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Nonlinear Dynamics - In the present article, a combination of numerical and experimental studies is undertaken to comprehend the influence of noise on the responses of continuous-time dynamical... 相似文献
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This work concerns the nature of chaotic dynamical processes. Sheldon Newhouse wrote on dynamical processes (depending on a parameter )x
x+1=T(x
n
; ), wherex is in the plane, such as might arise when studying Poincaré return maps for autonomous differential equations in IR3. He proved that if the system is chaotic there will very often be existing parameter values for which there are infinitely many periodic attractors coexisting in a bounded region of the plane, and that such parameter values would be dense in some interval. The fact that infinitely many coexisting sinks can occur brings into question the very nature of the foundations of chaotic dynamical processes. We prove, for an apparently typical situation, that Newhouse's construction yields only a set of parameter values of measure zero.This research was supported in part by grants from the Air Force Office of Scientific Research AFOSR 81-0217, the Consiglio Nazionale delle Ricerche-Comitato per le Matematiche, and the National Science Foundation DMS 84-19110On leave from: Dipartimento di Matematica G. Castel nuovo Universita di Roma La Sapienza P. le Aldo Moro 5, I-00185 Rome, Italy 相似文献
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LoSecco JM Bionta RM Biewitt G Bratton CB Casper D Chrysicopoulou P Claus R Cortez BG Errede S Foster GW Gajewski W Ganezer KS Goldhaber M Haines TJ Jones TW Kielczewska D Kropp WR Learned JG Lehmann E Park HS Reines F Schultz J Seidel S Shumard E Sinclair D Sobel HW Stone JL Sulak L Svoboda R van der Velde JC Wuest C 《Physical review letters》1985,54(21):2299-2301
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The linear stability of pipe flow implies that only perturbations of sufficient strength will trigger the transition to turbulence. In order to determine this threshold in perturbation amplitude we study the edge of chaos which separates perturbations that decay towards the laminar profile and perturbations that trigger turbulence. Using the lifetime as an indicator and methods developed in Skufca et al., Phys. Rev. Lett. 96, 174101 (2006), we show that superimposed on an overall 1/Re scaling predicted and studied previously there are small, nonmonotonic variations reflecting folds in the edge of chaos. By tracing the motion in the edge we find that it is formed by the stable manifold of a unique flow field that is dominated by a pair of downstream vortices, asymmetrically placed towards the wall. The flow field that generates the edge of chaos shows intrinsic chaotic dynamics. 相似文献
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This paper deals with the problem “Can a noisy orbit be tracked by a real orbit?” In particular, we will study the one-parameter family of tent maps and the one-parameter family of quadratic maps. We writeg μ for eitherf μ orF μ withf μ (x)=μx forx≦1/2 andf μ (x)=μ(1?x) forx≧1/2, andF μ (x)=μx(1?x). For a given μ we will say:g μ permits increased parameter shadowing if for each δ x >0 there exists someδ μ >0 and some δ f >0 such that every δ f -pseudog μ -orbit starting in some invariant interval can be δ x -shadowed by a realg α -orbit with α=μ+δ μ . We show thatg μ typically permits increased parameter shadowing. 相似文献
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John?F?StinsEmail author G?Caroline?M?van Baal Tinca?JC?Polderman Frank?C?Verhulst Dorret?I?Boomsma 《BMC neuroscience》2004,5(1):49