{"title":"Chaos synchronization of identical Sprott systems by active control","authors":"M. Daszkiewicz","doi":"10.12988/atam.2017.763","DOIUrl":"https://doi.org/10.12988/atam.2017.763","url":null,"abstract":"In this article we synchronize by active control method all 19 identical Sprott systems provided in paper [10]. Particularly, we find the corresponding active controllers as well as we perform (as an example) the numerical synchronization of two Sprott-A models.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"86 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128188578","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}
{"title":"Random matrix theory for low-frequency sound propagation in the ocean: a spectral statistics test","authors":"D. Makarov","doi":"10.1142/S2591728518500020","DOIUrl":"https://doi.org/10.1142/S2591728518500020","url":null,"abstract":"Problem of long-range sound propagation in the randomly-inhomogeneous deep ocean is considered. We examine a novel approach for modeling of wave propagation, developed by K.C.Hegewisch and S.Tomsovic. This approach relies on construction of a wavefield propagator using the random matrix theory (RMT). We study the ability of the RMT-based propagator to reproduce properties of the propagator corresponding to direct numerical solution of the parabolic equation. It is shown that mode coupling described by the RMT-based propagator is basically consistent with the direct Monte-Carlo simulation. The agreement is worsened only for relatively short distances, when long-lasting cross-mode correlations are significant. It is shown that the RMT-based propagator with properly chosen range step can reproduce some coherent features in spectral statistics.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121154897","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}
{"title":"Dynamics of slow and fast systems on complex networks","authors":"K. Gupta, G. Ambika","doi":"10.29195/iascs.01.01.0003","DOIUrl":"https://doi.org/10.29195/iascs.01.01.0003","url":null,"abstract":"We study the occurrence of frequency synchronised states with tunable emergent frequencies in a network of connected systems. This is achieved by the interplay between time scales of nonlinear dynamical systems connected to form a network, where out of N systems, m evolve on a slower time scale. In such systems, in addition to frequency synchronised states, we also observe amplitude death, synchronised clusters and multifrequency states. We report an interesting cross over behaviour from fast to slow collective dynamics as the number of slow systems m increases. The transition to amplitude death is analysed in detail for minimal network configurations of 3 and 4 systems which actually form possible motifs of the full network.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"62 24","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114052848","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}
{"title":"Slim Fractals: The Geometry of Doubly Transient Chaos","authors":"Xiaowen Chen, T. Nishikawa, A. Motter","doi":"10.1103/PhysRevX.7.021040","DOIUrl":"https://doi.org/10.1103/PhysRevX.7.021040","url":null,"abstract":"Traditional studies of chaos in conservative and driven dissipative systems have established a correspondence between sensitive dependence on initial conditions and fractal basin boundaries, but much less is known about the relation between geometry and dynamics in undriven dissipative systems. These systems can exhibit a prevalent form of complex dynamics, dubbed doubly transient chaos because not only typical trajectories but also the (otherwise invariant) chaotic saddles are transient. This property, along with a manifest lack of scale invariance, has hindered the study of the geometric properties of basin boundaries in these systems--most remarkably, the very question of whether they are fractal across all scales has yet to be answered. Here we derive a general dynamical condition that answers this question, which we use to demonstrate that the basin boundaries can indeed form a true fractal; in fact, they do so generically in a broad class of transiently chaotic undriven dissipative systems. Using physical examples, we demonstrate that the boundaries typically form a slim fractal, which we define as a set whose dimension at a given resolution decreases when the resolution is increased. To properly characterize such sets, we introduce the notion of equivalent dimension for quantifying their relation with sensitive dependence on initial conditions at all scales. We show that slim fractal boundaries can exhibit complex geometry even when they do not form a true fractal and fractal scaling is observed only above a certain length scale at each boundary point. Thus, our results reveal slim fractals as a geometrical hallmark of transient chaos in undriven dissipative systems.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"109 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132619748","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}
{"title":"Nonlinearity in Data with Gaps: Application to Ecological and Meteorological Datasets","authors":"Sandip V. George, G. Ambika","doi":"10.29195/iascs.01.01.0002","DOIUrl":"https://doi.org/10.29195/iascs.01.01.0002","url":null,"abstract":"Datagaps are ubiquitous in real world observational data. Quantifying nonlinearity in data having gaps can be challenging. Reported research points out that interpolation can affect nonlinear quantifiers adversely, artificially introducing signatures of nonlinearity where none exist. In this paper we attempt to quantify the effect that datagaps have on the multifractal spectrum ($f(alpha)$), in the absence of interpolation. We identify tolerable gap ranges, where the measures defining the $f(alpha)$ curve do not show considerable deviation from the evenly sampled case. We apply this to the multifractal spectra of multiple data-sets with missing data from the SMEAR database. The datasets we consider include ecological datasets from SMEAR I, namely CO$_2$ exchange variation, photosynthetically active radiation levels and soil moisture variation time series, and meteorological datasets from SMEAR II, namely dew point variation and air temperature variation. We could establish multifractality due to deterministic nonlinearity in two of these datasets, even in the presence of gaps.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"524 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126058899","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}
{"title":"Synchronization of Chaos","authors":"Deniz Eroglu, J. Lamb, T. Pereira","doi":"10.1142/9789814335799_0008","DOIUrl":"https://doi.org/10.1142/9789814335799_0008","url":null,"abstract":"Dynamical networks are important models for the behaviour of complex systems, modelling physical, biological and societal systems, including the brain, food webs, epidemic disease in populations, power grids and many other. Such dynamical networks can exhibit behaviour in which deterministic chaos, exhibiting unpredictability and disorder, coexists with synchronization, a classical paradigm of order. We survey the main theory behind complete, generalized and phase synchronization phenomena in simple as well as complex networks and discuss applications to secure communications, parameter estimation and the anticipation of chaos.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126979828","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}
{"title":"Persistence of Li-Yorke chaos in systems with relay","authors":"M. Akhmet, M. O. Fen, A. Kashkynbayev","doi":"10.14232/EJQTDE.2017.1.72","DOIUrl":"https://doi.org/10.14232/EJQTDE.2017.1.72","url":null,"abstract":"It is rigorously proved that the chaotic dynamics of the non-smooth system with relay function is persistent even if a chaotic perturbation is applied. We consider chaos in a modified Li-Yorke sense such that infinitely many almost periodic motions take place in its basis. It is demonstrated that the system under investigation possesses countable infinity of chaotic sets of solutions. Coupled Duffing oscillators are used to show the effectiveness of our technique, and simulations that support the theoretical results are represented. Moreover, a chaos control procedure based on the Ott-Grebogi-Yorke algorithm is proposed to stabilize the unstable almost periodic motions embedded in the chaotic attractor.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133650343","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}
{"title":"Conditional Lyapunov Exponent Criteria in terms of Ergodic Theory","authors":"Masaru Shintani, K. Umeno","doi":"10.1093/PTEP/PTX168","DOIUrl":"https://doi.org/10.1093/PTEP/PTX168","url":null,"abstract":"The conditional Lyapunov exponent is defined for investigating chaotic synchronization, in particular complete synchronization and generalized synchronization. We find that the conditional Lyapunov exponent is expressed as a formula in terms of ergodic theory. Dealing with this formula, we find what factors characterize the conditional Lyapunov exponent in chaotic systems.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128284491","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}
{"title":"On nonlinear fractional maps: Nonlinear maps with power-law memory","authors":"M. Edelman","doi":"10.1142/9789813202740_0005","DOIUrl":"https://doi.org/10.1142/9789813202740_0005","url":null,"abstract":"This article is a short review of the recent results on properties of nonlinear fractional maps which are maps with power- or asymptotically power-law memory. These maps demonstrate the new type of attractors - cascade of bifurcations type trajectories, power-law convergence/divergence of trajectories, period doubling bifurcations with changes in the memory parameter, intersection of trajectories, and overlapping of attractors. In the limit of small time steps these maps converge to nonlinear fractional differential equations.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128068065","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}
{"title":"On the synchronization of coupled forced negative conductance circuits: A numerical study","authors":"G. Sivaganesh","doi":"10.9790/4861-17002010611","DOIUrl":"https://doi.org/10.9790/4861-17002010611","url":null,"abstract":"In this paper, a numerical study on the complete synchronization phenomenon exhibited by coupled forced negative conductance circuits is presented. The nonlinear system exhibiting two types of chaotic attractors is studied for complete synchronization of the identical chaotic attractors through phase portraits under one type of coupling. The stability of the synchronized states is observed for different coupling schemes of the circuit variables through {emph{Master Stability Function}}. The Conditional lyapunov exponents explaining the dynamical behaviour of the driven system is presented.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126631502","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}
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