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arXiv: Chaotic Dynamics最新文献

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The Smaller (SALI) and the Generalized (GALI) Alignment Indices: Efficient Methods of Chaos Detection 较小(SALI)和广义(GALI)对准指标:混沌检测的有效方法
arXiv: Chaotic Dynamics Pub Date : 2014-12-20 DOI: 10.1007/978-3-662-48410-4_5
Charalampos Skokos, Thanos Manos, Thanos Manos
{"title":"The Smaller (SALI) and the Generalized (GALI) Alignment Indices: Efficient Methods of Chaos Detection","authors":"Charalampos Skokos, Thanos Manos, Thanos Manos","doi":"10.1007/978-3-662-48410-4_5","DOIUrl":"https://doi.org/10.1007/978-3-662-48410-4_5","url":null,"abstract":"","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133596529","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: 42
Identification of the oscillation period of chemical reactors by chaotic sampling of the conversion degree 利用转换度的混沌采样方法辨识化学反应器的振荡周期
arXiv: Chaotic Dynamics Pub Date : 2014-09-01 DOI: 10.2478/cpe-2014-0029
M. Lawnik, M. Berezowski
{"title":"Identification of the oscillation period of chemical reactors by chaotic sampling of the conversion degree","authors":"M. Lawnik, M. Berezowski","doi":"10.2478/cpe-2014-0029","DOIUrl":"https://doi.org/10.2478/cpe-2014-0029","url":null,"abstract":"To stabilize the periodic operation of a chemical reactor the oscillation period should be determined precisely in real time. The method discussed in the paper is based on adaptive sampling of the state variable with the use of chaotic mapping to itself. It enables precise determination of the oscillation period in real time and could be used for a proper control system, that can successfully control the process and maintain the oscillation period at a set level. The method was applied to a tank reactor and tubular reactor with recycle.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126411466","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
Computational Studies of Multiple-Particle Nonlinear Dynamics in a Spatio-Temporally periodic potential 时空周期势中多粒子非线性动力学的计算研究
arXiv: Chaotic Dynamics Pub Date : 2014-06-30 DOI: 10.1063/1.4885895
Owen D. Myers, Junru Wu, J. Marshall, C. Danforth
{"title":"Computational Studies of Multiple-Particle Nonlinear Dynamics in a Spatio-Temporally periodic potential","authors":"Owen D. Myers, Junru Wu, J. Marshall, C. Danforth","doi":"10.1063/1.4885895","DOIUrl":"https://doi.org/10.1063/1.4885895","url":null,"abstract":"The spatio-temporally periodic (STP) potential is interesting in Physics due to the intimate coupling between its time and spatial components. In this paper we begin with a brief discussion of the dynamical behaviors of a single particle in a STP potential and then examine the dynamics of multiple particles interacting in a STP potential via the electric Coulomb potential. For the multiple particle case, we focus on the occurrence of bifurcations when the amplitude of the STP potential varies. It is found that the particle concentration of the system plays an important role; the type of bifurcations that occur and the number of attractors present in the Poincar'e sections depend on whether the number of particles in the simulation is even or odd. In addition to the nonlinear dynamical approach we also discuss dependence of the squared fractional deviation of particles kinetic energy of the multiple particle system on the amplitude of the STP potential which can be used to elucidate certain transitions of states; this approach is simple and useful particularly for experimental studies of complicated interacting systems.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115241235","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
Quantum Mechanics of a Rotating Billiard 旋转台球的量子力学
arXiv: Chaotic Dynamics Pub Date : 2014-06-12 DOI: 10.7566/JPSCP.1.013116
N. Jha, S. Jain
{"title":"Quantum Mechanics of a Rotating Billiard","authors":"N. Jha, S. Jain","doi":"10.7566/JPSCP.1.013116","DOIUrl":"https://doi.org/10.7566/JPSCP.1.013116","url":null,"abstract":"Integrability of a square billiard is spontaneously broken as it rotates about one of its corners. The system becomes quasi-integrable where the invariant tori are broken with respect to a certain parameter, $lambda = 2E/omega^{2}$ where E is the energy of the particle inside the billiard and $omega$ is the angular frequency of rotation of billiard. We study the system classically and quantum mechanically in view of obtaining a correspondence in the two descriptions. Classical phase space in Poincar'{e} surface of section shows transition from regular to chaotic motion as the parameter $lambda$ is decreased. In the Quantum counterpart, the spectral statistics shows a transition from Poisson to Wigner distribution as the system turns chaotic with decrease in $lambda$. The wavefunction statistics however show breakdown of time-reversal symmetry as $lambda$ decreases.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121785671","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
Heterogeneous delays making parents synchronized: A coupled maps on Cayley tree model 异构延迟使父节点同步:Cayley树模型上的耦合映射
arXiv: Chaotic Dynamics Pub Date : 2014-06-04 DOI: 10.1063/1.4881978
Aradhana Singh, S. Jalan
{"title":"Heterogeneous delays making parents synchronized: A coupled maps on Cayley tree model","authors":"Aradhana Singh, S. Jalan","doi":"10.1063/1.4881978","DOIUrl":"https://doi.org/10.1063/1.4881978","url":null,"abstract":"We study the phase synchronized clusters in the diffusively coupled maps on the Cayley tree networks for heterogeneous delay values. Cayley tree networks comprise of two parts: the inner nodes and the boundary nodes. We find that heterogeneous delays lead to various cluster states, such as; (a) cluster state consisting of inner nodes and boundary nodes, and (b) cluster state consisting of only boundary nodes. The former state may comprise of nodes from all the generations forming self-organized cluster or nodes from few generations yielding driven clusters depending upon on the parity of heterogeneous delay values. Furthermore, heterogeneity in delays leads to the lag synchronization between the siblings lying on the boundary by destroying the exact synchronization among them. The time lag being equal to the difference in the delay values. The Lyapunov function analysis sheds light on the destruction of the exact synchrony among the last generation nodes. To the end we discuss the relevance of our results with respect to their applications in the family business as well as in understanding the occurrence of genetic diseases.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"289 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116583859","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
Nonlinear Lattice Waves in Random Potentials 随机电位中的非线性点阵波
arXiv: Chaotic Dynamics Pub Date : 2014-05-06 DOI: 10.1007/978-3-319-19015-0_1
S. Flach
{"title":"Nonlinear Lattice Waves in Random Potentials","authors":"S. Flach","doi":"10.1007/978-3-319-19015-0_1","DOIUrl":"https://doi.org/10.1007/978-3-319-19015-0_1","url":null,"abstract":"","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130484015","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
Fractional Maps and Fractional Attractors. Part II: Fractional Difference $alpha$-Families of Maps 分数映射和分数吸引子。第二部分:分数差分$alpha$-映射族
arXiv: Chaotic Dynamics Pub Date : 2014-04-19 DOI: 10.5890/dnc.2015.11.003
M. Edelman
{"title":"Fractional Maps and Fractional Attractors. Part II: Fractional Difference $alpha$-Families of Maps","authors":"M. Edelman","doi":"10.5890/dnc.2015.11.003","DOIUrl":"https://doi.org/10.5890/dnc.2015.11.003","url":null,"abstract":"In this paper we extend the notion of an $alpha$-family of maps to discrete systems defined by simple difference equations with the fractional Caputo difference operator. The equations considered are equivalent to maps with falling factorial-law memory which is asymptotically power-law memory. We introduce the fractional difference Universal, Standard, and Logistic $alpha$-Families of Maps and propose to use them to study general properties of discrete nonlinear systems with asymptotically power-law memory.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"103 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114401731","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: 28
Identification of fast-changing signals by means of adaptive chaotic transformations 基于自适应混沌变换的快速变化信号辨识
arXiv: Chaotic Dynamics Pub Date : 2014-04-10 DOI: 10.15388/NA.2014.2.2
M. Berezowski, M. Lawnik
{"title":"Identification of fast-changing signals by means of adaptive chaotic transformations","authors":"M. Berezowski, M. Lawnik","doi":"10.15388/NA.2014.2.2","DOIUrl":"https://doi.org/10.15388/NA.2014.2.2","url":null,"abstract":"The adaptive approach of strongly non-linear fast-changing signals identification is discussed. The approach is devised by adaptive sampling based on chaotic mapping in yourself of a signal. Presented sampling way may be utilized online in the automatic control of chemical reactor (throughout identification of concentrations and temperature oscillations in real-time), in medicine (throughout identification of ECG and EEG signals in real-time), etc. In this paper, we presented it to identify the Weierstrass function and ECG signal.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132257134","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
Desynchronization in an ensemble of globally coupled chaotic bursting neuronal oscillators by dynamic delayed feedback control 基于动态延迟反馈控制的全局耦合混沌破裂神经元振子集合的去同步
arXiv: Chaotic Dynamics Pub Date : 2014-03-08 DOI: 10.1142/S021797921450235X
Y. Che, Tingting Yang, R. Li, Huiyan Li, Chunxiao Han, Jiang Wang, Xile Wei
{"title":"Desynchronization in an ensemble of globally coupled chaotic bursting neuronal oscillators by dynamic delayed feedback control","authors":"Y. Che, Tingting Yang, R. Li, Huiyan Li, Chunxiao Han, Jiang Wang, Xile Wei","doi":"10.1142/S021797921450235X","DOIUrl":"https://doi.org/10.1142/S021797921450235X","url":null,"abstract":"In this paper, we propose a dynamic delayed feedback control approach for desynchronization of chaotic-bursting synchronous activities in an ensemble of globally coupled neuronal oscillators. We demonstrate that the difference signal between an ensemble's mean field and its time delayed state, filtered and fed back to the ensemble, can suppress the self-synchronization in the ensemble. These individual units are decoupled and stabilized at the desired desynchronized states while the stimulation signal reduces to the noise level. The effectiveness of the method is illustrated by examples of two different populations of globally coupled chaotic-bursting neurons. The proposed method has potential for mild, effective and demand-controlled therapy of neurological diseases characterized by pathological synchronization.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"2432 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130867857","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
Compound orbits break-up in constituents: an algorithm 复合轨道分解的组成:一种算法
arXiv: Chaotic Dynamics Pub Date : 2014-02-24 DOI: 10.15388/na.2015.1.8
J. Mart'in, A. G. G'omez, Mateo Moscoso, Daniel Rodr'iguez-P'erez
{"title":"Compound orbits break-up in constituents: an algorithm","authors":"J. Mart'in, A. G. G'omez, Mateo Moscoso, Daniel Rodr'iguez-P'erez","doi":"10.15388/na.2015.1.8","DOIUrl":"https://doi.org/10.15388/na.2015.1.8","url":null,"abstract":"In this paper decomposition of periodic orbits in bifurcation diagrams are derived in unidimensional dynamics system $x_{n+1}=f(x_{n};r)$, being $f$ an unimodal function. We proof a theorem which states the necessary and sufficient conditions for the break-up of compound orbits in their simpler constituents. A corollary to this theorem provides an algorithm for the computation of those orbits. This process closes the theoretical framework initiated in (Physica D, 239:1135--1146, 2010).","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127949193","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
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