共查询到20条相似文献,搜索用时 15 毫秒
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A. Tate 《Journal of statistical physics》1970,2(1):53-59
A way is suggested of incorporating the exact dynamics of a system into a statistical framework which is self-contained for low-order distribution functions. 相似文献
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Nonlinear feedback control of a novel hyperchaotic system and its circuit implementation 总被引:1,自引:0,他引:1 下载免费PDF全文
This paper reports a new hyperchaotic system by adding an
additional state variable into a three-dimensional chaotic dynamical
system. Some of its basic dynamical properties, such as the
hyperchaotic attractor, Lyapunov exponents, bifurcation diagram and
the hyperchaotic attractor evolving into periodic, quasi-periodic
dynamical behaviours by varying parameter k are studied. An effective
nonlinear feedback control method is used to suppress hyperchaos to
unstable equilibrium. Furthermore, a circuit is designed to realize
this new hyperchaotic system by electronic workbench (EWB).
Numerical simulations are presented to show these results. 相似文献
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K. R. Sreenivasan 《Pramana》2008,70(6):959-963
I summarize here the remarks made at the closing of the Conference and Research Workshop: Perspectives on Nonlinear Dynamics,
held in Trieste in July 2007.
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Zoheir Ziani Gaëtan Lévêque Saliya Coulibaly Abdelmajid Taki Abdellatif Akjouj 《Annalen der Physik》2020,532(10):2000240
The route to chaos of a plasmonic dimer formed of two identical nanoparticles with Kerr-type nonlinear response and illuminated by an external electric field is reported. It is shown that this system has a complex dynamical behavior with chaotic nature. This complexity is analyzed using Lyapunov exponents, the Kaplan–Yorke dimension, and correlation dimensions. The existence of familiar period-doubling sequences route to chaos is pointed out, and domains corresponding to the onset of period doubling and chaos in the plane of parameters are evidenced. 相似文献
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The maximum Lyapunov exponent is computed numerically for the double-well oscillator in a heat bath. Positive exponents are found in a wide range of friction coefficients in the low-damping regime. 相似文献
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A theory of extremes is developed for chaotic dynamical systems and illustrated on representative models of fully developed chaos and intermitent chaos. The cumulative distribution and its associated density for the largest value occurring in a data set, for monotonically increasing (or decreasing) sequences, and for local maxima are evaluated both analytically and numerically. Substantial differences from the classical statistical theory of extremes are found, arising from the deterministic origin of the underlying dynamics. 相似文献
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Olivier Martin 《Journal of statistical physics》1985,41(1-2):249-261
It is shown that stochastic equations can have stable solutions. In particular, there exists stochastic dynamics for which the motion is both ergodic and stable, so that all trajectories merge with time. We discuss this in the context of Monte Carlo-type dynamics, and study the convergence of nearby trajectories as the number of degrees of freedom goes to infinity and as a critical point is approached. A connection with critical slowdown is suggested. 相似文献
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Based on local erosion rule and fluctuations in rainfall, geology and parameters of a river channel, a generalized Langevin equation is proposed to describe the random prolongation of a river channel. This equation is transformed into the Fokker–Plank equation to follow the early evolution of a river network and the variation of probability distribution of channel lengths. The general solution of the equation is in the product form of two terms. One term is in power form and the other is in exponent form. This distribution shows a complete history of a river network evolving from its infancy to “adulthood”). The infancy is characterized by the Gaussian distribution of the channel lengths, while the adulthood is marked by a power law distribution of the channel lengths. The variation of the distribution from the Gaussian to the power law displays a gradual developing progress of the river network. The distribution of basin areas is obtained by means of Hack’s law. These provide us with new understandings towards river networks. 相似文献
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The dynamics of a discrete-time neural network model are investigated. First, a numerical survey of network power spectra is reported for networks of varying size with random weight matrices and initial states. The steepness of the logistic function and a symmetry measure of the weight matrix are taken as control parameters. Summary statistics are presented to give gross measures of the model's temporal activity in parameter space. Second, a detailed study of the dynamics of a particular network is described. Complex dynamical behavior is observed, including Hopf bifurcations, the Ruelle-Takens-Newhouse route to chaos (showing mode-locking at rational winding numbers and the destruction of an invariant torus), and the period-doubling route to chaos. 相似文献
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Finite clusters of atoms or molecules, typically composed of about 50 particles (and often as few as 13 or even less) have
proved to be useful prototypes of systems undergoing phase transitions. Analogues of the solid-liquid melting transition,
surface melting, structural phase transitions and the glass transition have been observed in cluster systems. The methods
of nonlinear dynamics can be applied to systems of this size, and these have helped elucidate the nature of the microscopic
dynamics, which, as a function of internal energy (or ‘temperature’) can be in a solidlike, liquidlike, or even gaseous state.
The Lyapunov exponents show a characteristic behaviour as a function of energy, and provide a reliable signature of the solid-liquid
melting phase transition. The behaviour of such indices at other phase transitions has only partially been explored. These
and related applications are reviewed in the present article. 相似文献
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Statistical equilibrium states for a linear transport equation were defined in a previous work. We consider here the two-dimensional case: we show that under some mild assumptions these equilibrium states actually describe the long-time dynamics of the system. 相似文献
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Algebraic dynamics approach and algebraic dynamics algorithm for the solution of nonlinear partial differential equations
are applied to the nonlinear advection equation. The results show that the approach is effective for the exact analytical
solution and the algorithm has higher precision than other existing algorithms in numerical computation for the nonlinear
advection equation.
Supported by the National Natural Science Foundation of China (Grant Nos. 90503008 and 10775100), the Doctoral Program Foundation
from the Ministry of Education of China, and the Center of Theoretical Nuclear Physics of HIRFL of China 相似文献
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Andrea Crisanti Giovanni Paladin Angelo Vulpiani 《Journal of statistical physics》1988,53(3-4):583-601
We study the behavior of the generalized Lyapunov exponents for chaotic symplectic dynamical systems and products of random matrices in the limit of large dimensionsD. For products of random matrices without any particular structure the generalized Lyapunov exponents become equal in this limit and the value of one of the generalized Lyapunov exponents is obtained by simple arguments. On the contrary, for random symplectic matrices with peculiar structures and for chaotic symplectic maps the generalized Lyapunov exponents remains different forD , indicating that high dimensionality cannot always destroy intermittency. 相似文献
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This paper presents the finding of a novel chaotic system
with one source and two saddle-foci in a simple three-dimensional
(3D) autonomous continuous time Hopfield neural network. In
particular, the system with one source and two saddle-foci has a
chaotic attractor and a periodic attractor with different initial
points, which has rarely been reported in 3D autonomous systems. The
complex dynamical behaviours of the system are further investigated
by means of a Lyapunov exponent spectrum, phase portraits and
bifurcation analysis. By virtue of a result of horseshoe theory in
dynamical systems, this paper presents rigorous computer-assisted
verifications for the existence of a horseshoe in the system for a
certain parameter. 相似文献
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P. I. Belobrov A. G. Tret'yakov G. M. Zaslavsky 《Journal of statistical physics》1985,38(1-2):393-404
To study equilibrium structures of magnetoelastic chains we have introduced an equivalent system and examined the whole class of its solutions. Appearance of various structures of the chain is due to the choice of an appropriate minimizing solution of the equivalent dynamic system. Commensurate and incommensurate structures, transitions from ferromagnetic to antiferromagnetic states, and transitions to the states with alternating clusters of ordered spins are obtained. Conditions for appearance of chaotic structures and amorphous magnetic states of the chain are discussed. 相似文献