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Vibrational Resonance in the Duffing Oscillator with Distributed Time-Delayed Feedback 分布时滞反馈Duffing振荡器的振动共振
arXiv: Chaotic Dynamics Pub Date : 2015-04-16 DOI: 10.5890/jand.2015.11.006
C. Jeevarathinam, S. Rajasekar, M. Sanjuán
{"title":"Vibrational Resonance in the Duffing Oscillator with Distributed Time-Delayed Feedback","authors":"C. Jeevarathinam, S. Rajasekar, M. Sanjuán","doi":"10.5890/jand.2015.11.006","DOIUrl":"https://doi.org/10.5890/jand.2015.11.006","url":null,"abstract":"We analyze the vibrational resonance in the Duffing oscillator system in the presence of (i) a gamma distributed time-delayed feedback and (ii) integrative time-delayed (uniformly distributed time delays over a finite interval) feedback. Particularly, applying a theoretical procedure we obtain an expression for the response amplitude $Q$ at the low-frequency of the driving biharmonic force. For both double-well potential and single-well potential cases we are able to identify the regions in parameter space where either (i) two resonances, (ii) a single resonance or (iii) no resonance occur. Theoretically predicted values of $Q$ and the values of a control parameter at which resonance occurs are in good agreement with our numerical simulation. The analysis shows a strong influence of both types of time-delayed feedback on vibrational resonance.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125231700","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: 11
Coupled systems with hyperchaos and quasiperiodicity 具有超混沌和准周期性的耦合系统
arXiv: Chaotic Dynamics Pub Date : 2015-04-03 DOI: 10.5890/JAND.2016.06.003
A. Kuznetsov, Y. Sedova
{"title":"Coupled systems with hyperchaos and quasiperiodicity","authors":"A. Kuznetsov, Y. Sedova","doi":"10.5890/JAND.2016.06.003","DOIUrl":"https://doi.org/10.5890/JAND.2016.06.003","url":null,"abstract":"A model with hyperchaos is studied by means of Lyapunov two-parameter analysis. The regions of chaos and hyperchaos, as well as autonomous quasiperiodicity are identified. We discuss the picture of domains of different regimes in the parameter plane of coupled systems, corresponding to the cases of interaction of quasiperiodic and hyperchaotic subsystems.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128250373","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: 6
Comparison of Very Smooth Cell-Model Trajectories Using Five Symplectic and Two Runge-Kutta Integrators 使用五个辛积分器和两个龙格-库塔积分器比较非常光滑的细胞模型轨迹
arXiv: Chaotic Dynamics Pub Date : 2015-04-02 DOI: 10.12921/CMST.2015.21.03.001
W. G. Hoover, C. G. Hoover
{"title":"Comparison of Very Smooth Cell-Model Trajectories Using Five Symplectic and Two Runge-Kutta Integrators","authors":"W. G. Hoover, C. G. Hoover","doi":"10.12921/CMST.2015.21.03.001","DOIUrl":"https://doi.org/10.12921/CMST.2015.21.03.001","url":null,"abstract":"Time-reversible symplectic methods, which are precisely compatible with Liouville's phase-volume-conservation theorem, are often recommended for computational simulations of Hamiltonian mechanics. Lack of energy drift is an apparent advantage of such methods. But all numerical methods are susceptible to Lyapunov instability, which severely limits the maximum time for which chaotic solutions can be \"accurate\". The \"advantages\" of higher-order methods are lost rapidly for typical chaotic Hamiltonians. We illustrate these difficulties for a useful reproducible test case, the two-dimensional one-particle cell model with specially smooth forces. This Hamiltonian problem is chaotic and occurs on a three-dimensional constant-energy shell, the minimum dimension for chaos. We benchmark the problem with quadruple-precision trajectories using the fourth-order Candy-Rozmus, fifth-order Runge-Kutta, and eighth-order Schlier-Seiter-Teloy integrators. We compare the last, most-accurate particle trajectories to those from six double-precision algorithms, four symplectic and two Runge-Kutta.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132971887","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: 15
Fast Fermi Acceleration and Entropy Growth 快速费米加速和熵增长
arXiv: Chaotic Dynamics Pub Date : 2015-03-13 DOI: 10.1051/MMNP/201510304
T. Pereira, D. Turaev
{"title":"Fast Fermi Acceleration and Entropy Growth","authors":"T. Pereira, D. Turaev","doi":"10.1051/MMNP/201510304","DOIUrl":"https://doi.org/10.1051/MMNP/201510304","url":null,"abstract":"Fermi acceleration is the process of energy transfer from massive objects in slow motion to light objects that move fast. The model for such process is a time-dependent Hamiltonian system. As the parameters of the system change with time, the energy is no longer conserved, which makes the acceleration possible. One of the main problems is how to generate a sustained and robust energy growth. We show that the non-ergodicity of any chaotic Hamiltonian system must universally lead to the exponential growth of energy at a slow periodic variation of parameters. We build a model for this process in terms of a Geometric Brownian Motion with a positive drift and relate it to the entropy increase.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"171 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117312305","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: 7
A Structure behind Primitive Chaos 原始混沌背后的结构
arXiv: Chaotic Dynamics Pub Date : 2015-03-12 DOI: 10.7566/JPSJ.84.064007
Y. Ogasawara
{"title":"A Structure behind Primitive Chaos","authors":"Y. Ogasawara","doi":"10.7566/JPSJ.84.064007","DOIUrl":"https://doi.org/10.7566/JPSJ.84.064007","url":null,"abstract":"Recently, a new concept, primitive chaos, was proposed, as a concept closely related to the fundamental problems of physics itself such as determinism, causality, free will, predictability, and irreversibility [J. Phys. Soc. Jpn. {bf 79}, 15002 (2010)]. This letter reveals a structure hidden behind the primitive chaos; under some conditions, a new primitive chaos is constructed from the original primitive chaos, this procedure can be repeated, and the hierarchic structure of the primitive chaos is obtained. This implies such a picture that new events and causality is constructed from the old ones, with the aid of the concept of a coarse graining. As an application of this structure, interesting facts are revealed for the essential condition of the primitive chaos and for the chaotic behaviors.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121400271","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: 1
Sinai-Ruelle-Bowen measures for piecewise hyperbolic maps with two directions of instability in three-dimensional spaces 三维空间中具有两个不稳定方向的分段双曲图的Sinai-Ruelle-Bowen测度
arXiv: Chaotic Dynamics Pub Date : 2015-02-19 DOI: 10.3934/dcds.2016.36.2873
Xu Zhang
{"title":"Sinai-Ruelle-Bowen measures for piecewise hyperbolic maps with two directions of instability in three-dimensional spaces","authors":"Xu Zhang","doi":"10.3934/dcds.2016.36.2873","DOIUrl":"https://doi.org/10.3934/dcds.2016.36.2873","url":null,"abstract":"A class of piecewise $C^2$ Lozi-like maps in three-dimensional Euclidean spaces is introduced, and the existence of Sinai-Ruelle-Bowen measures is studied, where the dimension of the instability is equal to two. Further, an example with computer simulations is provided to illustrate the theoretical results.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117352141","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: 2
Stability of real parametric polynomial discrete dynamical systems 实参数多项式离散动力系统的稳定性
arXiv: Chaotic Dynamics Pub Date : 2015-02-01 DOI: 10.1155/2015/680970
F. Franco-Medrano, F. Solis
{"title":"Stability of real parametric polynomial discrete dynamical systems","authors":"F. Franco-Medrano, F. Solis","doi":"10.1155/2015/680970","DOIUrl":"https://doi.org/10.1155/2015/680970","url":null,"abstract":"We extend and improve the existing characterization of the dynamics of general quadratic real polynomial maps with coefficients that depend on a single parameter $lambda$, and generalize this characterization to cubic real polynomial maps, in a consistent theory that is further generalized to real $m$-th degree real polynomial maps. In essence, we give conditions for the stability of the fixed points of any real polynomial map with real fixed points. In order to do this, we have introduced the concept of Canonical Polynomial Maps which are topologically conjugate to any polynomial map of the same degree with real fixed points. The stability of the fixed points of canonical polynomial maps has been found to depend solely on a special function termed Product Position Function for a given fixed point. The values of this product position determine the stability of the fixed point in question, when it bifurcates, and even when chaos arises, as it passes through what we have termed stability bands. The exact boundary values of these stability bands are yet to be calculated for regions of type greater than one for polynomials of degree higher than three.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125023288","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: 1
Chaotic Boltzmann machines with two elements 双元混沌玻尔兹曼机
arXiv: Chaotic Dynamics Pub Date : 2015-01-28 DOI: 10.11188/seisankenkyu.66.315
H. Suzuki
{"title":"Chaotic Boltzmann machines with two elements","authors":"H. Suzuki","doi":"10.11188/seisankenkyu.66.315","DOIUrl":"https://doi.org/10.11188/seisankenkyu.66.315","url":null,"abstract":"In this brief note, we show that chaotic Boltzmann machines truly yield samples from the probabilistic distribution of the corresponding Boltzmann machines if they are composed of only two elements. This note is an English translation (with slight modifications) of the article originally written in Japanese [H. Suzuki, Seisan Kenkyu 66 (2014), 315-316].","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"57 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114060240","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: 0
The Relative Lyapunov Indicators: Theory and Application to Dynamical Astronomy 相对李亚普诺夫指示器:理论及其在动力天文学中的应用
arXiv: Chaotic Dynamics Pub Date : 2015-01-28 DOI: 10.1007/978-3-662-48410-4_6
Zsolt S'andor, N. Maffione
{"title":"The Relative Lyapunov Indicators: Theory and Application to Dynamical Astronomy","authors":"Zsolt S'andor, N. Maffione","doi":"10.1007/978-3-662-48410-4_6","DOIUrl":"https://doi.org/10.1007/978-3-662-48410-4_6","url":null,"abstract":"","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115481627","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: 3
New chaos indicators for systems with extremely small Lyapunov exponents 极小李雅普诺夫指数系统的新混沌指标
arXiv: Chaotic Dynamics Pub Date : 2015-01-01 DOI: 10.1142/9789813202740_0011
K. Okubo, K. Umeno
{"title":"New chaos indicators for systems with extremely small Lyapunov exponents","authors":"K. Okubo, K. Umeno","doi":"10.1142/9789813202740_0011","DOIUrl":"https://doi.org/10.1142/9789813202740_0011","url":null,"abstract":"We propose new chaos indicators for systems with extremely small positive Lyapunov exponents. These chaos indicators can firstly detect a sharp transition between the Arnold diffusion regime and the Chirikov diffusion regime of the Froeschl'e map and secondly detect chaoticity in systems with zero Lyapunov exponent such as the Boole transformation and the $S$-unimodal function to characterize sub-exponential diffusions.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124348179","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: 0
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