arXiv: Chaotic Dynamics最新文献_第5页

Spreading, Nonergodicity, and Selftrapping: A Puzzle of Interacting Disordered Lattice Waves 扩散、非遍历性和自陷:一个相互作用无序晶格波的谜题

arXiv: Chaotic Dynamics Pub Date : 2015-12-03 DOI: 10.1007/978-3-319-24871-4_3

S. Flach

引用次数: 5

Exact Lyapunov exponents of the generalized Boole transformations 广义布尔变换的精确Lyapunov指数

arXiv: Chaotic Dynamics Pub Date : 2015-10-29 DOI: 10.1093/ptep/ptv195

K. Umeno, K. Okubo

引用次数: 13

Exogenous Versus Endogenous for Chaotic Business Cycles 混沌商业周期的外生与内生

arXiv: Chaotic Dynamics Pub Date : 2015-09-03 DOI: 10.5890/DNC.2016.06.001

M. Akhmet, Z. Akhmetova, M. O. Fen

{"title":"Exogenous Versus Endogenous for Chaotic Business Cycles","authors":"M. Akhmet, Z. Akhmetova, M. O. Fen","doi":"10.5890/DNC.2016.06.001","DOIUrl":"https://doi.org/10.5890/DNC.2016.06.001","url":null,"abstract":"We propose a novel approach to generate chaotic business cycles in a deterministic setting. Rather than producing chaos endogenously, we consider aggregate economic models with limit cycles and equilibriums, subject them to chaotic exogenous shocks and obtain chaotic cyclical motions. Thus, we emphasize that chaotic cycles, which are inevitable in economics, are not only interior properties of economic models, but also can be considered as a result of interaction of several economical systems. This provides a comprehension of chaos (unpredictability, lack of forecasting) and control of chaos as a global economic phenomenon from the deterministic point of view. \u0000We suppose that the results of our paper are contribution to the mixed exogenous-endogenous theories of business cycles in classification by P.A. Samuelson [76]. Moreover, they demonstrate that the irregularity of the extended chaos can be structured, and this distinguishes them from the generalized synchronization. The advantage of the knowledge of the structure is that by applying instruments, which already have been developed for deterministic chaos one can control the chaos, emphasizing a parameter or a type of motion. For the globalization of cyclic chaos phenomenon we utilize new mechanisms such that entrainment by chaos, attraction of chaotic cycles by equilibriums and bifurcation of chaotic cycles developed in our earlier papers.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124380028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5

Low-Dimensional Galerkin Approximations of Nonlinear Delay Differential Equations 非线性时滞微分方程的低维伽辽金近似

arXiv: Chaotic Dynamics Pub Date : 2015-09-02 DOI: 10.3934/DCDS.2016.36.4133

M. Chekroun, M. Ghil, Honghu Liu, Shouhong Wang

{"title":"Low-Dimensional Galerkin Approximations of Nonlinear Delay Differential Equations","authors":"M. Chekroun, M. Ghil, Honghu Liu, Shouhong Wang","doi":"10.3934/DCDS.2016.36.4133","DOIUrl":"https://doi.org/10.3934/DCDS.2016.36.4133","url":null,"abstract":"This article revisits the approximation problem of systems of nonlinear delay differential equations (DDEs) by a set of ordinary differential equations (ODEs). We work in Hilbert spaces endowed with a natural inner product including a point mass, and introduce polynomials orthogonal with respect to such an inner product that live in the domain of the linear operator associated with the underlying DDE. These polynomials are then used to design a general Galerkin scheme for which we derive rigorous convergence results and show that it can be numerically implemented via simple analytic formulas. The scheme so obtained is applied to three nonlinear DDEs, two autonomous and one forced: (i) a simple DDE with distributed delays whose solutions recall Brownian motion; (ii) a DDE with a discrete delay that exhibits bimodal and chaotic dynamics; and (iii) a periodically forced DDE with two discrete delays arising in climate dynamics. In all three cases, the Galerkin scheme introduced in this article provides a good approximation by low-dimensional ODE systems of the DDE's strange attractor, as well as of the statistical features that characterize its nonlinear dynamics.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125846742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 26

Self-sustained irregular activity in an ensemble of neural oscillators 神经振荡系统中自我维持的不规则活动

arXiv: Chaotic Dynamics Pub Date : 2015-08-27 DOI: 10.1103/PhysRevX.6.011015

E. Ullner, A. Politi

{"title":"Self-sustained irregular activity in an ensemble of neural oscillators","authors":"E. Ullner, A. Politi","doi":"10.1103/PhysRevX.6.011015","DOIUrl":"https://doi.org/10.1103/PhysRevX.6.011015","url":null,"abstract":"An ensemble of pulse-coupled phase-oscillators is thoroughly analysed in the presence of a mean-field coupling and a dispersion of their natural frequencies. In spite of the analogies with the Kuramoto setup, a much richer scenario is observed. The \"synchronised phase\", which emerges upon increasing the coupling strength, is characterized by highly-irregular fluctuations: a time-series analysis reveals that the dynamics of the order parameter is indeed high-dimensional. The complex dynamics appears to be the result of the non-perturbative action of a suitably shaped phase-response curve. Such mechanism differs from the often invoked balance between excitation and inhibition and might provide an alternative basis to account for the self-sustained brain activity in the resting state. The potential interest of this dynamical regime is further strengthened by its (microscopic) linear stability, which makes it quite suited for computational tasks. The overall study has been performed by combining analytical and numerical studies, starting from the linear stability analysis of the asynchronous regime, to include the Fourier analysis of the Kuramoto order parameter, the computation of various types of Lyapunov exponents, and a microscopic study of the inter-spike intervals.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"109 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115682765","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 26

Weak Chaos, Infinite Ergodic Theory, and Anomalous Dynamics 弱混沌，无限遍历理论和异常动力学

arXiv: Chaotic Dynamics Pub Date : 2015-07-15 DOI: 10.1007/978-1-4614-6962-9_1

Rainer Klages

引用次数: 20

Statistics of time delay and scattering correlation functions in chaotic systems I. Random Matrix Theory 混沌系统中时延和散射相关函数的统计1 .随机矩阵理论

arXiv: Chaotic Dynamics Pub Date : 2015-06-22 DOI: 10.1063/1.4922746

M. Novaes

引用次数: 30

Statistics of time delay and scattering correlation functions in chaotic systems II. Semiclassical Approximation 混沌系统中时延和散射相关函数的统计2。半经典近似

arXiv: Chaotic Dynamics Pub Date : 2015-06-22 DOI: 10.1063/1.4922745

M. Novaes

引用次数: 21

Mesochronic classification of trajectories in incompressible 3D vector fields over finite times 有限时间内不可压缩三维矢量场中轨迹的中时分类

arXiv: Chaotic Dynamics Pub Date : 2015-06-17 DOI: 10.3934/dcdss.2016035

Marko Budivsi'c, S. Siegmund, Doan Thai Son, Igor Mezi'c

{"title":"Mesochronic classification of trajectories in incompressible 3D vector fields over finite times","authors":"Marko Budivsi'c, S. Siegmund, Doan Thai Son, Igor Mezi'c","doi":"10.3934/dcdss.2016035","DOIUrl":"https://doi.org/10.3934/dcdss.2016035","url":null,"abstract":"The mesochronic velocity is the average of the velocity field along trajectories generated by the same velocity field over a time interval of finite duration. In this paper we classify initial conditions of trajectories evolving in incompressible vector fields according to the character of motion of material around the trajectory. In particular, we provide calculations that can be used to determine the number of expanding directions and the presence of rotation from the characteristic polynomial of the Jacobian matrix of mesochronic velocity. In doing so, we show that (a) the mesochronic velocity can be used to characterize dynamical deformation of three-dimensional volumes, (b) the resulting mesochronic analysis is a finite-time extension of the Okubo--Weiss--Chong analysis of incompressible velocity fields, (c) the two-dimensional mesochronic analysis from Mezic et al. emph{A New Mixing Diagnostic and Gulf Oil Spill Movement}, Science 330, (2010), 486-489, extends to three-dimensional state spaces. Theoretical considerations are further supported by numerical computations performed for a dynamical system arising in fluid mechanics, the unsteady Arnold--Beltrami--Childress (ABC) flow.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131675849","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 9

Targeting engineering synchronization in chaotic systems 混沌系统的目标工程同步

arXiv: Chaotic Dynamics Pub Date : 2015-06-14 DOI: 10.1142/S0129183116500066

Sourav K. Bhowmick, D. Ghosh

引用次数: 2