The Experts below are selected from a list of 294 Experts worldwide ranked by ideXlab platform
S P Kuznetsov - One of the best experts on this subject based on the ideXlab platform.
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a Strange Attractor of the smale williams type in the chaotic dynamics of a physical system
Journal of Experimental and Theoretical Physics, 2006Co-Authors: S P Kuznetsov, E P SeleznevAbstract:A nonautonomous nonlinear system is constructed and implemented as an experimental device. As represented by a 4D stroboscopic Poincare map, the system exhibits a Smale-Williams-type Strange Attractor. The system consists of two coupled van der Pol oscillators whose frequencies differ by a factor of two. The corresponding Hopf bifurcation parameters slowly vary as periodic functions of time in antiphase with one another; i.e., excitation is alternately transferred between the oscillators. The mechanisms underlying the system’s chaotic dynamics and onset of chaos are qualitatively explained. A governing system of differential equations is formulated. The existence of a chaotic Attractor is confirmed by numerical results. Hyperbolicity is verified numerically by performing a statistical analysis of the distribution of the angle between the stable and unstable subspaces of manifolds of the chaotic invariant set. Experimental results are in qualitative agreement with numerical predictions.
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example of a physical system with a hyperbolic Attractor of the smale williams type
Physical Review Letters, 2005Co-Authors: S P KuznetsovAbstract:A simple and transparent example of a nonautonomous flow system with a hyperbolic Strange Attractor is suggested. The system is constructed on the basis of two coupled van der Pol oscillators, the characteristic frequencies differ twice, and the parameters controlling generation in both oscillators undergo a slow periodic counterphase variation in time. In terms of stroboscopic Poincare sections, the respective 4D mapping has a hyperbolic Strange Attractor of the Smale-Williams type. Qualitative reasoning and quantitative data of numerical computations are presented and discussed, e.g., Lyapunov exponents and their parameter dependencies. A special test for hyperbolicity based on analysis of distributions of angles between stable and unstable subspaces of a chaotic trajectory is performed.
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an example of physical system with hyperbolic Attractor of smale williams type
arXiv: Chaotic Dynamics, 2005Co-Authors: S P KuznetsovAbstract:A simple and transparent example of a non-autonomous flow system, with hyperbolic Strange Attractor is suggested. The system is constructed on a basis of two coupled van der Pol oscillators, the characteristic frequencies differ twice, and the parameters controlling generation in both oscillators undergo a slow periodic counter-phase variation in time. In terms of stroboscopic Poincar\'{e} section, the respective four-dimensional mapping has a hyperbolic Strange Attractor of Smale - Williams type. Qualitative reasoning and quantitative data of numerical computations are presented and discussed, e.g. Lyapunov exponents and their parameter dependencies. A special test for hyperbolicity based on statistical analysis of distributions of angles between stable and unstable subspaces of a chaotic trajectory has been performed. Perspectives of further comparative studies of hyperbolic and non-hyperbolic chaotic dynamics in physical aspect are outlined.
N Zymaris - One of the best experts on this subject based on the ideXlab platform.
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preseismic electric signals generated by critical stress loading of the lithosphere a review of the type of signals obtained from a long lasted 1999 to 2012 experiment conducted in greece
arXiv: Geophysics, 2012Co-Authors: C Thanassoulas, V Klentos, G Verveniotis, N ZymarisAbstract:In this work a review is made of the various preseismic electric signals that have been observed before large EQs in Greece during the period of 1999 to 2012. The observed preseismic electric signals comply quite well with the theoretical ones that are expected to be generated by a large scale piezoelectric mechanism been activatsd at the focal area due to its excess stress-load. Preseismic electric signals of the total piezoelectric field, its first time derivative, its oscillation due to M1 and K1 tidal components have been observed by single monitoring sites during the actual 1999 to 2012 experiment in Greece. Moreover, the "Strange Attractor like" electric preseismic signal was detected by the simultaneously use of two distant monitoring sites. It is demonstrated that the preseismic electric signals can not only determine quite accurately a very short time window for the EQ occurrence and its epicentral location but the latter can be achieved without any prior knowledge of the geological, tectonic setting or past seismic history of the seismogenic area. The predicted pending EQ is treated as a single isolated destructive nature event which sends clear warning signals well before its occurrence. Real examples are presented from the Greek territory. Key words: piezoelectricity, electric preseismic signals, Strange Attractor like, earthquake prediction.
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preseismic oscillating electric field Strange Attractor like precursor of t 6 months triggered by ssa tidal wave application on large ms 6 0r eqs in greece october 1st 2006 december 2nd 2008
arXiv: Geophysics, 2009Co-Authors: C Thanassoulas, V Klentos, G Verveniotis, N ZymarisAbstract:In this work the preseismic "Strange Attractor like" precursor is studied, in the domain of the Earth's oscillating electric field for T = 6 months. It is assumed that the specific oscillating electric field is generated by the corresponding lithospheric oscillation, triggered by the Ssa tidal wave of the same wave length (6 months) under excess strain load conditions met in the focal area of a future large earthquake. The analysis of the recorded Earth's oscillating electric field by the two distant monitoring sites of PYR and HIO and for a period of time of 26 months (October 1st, 2006 - December 2nd, 2008) suggests that the specific precursor can successfully resolve the predictive time window in terms of months and for a "swarm" of large EQs (Ms > 6.0R), in contrast to the resolution obtained by the use of electric fields of shorter (T = 1, 14 days, single EQ identification) wave length. More over, the fractal character of the "Strange Attractor like" precursor in the frequency domain is pointed out. Finally, a proposal is made that concerns the continuous monitoring of the specific preseismic Attractor in distinct different wave lengths of the oscillating Earth's electric field so that an early warning system can be utilized. As a refinement of the "Strange Attractor like" methodology, the guide lines of a generalized inversion scheme are presented so that the epicenter of the driving mechanism (seismic epicentral area) can be estimated in a least squares sense.
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preseismic oscillating electric field Strange Attractor like precursor of t 14 days triggered by m1 tidal wave application on large ms 6 0r eqs in greece march 18th 2006 november 17th 2008
arXiv: Geophysics, 2009Co-Authors: C Thanassoulas, V Klentos, G Verveniotis, N ZymarisAbstract:The "Strange Attractor like" precursor, calculated from the Earth's oscillating electric field registered at PYR and HIO monitoring sites located in Greece, is studied in the domain of T = 14 days. It is assumed that the generating precursory signals focal mechanism is triggered by the corresponding M1 (moon declination) tidal wave. The obtained results from the analysis of eight (8) cases of large (Ms>6.0R) EQs that occurred from March 18th, 2006 to November 17th, 2008 suggest the validity of the method. Moreover, it is found that the specific methodology applied for T = 14 days behaves very closely to the same one when applied for T = 1 day even though there is a resolution decrease in the calculated predictive time window for the occurrence of the oncoming large EQ. It is speculated that this type of precursor, once it is present in one distinct oscillating component of the seismic precursory generated electric field, then, most probably, it is present in most of its other oscillating components. The latter suggests the investigation of the preseismic precursory electric field at its longer wavelengths i.e. components triggered by the Ssa (6 months, moon declination) oscillating components. The large value of the obtained success rate (predicted EQs / total no. of large EQs) suggests its use as a time prediction tool in the domain of the "short-term prediction".
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preseismic electric field Strange Attractor like precursor analysis applied on large ms 5 5r eqs which occurred in greece during december 1st 2007 april 30th 2008
arXiv: Geophysics, 2008Co-Authors: C Thanassoulas, V Klentos, G Verveniotis, N ZymarisAbstract:In order to investigate the capability of the preseismic electric field "Strange Attractor like" precursor as a time predictor of a large EQ within a short time window (short-term prediction), the specific methodology was applied on the Earth's electric field recorded during a rather long seismically active period (December 1st, 2007 - April 30th, 2008) of Greece. During this period of time a number (8) of large (Ms > 5.5R) earthquakes took place. The particular analysis is presented in detail for the following EQs: the Monemvasia EQ (January 6th 2008, Ms = 6.6R), the Methoni EQs (February 14th 2008 Ms = 6.7R, February 19th 2008 Ms = 5.6R, February 20th 2008 Ms = 6.5R, February 26th 2008 Ms = 5.7R), the Skyros EQ (March 19th 2008 Ms = 5.5R) and the Mid Southern Creta EQ (March 28th 2008 Ms = 5.6R). The obtained results from the analysis of the afore mentioned EQs, in conjunction to the ones obtained from an earlier presentation of the particular methodology (Thanassoulas et al. 2008a), suggest: an average time of initiation of the preseismic precursor of the order of (9) days before the EQ occurrence, a precursor average duration of the order of (7) days, while the elapsed time between the end of the precursor till the EQ occurrence time is, at average, only (2) days. These results suggest an objective and easy to apply method for the short-term EQ prediction, based on the registration of the Earth's electric field on ground surface.
Nail Akhmediev - One of the best experts on this subject based on the ideXlab platform.
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soliton as Strange Attractor nonlinear synchronization and chaos
Physical Review Letters, 2005Co-Authors: Jose M Sotocrespo, Nail AkhmedievAbstract:We show that dissipative solitons can have dynamics similar to that of a Strange Attractor in lowdimensional systems. Using a model of a passively mode-locked fiber laser as an example, we show that soliton pulsations with periods equal to several round-trips of the cavity can be chaotic, even though they are synchronized with the round-trip time. The chaotic part of this motion is quantified using a twodimensional map and estimating the Lyapunov exponent. We found a specific route to chaotic motion that occurs through the creation, increase, and overlap of ‘‘islands’’ of chaos rather than through multiplication of frequencies.
Mary A Selvam - One of the best experts on this subject based on the ideXlab platform.
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universal quantification for deterministic chaos in dynamical systems
arXiv: General Physics, 2000Co-Authors: Mary A SelvamAbstract:A cell dynamical system model for deterministic chaos enables precise quantification of the round-off error growth,i.e., deterministic chaos in digital computer realizations of mathematical models of continuum dynamical systems. The model predicts the following: (a) The phase space trajectory (Strange Attractor) when resolved as a function of the computer accuracy has intrinsic logarithmic spiral curvature with the quasiperiodic Penrose tiling pattern for the internal structure. (b) The universal constant for deterministic chaos is identified as the steady-state fractional round-off error k for each computational step and is equal to 1 /sqr(tau) (=0.382) where tau is the golden mean. (c) The Feigenbaum's universal constants a and d are functions of k and, further, the expression 2(a**2) = (pie)*d quantifies the steady-state ordered emergence of the fractal geometry of the Strange Attractor. (d) The power spectra of chaotic dynamical systems follow the universal and unique inverse power law form of the statistical normal distribution.
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universal quantification for deterministic chaos in dynamical systems
Applied Mathematical Modelling, 1993Co-Authors: Mary A SelvamAbstract:Abstract A cell dynamical system model for deterministic chaos enables precise quantification of the round-off error growth, i.e., deterministic chaos in digital computer realizations of mathematical models of continuum dynamical systems. The model predicts the following: (a) The phase space trajectory (Strange Attractor) when resolved as a function of the computer accuracy has intrinsic logarithmic spiral curvature with the quasiperiodic Penrose tiling pattern for the internal structure. (b) The universal constant for deterministic chaos is identified as the steady-state fractional round-off error k for each computational step and is equal to 1/τ2 ( = 0.382) where τ is the golden mean. k being less than half accounts for the fractal (broken) Euclidean geometry of the Strange Attractor. (c) The Feigenbaum's universal constantsa and d are functions of k and, further, the expression 2a2 = πd quantifies the steady-state ordered emergence of the fractal geometry of the Strange Attractor. (d) The power spectra of chaotic dynamical systems follow the universal and unique inverse power law form of the statistical normal distribution. The model prediction of (d) is verified for the Lorenz Attractor and for the computable chaotic orbits of Bernoulli shifts, pseudorandom number generators, and cat maps.
Charles H J Godfray - One of the best experts on this subject based on the ideXlab platform.
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chaos in ecology is mother nature a Strange Attractor
Annual Review of Ecology Evolution and Systematics, 1993Co-Authors: Alan Hastings, Carole L Hom, Stephen P Ellner, Peter Turchin, Charles H J GodfrayAbstract:We review the role of chaos and the study of chaos in ecology. We use sensitive dependence on initial conditions as the best heuristic definition of chaos. This definition forms the common theme for our review of approaches for demonstrating the importance of chaos in ecology. We emphasize that this
