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Chaos-Chaos intermittency and 1/F noise in Chua's Circuit 蔡氏电路中的混沌-混沌间歇和1/F噪声
Chua's Circuit Pub Date : 1994-02-01 DOI: 10.1142/S0218127494000083
V. Anishchenko, A. Neiman, L. Chua
{"title":"Chaos-Chaos intermittency and 1/F noise in Chua's Circuit","authors":"V. Anishchenko, A. Neiman, L. Chua","doi":"10.1142/S0218127494000083","DOIUrl":"https://doi.org/10.1142/S0218127494000083","url":null,"abstract":"Statistical and dynamical properties of the “chaos-chaos” type intermittency in Chua’s circuit are studied by numerical simulation methods. It is shown that at the onset of this intermittency phenomenon, the power spectrum of the associated time series has the shape of 1/f noise. The influence of external noise and computer calculation errors on the form of the spectrum and other process characteristics are analyzed. The structure and scaling of the Poincare map at the transition threshold are also discussed.","PeriodicalId":216872,"journal":{"name":"Chua's Circuit","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128545631","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: 12
Cycles of Chaotic Intervals in a Time-delayed Chua's Circuit 延时蔡氏电路中混沌区间的循环
Chua's Circuit Pub Date : 1993-12-01 DOI: 10.1142/S0218127493001215
Y. Maistrenko, V. Maistrenko, L. Chua
{"title":"Cycles of Chaotic Intervals in a Time-delayed Chua's Circuit","authors":"Y. Maistrenko, V. Maistrenko, L. Chua","doi":"10.1142/S0218127493001215","DOIUrl":"https://doi.org/10.1142/S0218127493001215","url":null,"abstract":"We study the bifurcations of attractors of a one-dimensional 2-segment piecewise-linear map. We prove that the parameter regions of existence of stable point cycles γ are separated by regions of existence of stable interval cycles Γ containing chaotic everywhere dense trajectories. Moreover, we show that the period-doubling phenomenon for cycles of chaotic intervals is characterized by two universal constants δ and α, whose values are calculated from explicit formulas.","PeriodicalId":216872,"journal":{"name":"Chua's Circuit","volume":"296 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120938608","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: 115
Chua's Circuit: A Paradigm for Chaos 蔡氏电路:混沌的范例
Chua's Circuit Pub Date : 1993-11-01 DOI: 10.1142/1997
R. Madan
{"title":"Chua's Circuit: A Paradigm for Chaos","authors":"R. Madan","doi":"10.1142/1997","DOIUrl":"https://doi.org/10.1142/1997","url":null,"abstract":"Strange attractors and dynamical models, L.P. Shil'nikov from the Chua circuit to the generalized Chua map, R. Brown bispectral analysis of Chua's circuit, S. Elgar and M.P. Kennedy sound and music from Chua's low-level visual sensing, E.J. Altman chaos synchronization in Chua's circuit, L.O. Chua et al controlling chaos in Chua's circuit, G.A. Johnson et al controlling of chaos in the driven Chua's circuit, K. Murali and M. Lakshmanan controlling Chua's circuit, G-R. Chen and X-N. Dong distortion control of chaotic systems - the Chua's circuit, R. Genesio and A. Tesi control of Chua's circuit, T. Hartley and F. Mossayebi reconstructing the dynamics of Chua's circuit, J. Glover and A. Mees travelling wavefront and its failure in a one-dimensional array of Chua's circuit, V. Perez-Munuzuri et al n-dimensional canonical Chua's circuit, Lj Kocarev et al. (Part contents).","PeriodicalId":216872,"journal":{"name":"Chua's Circuit","volume":"83 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114787290","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: 756
Spatial Disorder and wave Fronts in a Chain of coupled Chua's Circuits 耦合蔡氏电路链中的空间无序和波阵面
Chua's Circuit Pub Date : 1993-10-01 DOI: 10.1142/S0218127493001021
V. Nekorkin, L. Chua
{"title":"Spatial Disorder and wave Fronts in a Chain of coupled Chua's Circuits","authors":"V. Nekorkin, L. Chua","doi":"10.1142/S0218127493001021","DOIUrl":"https://doi.org/10.1142/S0218127493001021","url":null,"abstract":"Dynamics of a chain of coupled Chua's circuits is investigated. Existence of spatial disorder is revealed. Dynamics of wave fronts in the limiting case of a continuous medium is studied.","PeriodicalId":216872,"journal":{"name":"Chua's Circuit","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114815765","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: 35
Experimental Observation of Antimonotonicity in Chua's Circuit 蔡氏电路反单调性的实验观察
Chua's Circuit Pub Date : 1993-08-01 DOI: 10.1142/S0218127493000878
L. Kocarev, K. S. Halle, K. Eckert, L. Chua
{"title":"Experimental Observation of Antimonotonicity in Chua's Circuit","authors":"L. Kocarev, K. S. Halle, K. Eckert, L. Chua","doi":"10.1142/S0218127493000878","DOIUrl":"https://doi.org/10.1142/S0218127493000878","url":null,"abstract":"Two different bifurcation patterns are experimentally observed in Chua's circuit. They show that antimonotonicity — inevitable reversals of period-doubling sequences, is a typical phenomenon in Chua's circuit.","PeriodicalId":216872,"journal":{"name":"Chua's Circuit","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114382877","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: 104
Two-parameter Study of Transition to Chaos in Chua's Circuit: Renormalization Group, Universality and Scaling 蔡氏电路向混沌过渡的双参数研究:重整化群、普适性和标度
Chua's Circuit Pub Date : 1993-08-01 DOI: 10.1142/S0218127493000799
A. Kuznetsov, S. Kuznetsov, I. Sataev, L. Chua
{"title":"Two-parameter Study of Transition to Chaos in Chua's Circuit: Renormalization Group, Universality and Scaling","authors":"A. Kuznetsov, S. Kuznetsov, I. Sataev, L. Chua","doi":"10.1142/S0218127493000799","DOIUrl":"https://doi.org/10.1142/S0218127493000799","url":null,"abstract":"A complex fine structure in the topography of regions of different dynamical behavior near the onset of chaos is investigated in a parameter plane of the 1D Chua's map, which describes approximately the dynamics of Chua's circuit. Besides piecewise-smooth Feigenbaum critical lines, the boundary of chaos contains an infinite set of codimension-2 critical points, which may be coded by itineraries on a binary tree. Renormalization group analysis is applied which is a generalization of Feigenbaum's theory for codimension-2 critical points. Multicolor high-resolution maps of the parameter plane show that in regions near critical points having periodic codes, the infinitely intricate topography of the parameter plane reveals a property of self-similarity.","PeriodicalId":216872,"journal":{"name":"Chua's Circuit","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128682709","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: 23
The effects of Symmetry Breaking in Chua's Circuit and Related piecewise-linear dynamical Systems 蔡氏回路及相关片线性动力系统中的对称性破坏效应
Chua's Circuit Pub Date : 1993-08-01 DOI: 10.1142/S0218127493000805
C. Kahlert
{"title":"The effects of Symmetry Breaking in Chua's Circuit and Related piecewise-linear dynamical Systems","authors":"C. Kahlert","doi":"10.1142/S0218127493000805","DOIUrl":"https://doi.org/10.1142/S0218127493000805","url":null,"abstract":"The behavior of transfer and return maps in the intermediate region of Chua's circuit and related systems undergoes a number of changes as the symmetry of the dynamics is broken, i.e., the separating planes are moved away from symmetric positions. We employ the technique of maps induced by the flow of the system and construct the critical curves for the maps in the intermediate region of state space. The influence of a broken symmetry on the critical curves and the flow is discussed in depth. We demonstrate that any breaking of symmetry potentially weakens and eventually destroys the chaos producing mechanisms.","PeriodicalId":216872,"journal":{"name":"Chua's Circuit","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126547176","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: 20
Unimodal interval Maps obtained from the modified Chua equations 由修正Chua方程得到的单峰区间映射
Chua's Circuit Pub Date : 1993-04-01 DOI: 10.1142/S0218127493000246
M. Misiurewicz
{"title":"Unimodal interval Maps obtained from the modified Chua equations","authors":"M. Misiurewicz","doi":"10.1142/S0218127493000246","DOIUrl":"https://doi.org/10.1142/S0218127493000246","url":null,"abstract":"Following Brown [1992, 1993] we study maps of the real line into itself obtained from the modified Chua equations. We fix our attention on a one-parameter family of such maps, which seems to be typical. For a large range of parameters, invariant intervals exist. In such an invariant interval, the map is piecewise continuous, with most of pieces of continuity mapped in a monotone way onto the whole interval. However, on the central piece there is a critical point. This allows us to find sometimes a smaller invariant interval on which the map is unimodal. In such a way, we get one-parameter families of smooth unimodal maps, very similar to the well-known family of logistic maps x ↦ ax(1−x). We study more closely one of those and show that these maps have negative Schwarzian derivative. This implies the existence of at most one attracting periodic orbit. Moreover, there is a set of parameters of positive measure for which chaos occurs.","PeriodicalId":216872,"journal":{"name":"Chua's Circuit","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121518516","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
Transmission of Digital signals by Chaotic Synchronization 数字信号的混沌同步传输
Chua's Circuit Pub Date : 1992-12-01 DOI: 10.1142/S0218127492000562
U. Parlitz, L. Chua, L. Kocarev, K. S. Halle, Alain Shang
{"title":"Transmission of Digital signals by Chaotic Synchronization","authors":"U. Parlitz, L. Chua, L. Kocarev, K. S. Halle, Alain Shang","doi":"10.1142/S0218127492000562","DOIUrl":"https://doi.org/10.1142/S0218127492000562","url":null,"abstract":"The transmission of digital signals by means of chaotic synchronization is demonstrated, numerically as well as experimentally, via Chua’s circuit.","PeriodicalId":216872,"journal":{"name":"Chua's Circuit","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127470707","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: 566
Signal Amplification via Chaos: Experimental Evidence 混沌信号放大:实验证据
Chua's Circuit Pub Date : 1992-12-01 DOI: 10.1142/S021812749200063X
K. S. Halle, L. Chua, V. Anishchenko, M. A. Safonova
{"title":"Signal Amplification via Chaos: Experimental Evidence","authors":"K. S. Halle, L. Chua, V. Anishchenko, M. A. Safonova","doi":"10.1142/S021812749200063X","DOIUrl":"https://doi.org/10.1142/S021812749200063X","url":null,"abstract":"Experimental evidence showing the existence of signal amplification via perturbation of periodic and chaotic orbits in an electronic circuit is presented.","PeriodicalId":216872,"journal":{"name":"Chua's Circuit","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115340357","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
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