest wind-tree model. This is an one-particle system whose dynamics is rather complex (e.g., it appears to be diffusive at equilibrium), but its Lyapunov exponents are nonpositive. For small applied field, the system exhibits a very long transient, during which the dynamics is roughly chaotic, followed by asymptotic collapse on a periodic orbit. During the transient, the dynamics is diffusive, and the fluctuations of the current are found to be in agreement with the fluctuation formula, despite the lack of real hyperbolicity. These results also constitute an example which manifests the difference between the fluctuation formula and the Evans–Searles identity. 相似文献
994.
The paper is concerned with a hybrid finite element formulation for the geometrically exact dynamics of rods with applications to chaotic motion. The rod theory is developed for in-plane motions using the direct approach where the rod is treated as a one-dimensional Cosserat line. Shear deformation is included in the formulation. Within the elements, a linear distribution of the kinematical fields is combined with a constant distribution of the normal and shear forces. For time integration, the mid-point rule is employed. Various numerical examples of chaotic motion of straight and initially curved rods are presented proving the powerfulness and applicability of the finite element formulation. 相似文献
995.
By means of the generalized cell-mapping digraph (GCMD) method, we studybifurcations governing the escape of periodically forced oscillatorsfrom a potential well, in which a chaotic saddle plays an extremelyimportant role. In this paper, we find the chaotic saddle anddemonstrate that it is embedded in a strange fractalbasin boundary which has the Wada property that any point that is on theboundary of that basin is also simultaneously on the boundary of atleast two other basins. The chaotic saddle in the Wada basin boundary,by colliding with a chaotic attractor, leads to a chaotic boundarycrisis with indeterminate outcome. A local saddle-node fold bifurcation,if the saddle of the saddle-node fold is located in tangency with thechaotic saddle in the Wada basin boundary, also results in a strangeglobal phenomenon, namely that the local saddle-node fold bifurcation hasglobally indeterminate outcome. We also investigate the origin andevolution of the chaotic saddle in the Wada basin boundary, particularlyconcentrating on its discontinuous bifurcations (metamorphoses). Wedemonstrate that the chaotic saddle in the Wada basin boundary iscreated by a collision between two chaotic saddles in differentfractal basin boundaries. After a final escape bifurcation, there onlyexists the attractor at infinity and a chaotic saddle with a beautifulpattern is left behind in the phase space. 相似文献
996.
A new approach based on analysis of the wandering trajectories is applied to investigate an appearance of chaotic vibrations in many-well potential systems. The chaotic behavior regions were found in the both amplitude–frequency of excitation and amplitude–damping coefficient plane. The phase plane of initial conditions has been investigated taking into account different values of an external periodic excitation. It demonstrated remarkable agreement with investigations based on homoclinic and heteroclinic bifurcation criteria for chaos, computations of Lyapunov exponents and fractal basin boundaries. The presented technique is very effective, convenient to use, and can be applied to the investigation of a wide class of problems. 相似文献
997.
Multisine time-series are sums of discrete-time sines with deterministic amplitudes and phase shifts chosen in a special way.
In this paper a new recursive approach to synthesis and simulation of multisine time-series with predefined spectral properties,
is presented. On the basis of the power spectral density function and phase shifts chosen with some well-defined properties,
the finite discrete Fourier transform of multisine time-series is synthesised and the corresponding multisine time-series
is simulated by performing an inverse discrete Fourier transform of the synthesised spectrum. In the approach the phase shifts
needed to synthesise and simulate N-sample multisine random time-series are calculated using
-sample multisine time-series obtained in the previous iteration. A transformation of the phase shifts into the corresponding
N-sample multisine time-series is called a multisine transformation. Its properties are discussed. Applications of the multisine
transformation to generation of uniformly distributed random numbers as well as to simulation of realisations for multisine
approximations of wide-sense stationary random processes given by their power spectral densities are included. 相似文献
998.
999.
Is There Chaotic Synchronization in Space Extend Systems? 总被引:2,自引:0,他引:2
Based on coupled map lattice (CML), the chaotic synchronous pattern in space extend systems is discussed. Making use of the criterion for the existence and the conditions of stability, we find an important difference between chaotic and nonchaotic movements in synchronization. A few numerical results are presented. 相似文献
1000.
Nonlinear oscillations and chaotic motions in a road vehicle system with driver steering control 总被引:5,自引:0,他引:5
The nonlinear dynamics of a differential system describing the motion of a vehicle driven by a pilot is examined. In a first step, the stability of the system near the critical speed is analyzed by the bifurcation method in order to characterize its behavior after a loss of stability. It is shown that a Hopf bifurcation takes place, the stability of limit cycles depending mainly on the vehicle and pilot model parameters. In a second step, the front wheels of the vehicle are assumed to be subjected to a periodic disturbance. Chaotic and hyperchaotic motions are found to occur for some range of the speed parameter. Numerical simulations, such as bifurcation diagrams, Poincaré maps, Fourier spectrums, projection of trajectories, and Lyapunov exponents are used to establish the existence of chaotic attractors. Multiple attractors may coexist for some values of the speed, and basins of attraction for such attractors are shown to have fractal geometries. 相似文献