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1.
Hyperchaos--chaos--Hyperchaos Transition in a Class of On--Off Intermittent Systems Driven by a Family of Generalized Lorenz Systems 下载免费PDF全文
Blowout bifurcation in nonlinear systems occurs when a chaotic attractor lying in some symmetric subspace becomes transversely unstable. A class of five-dimensional continuous autonomous systems is considered, in which a two-dimensional subsystem is driven by a family of generalized Lorenz systems. The systems have some common dynamical characters. As the coupling parameter changes, blowout bifurcations occur in these systems and brings on change of the systems' dynamics. After the bifurcation the phenomenon of on-off intermittency appears. It is observed that the systems undergo a symmetric hyperchaos-chaos-hyperchaos transition via or after blowout bifurcations. An example of the systems is given, in which the drive system is the Chen system. We investigate the dynamical behaviour before and after the blowout bifurcation in the systems and make an analysis of the transition process. It is shown that in such coupled chaotic continuous systems, blowout bifurcation leads to a transition from chaos to hyperchaos for the whole systems, which provides a route to hyperchaos. 相似文献
2.
The chaotic transition is observed in a three-coupled phase-locked loop (PLL) system in both experiments and numerical simulations. In this system, three PLL oscillators are connected with the periodic boundary condition. Intermittency is found in partially synchronized phase, in which two of three oscillators synchronize with each other and form a pair, and the chaotic transition occurs due to the recombination of synchronized pairs so that different pair is re-formed. In this phase, on-off intermittency is also observed and statistical analyses are carried out for on-off intermittent time series. This intermittency is considered as a hybrid type of intermittency with both on-off intermittency and intermittency due to the recombination of synchronized pairs present in the same time series. We also show the chaotic transition phenomena in a three-coupled logistic map system. (c) 2001 American Institute of Physics. 相似文献
3.
In this Letter, an electrical circuit is built for realizing the multi-state intermittency generated by a simple force-driven chaotic system. The intermittency phenomenon and its underlaying mechanism are analyzed, and the experimental results are discussed. It is shown that, with two classes of invariant subspaces, the number of the laminar states and the distance between the adjacent laminar states of the created multi-state on-off intermittency can be arbitrarily changed by manipulating the control parameters. 相似文献
4.
Previous studies of on-off intermittency in continuum systems are generally in the synchronization of identical chaotic oscillators or in the nonlinear systems driven by the Duffing oscillator. In this paper, one-state on-off intermittency and two-state on-off intermittency are observed in two five-dimensional continuum systems, respectively. The systems have skew product structure in which a two-dimensional subsystem is driven by the well-known Lorenz chaotic system. Moreover, the phenomenon of intermingled basins is observed below the blowout bifurcation. The statistical properties of the intermittency in the systems are investigated. It is shown that the distribution of the laminar phase duration time follows a power law, and that of the burst phase amplitude shows a −1 power law, which coincide with the basic statistical characteristics of on-off intermittency. 相似文献
5.
Thermal measurements on a converting dilute3He-superfluid4He solution in the quasiperiodic regime show a transition from a mode-locked periodic state to chaotic time dependence via intermittency. The type of intermittency is discussed in the context of standard models of the phenomenon. In a region just below the onset of intermittency, injection of external multiplicative noise with noise amplitude above a certain threshold level induces the chaotic state. This noise-induced transition can be understood to be due to perturbations of a system with a barely stable attractor; the noise causes the system to escape the weakly attracting periodic points. We present a numerical simulation of a 1D map with external noise which explains some aspects of the noise-induced behavior, and a 2D map which has certain features of the intermittency. 相似文献
6.
Circuit implementation and multiform intermittency in ahyper-chaotic model extended from Lorenz system 下载免费PDF全文
<正>This paper presents a non-autonomous hyper-chaotic system,which is formed by adding a periodic driving signal to a four-dimensional chaotic model extended from the Lorenz system.The resulting non-autonomous hyper-chaotic system can display any dynamic behaviour among the periodic orbits,intermittency,chaos and hyper-chaos by controlling the frequency of the periodic signal.The phenomenon has been well demonstrated by numerical simulations,bifurcation analysis and electronic circuit realization.Moreover,the system is concrete evidence for the presence of Pomeau-Manneville Type-Ⅰintermittency and crisis-induced intermittency.The emergence of a different type of intermittency is similarly subjected to the frequency of periodic forcing.By statistical analysis,power scaling laws consisting in different intermittency are obtained for the lifetime in the laminar state between burst states. 相似文献
7.
We studied the mechanism behind the connection between the transition to chaos of random dynamical systems and the synchronization of chaotic maps driven by external common noises. Near the chaotic transition, the spatial size of random dynamical systems shows an extreme intermittent behavior. By calculating the scaling exponents, we have found that the origin of this intermittent behavior is on-off intermittency. This led us to conclude that chaotic transitions through on-off intermittency can be regarded as a route for random dynamical systems. To clarify this argument, a two-dimensional random dynamical system and two coupled logistic maps driven by external common noises were analyzed. 相似文献
8.
Alexander E. HramovAlexey A. Koronovskii Maria K. KurovskayaOlga I. Moskalenko 《Physics letters. A》2011,375(15):1646-1652
In this Letter we compare the characteristics of two types of the intermittent behavior (type-I intermittency in the presence of noise and eyelet intermittency taking place in the vicinity of the chaotic phase synchronization boundary) supposed hitherto to be different phenomena. We show that these effects are the same type of dynamics observed under different conditions. The correctness of our conclusion is confirmed by the consideration of different sample systems, such as quadratic map, Van der Pol oscillator and Rössler system. Consideration of the problem concerning the upper boundary of the intermittent behavior also confirms the validity of the statement on the equivalence of type-I intermittency in the presence of noise and eyelet intermittency observed in the onset of phase synchronization. 相似文献
9.
《Physics letters. A》1999,259(5):355-365
We describe a type of intermittency present in a strange nonchaotic attractor of a quasiperiodically forced system. This has a similar scaling behaviour to the intermittency found in an attractor-merging crisis of chaotic attractors. By studying rational approximations to the irrational forcing we present a reasoning behind this scaling, which also provides insight into the mechanism which creates the strange nonchaotic attractor. 相似文献
10.
D. I. Danilov A. A. Koronovskii O. I. Moskalenko 《Bulletin of the Russian Academy of Sciences: Physics》2013,77(12):1460-1462
The intermittent behavior of spatially extended systems is investigated using the example of unidirectionally coupled Pierce diodes. It isshown that the same type of intermittency as in finite-scaled systems is characteristic of this system near the boundary of the chaotic phase synchronization regime, i.e., needle-eye type intermittency, which is in fact also equivalent to type I intermittency with noise in the supercritical region. 相似文献
11.
We study a phenomenon of noise-induced intermittency for the stochastically forced one-dimensional discrete-time system near tangent bifurcation. In a subcritical zone, where the deterministic system has a single stable equilibrium, even small noises generate large-amplitude chaotic oscillations and intermittency. We show that this phenomenon can be explained by a high stochastic sensitivity of this equilibrium. For the analysis of this system, we suggest a constructive method based on stochastic sensitivity functions and confidence intervals technique. An explicit formula for the value of the noise intensity threshold corresponding to the onset of noise-induced intermittency is found. On the basis of our approach, a parametrical diagram of different stochastic regimes of intermittency and asymptotics are given. 相似文献
12.
In this paper,the chaotic behaviors in an erbium-doped fiber(EDF) single-ring laser(EDFSRL) are investigated experimentally by using the loss modulation method.An electro-optic modulator(EOM) made of LiNbO 3 crystal is added to the system.Thus,by changing the modulation voltage and the modulation frequency of the EOM,the freedom of the EDFSRL system is increased.The chaotic characteristics of the system are studied by observing the time series and the power spectra.The experimental results indicate that the erbium-doped fiber single-ring laser system can enter into chaos states through period-doubling bifurcation and intermittency routes. 相似文献
13.
The intermittent behavior at the boundary of phase synchronization in the presence of noise is investigated. It is shown that in a certain range of the coupling parameter and noise intensity, the system experiences the intermittency of needle’s eye- and ring-type intermittencies. The basic results are demonstrated with two unidirectionally coupled Ressler chaotic oscillators. 相似文献
14.
15.
The transition to turbulence via spatiotemporal intermittency is investigated for coupled maps defined on generalized Sierpinski gaskets, a class of deterministic fractal lattices. Critical exponents that characterize the onset of intermittency are computed as a function of the fractal dimension of the lattice. Windows of spatiotemporal intermittency are found as the coupling parameter is varied for lattices with a fractal dimension greater than two. This phenomenon is associated with a collective chaotic behavior of the fractal array of coupled maps. 相似文献
16.
Feudel U Neiman A Pei X Wojtenek W Braun H Huber M Moss F 《Chaos (Woodbury, N.Y.)》2000,10(1):231-239
We study global bifurcations of the chaotic attractor in a modified Hodgkin-Huxley model of thermally sensitive neurons. The control parameter for this model is the temperature. The chaotic behavior is realized over a wide range of temperatures and is visualized using interspike intervals. We observe an abrupt increase of the interspike intervals in a certain temperature region. We identify this as a homoclinic bifurcation of a saddle-focus fixed point which is embedded in the chaotic attractors. The transition is accompanied by intermittency, which obeys a universal scaling law for the average length of trajectory segments exhibiting only short interspike intervals with the distance from the onset of intermittency. We also present experimental results of interspike interval measurements taken from the crayfish caudal photoreceptor, which qualitatively demonstrate the same bifurcation structure. (c) 2000 American Institute of Physics. 相似文献
17.
The dynamics of a system with three parametrically coupled waves with delayed feedback is considered. Results of the detailed numerical simulation of the onset of self-modulation, as well as complex dynamic and chaotic regimes, are presented. The relation of self-modulation regimes with the formation and propagation of solitons is investigated. It is discovered that as the pump parameter increases, the synchronization of phases of the interacting waves, which is characteristic of stationary generation and periodic self-modulation regimes, is violated, and the system goes to a chaotic regime via intermittency. 相似文献
18.
Many chaotic dynamical systems of physical interest present a strong form of nonhyperbolicity called unstable dimension variability (UDV), for which the chaotic invariant set contains periodic orbits possessing different numbers of unstable eigendirections. The onset of UDV is usually related to the loss of transversal stability of an unstable fixed point embedded in the chaotic set. In this paper, we present a new mechanism for the onset of UDV, whereby the period of the unstable orbits losing transversal stability tends to infinity as we approach the onset of UDV. This mechanism is unveiled by means of a periodic orbit analysis of the invariant chaotic attractor for two model dynamical systems with phase spaces of low dimensionality, and seems to depend heavily on the chaotic dynamics in the invariant set. We also described, for these systems, the blowout bifurcation (for which the chaotic set as a whole loses transversal stability) and its relation with the situation where the effects of UDV are the most intense. For the latter point, we found that chaotic trajectories off, but very close to, the invariant set exhibit the same scaling characteristic of the so-called on-off intermittency. 相似文献
19.
We present a new chaotic system of three coupled ordinary differential equations, limited to quadratic nonlinear terms. A
wide variety of dynamical regimes are reported. For some parameters, chaotic reversals of the amplitudes are produced by crisis-induced
intermittency, following a mechanism different from what is generally observed in similar deterministic models. Despite its
simplicity, this system therefore generates a rich dynamics, able to model more complex physical systems. In particular, a
comparison with reversals of the magnetic field of the Earth shows a surprisingly good agreement, and highlights the relevance
of deterministic chaos to describe geomagnetic field dynamics. 相似文献
20.
A chaotic firing pattern, characterized by non-smooth features and generated through the routine of intermittency from period 3, is observed in biological experiments on a neural firing pacemaker and reproduced in simulations by using a theoretical neuronal model with multiple time scales. This chaotic activity exhibits a scale law very similar to those of both the type-Ⅰ intermitteney generated in smooth systems and the type-Ⅴ intermittency in non-smooth systems. 相似文献