共查询到20条相似文献,搜索用时 15 毫秒
1.
2.
A. M. Perelomov 《Communications in Mathematical Physics》1978,63(1):9-11
A simple relation between certain dynamical systems is established. 相似文献
3.
In recent years, it is observed that the third-order explicit autonomous differential equation, named as jerk equation, represents
an interesting sub-class of dynamical systems that can exhibit many major features of the regular and chaotic motion. In this
paper, we investigate the global dynamics of a special family of jerk systems {ie075-01}, whereG(x) is a non-linear function, which are known to exhibit chaotic behaviour at some parameter values. We particularly identify
the regions of parameter space with different asymptotic dynamics using some analytical methods as well as extensive Lyapunov
spectra calculation in complete parameter space. We also investigate the effect of weakening as well as strengthening of the
non-linearity in theG(x) function on the global dynamics of these jerk dynamical systems. As a result, we reach to an important conclusion for these
jerk dynamical systems that a certain amount of non-linearity is sufficient for exhibiting chaotic behaviour but increasing
the non-linearity does not lead to larger regions of parameter space exhibiting chaos. 相似文献
4.
5.
We propose an improved method to estimate the varying topology of discrete-time dynamical networks using autosynchronization. The networks considered in this paper can be weighted or unweighted and directed or undirected, and the dynamics of each node can be nonuniform. Furthermore, we suggest using a moving-average filter to suppress the influence of noise on parameter estimation. Finally, several examples are illustrated to verify the theoretical results by numerical simulation. 相似文献
6.
We describe scaling laws for a control parameter for various sequences of bifurcations of the LSn mixed-mode regimes consisting of single large amplitude maximum followed by n small amplitude peaks. These regimes are obtained in a normalized version of a simple three-variable polynomial model that contains only one nonlinear cubic term. The period adding bifurcations for LSn patterns scales as 1/n at low n and as 1/n2 at sufficiently large values of n. Similar scaling laws 1/k at low k and 1/k2 at sufficiently high values of k describe the period adding bifurcations for complex k(LSn)(LS(n + 1)) patterns. A finite number of basic LSn patterns and infinite sequences of complex k(LSn)(LS(n + 1)) patterns exist in the model. Each periodic pattern loses its stability by the period doubling bifurcations scaled by the Feigenbaum law. Also an infinite number of the broken Farey trees exists between complex periodic orbits. A family of 1D return maps constructed from appropriate Poincaré sections is a very fruitful tool in studies of the dynamical system. Analysis of this family of maps supports the scaling laws found using the numerical integration of the model. 相似文献
7.
Autonomous systems,dynamical systems,LPTI symmetries,topology of trajectories,and periodic solutions
G. Gaeta 《International Journal of Theoretical Physics》1993,32(1):191-199
In the case of autonomous dynamical systems, it is better to base symmetry considerations on trajectories than on full solutions. In this setting topological arguments can be used; a special role is played in this context by time-independent Lie-point symmetries. As an application of this approach, we obtain results on the existence of stationary and/or periodic solutions. 相似文献
8.
B.A. Malomed 《Physica D: Nonlinear Phenomena》1983,8(3):343-352
The paper treats a dynamical system consisting of two quasiharmonic limit cycles cut off by stall lines. A phase trajectory inside a cycle jumps infinitely quickly to another cycle after having reached the stall line. This dynamical system can be interpreted as an asymptotical form of a system of three differential equations admitting separation of fast and slow motions. The explicit conditions on parameters of the system providing its stochastic behaviour, i.e. local instability of all trajectories, are obtained by means of investigation of the Poincaré mapping. A lower estimate for the topological entropy of the system is also obtained. The appendix concerns investigation of some properties of a system consisting of stochastic oscillators of the most simple kind connected by diffusion. 相似文献
9.
Adaptive lag synchronization of uncertain dynamical systems with time delays via simple transmission lag feedback 下载免费PDF全文
In this paper we present an adaptive scheme to achieve lag synchronization for uncertain dynamical systems with time delays and unknown parameters. In contrast to the nonlinear feedback scheme reported in the previous literature, the proposed controller is a linear one which only involves simple feedback information from the drive system with signal popagation lags. Besides, the unknown parameters can also be identified via the proposed updating laws in spite of the existence of model delays and transmission lags, as long as the linear independence condition between the related function elements is satisfied. Two examples, i.e., the Mackey-Glass model with single delay and the Lorenz system with multiple delays, are employed to show the effectiveness of this approach. Some robustness issues are also discussed, which shows that the proposed scheme is quite robust in switching and noisy environment. 相似文献
10.
By treating combinatorial games as dynamical systems, we are able to address a longstanding open question in combinatorial game theory, namely, how the introduction of a "pass" move into a game affects its behavior. We consider two well known combinatorial games, 3-pile Nim and 3-row Chomp. In the case of Nim, we observe that the introduction of the pass dramatically alters the game's underlying structure, rendering it considerably more complex, while for Chomp, the pass move is found to have relatively minimal impact. We show how these results can be understood by recasting these games as dynamical systems describable by dynamical recursion relations. From these recursion relations, we are able to identify underlying structural connections between these "games with passes" and a recently introduced class of "generic (perturbed) games." This connection, together with a (non-rigorous) numerical stability analysis, allows one to understand and predict the effect of a pass on a game. 相似文献
11.
12.
S. Harris 《Journal of statistical physics》1970,2(4):379-385
A model Liouville equation is proposed for a system composed of an ion moving in a solvent fluid. Using this model, explicit results are obtained for the Ohmic conductivityL and the Hall conductivityh. These results are then used to calculate the Hall coefficientR = ehL–2, which is a measure of the effect of non-Brownian motion, for several charge carriers of interest. Our results are in agreement with earlier findings based on a stochastic model which predictR > 1 for H+(aq). Our results also indicate thatR 1 for charge carriers such as Na+, Cl–, and K+ which have a mass greater than that of a solvent molecule (here taken as 18 amu).This research was supported in part by grants from the National Science Foundation and by the Research Foundation of the State University of New York. 相似文献
13.
Benzi R 《Physical review letters》2005,95(2):024502
In this Letter, we study a simple hydrodynamical model showing abrupt flow reversals at random times. For a suitable range of parameters, we show that the dynamics of flow reversal is accurately described by stochastic differential equations, where the noise represents the effect of turbulence. 相似文献
14.
15.
16.
We demonstrate with a minimal example that in Filippov systems (dynamical systems governed by discontinuous but piecewise smooth vector fields) stable periodic motion with sliding is not robust with respect to stable singular perturbations. We consider a simple dynamical system that we assume to be a quasi-static approximation of a higher-dimensional system containing a fast stable subsystem. We tune a system parameter such that a stable periodic orbit of the simple system touches the discontinuity surface: this is the so-called grazing-sliding bifurcation. The periodic orbit remains stable, and its local return map becomes piecewise linear. However, when we take into account the fast dynamics the local return map of the periodic orbit changes qualitatively, giving rise to, for example, period-adding cascades or small-scale chaos. 相似文献
17.
Roberto Markarian 《Journal of statistical physics》1995,80(5-6):1207-1239
We prove statistical properties of two-dimensional hyperbolic dynamical systems with singularities. Bunimovich, Sinai, and Chernov proved a theorem on the subexponential decay of correlations and a central limit theorem for billiard systems. In this paper we use their techniques to prove the same results for abstract systems. 相似文献
18.
19.
20.
In this paper we demonstrate how to construct signals (time series) of continuous-time dynamical systems that exhibit a given symbolic dynamics. This is achieved without construction of the ordinary differential equations that generate the flow. This construction is of theoretical interest and is useful as a source of dynamical data that can be used to test various data analysis algorithms. 相似文献