Robust communication via synchronization between nonchaotic strange attractors

Zhou, Changsong; Tian-Lun, Chen

doi:10.1209/epl/i1997-00235-7

Cited by 48 publications

(26 citation statements)

References 15 publications

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“…Like regular attractors, their dynamics is nonchaotic; like typical chaotic attractors, they exhibit fractal phase space structure. Furthermore, SNAs are related to Anderson localization in the Schrödinger equation with a spatially quasiperiodic potential [18], and they may have a practical application in secure communication [19]. Therefore, dynamical transitions in quasiperiodically forced systems have become a topic of considerable current interest.…”

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confidence: 99%

Mechanism for the intermittent route to strange nonchaotic attractors

2003

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Intermittent strange nonchaotic attractors (SNAs) appear typically in quasiperiodically forced period-doubling systems. As a representative model, we consider the quasiperiodically forced logistic map and investigate the mechanism for the intermittent route to SNAs using rational approximations to the quasiperiodic forcing. It is thus found that a smooth torus is transformed into an intermittent SNA via a phase-dependent saddle-node bifurcation when it collides with a new type of "ring-shaped" unstable set. Besides this intermittent transition, other transitions such as the interior, boundary, and band-merging crises may also occur through collision with the ring-shaped unstable sets. Hence the ring-shaped unstable sets play a central role for such dynamical transitions. Furthermore, these kinds of dynamical transitions seem to be "universal," in the sense that they occur typically in a large class of quasiperiodically forced period-doubling systems. Recently much attention has been paid to the study of quasiperiodically forced systems because of the generic appearance of strange nonchaotic attractors (SNAs) [1]. SNAs were first described by Grebogi et al. [2] and since then have been extensively investigated both numerically [3,4,5,6,7,8,9,10,11,12,13,14,15,16] and experimentally [17]. SNAs exhibit some properties of regular as well as chaoic attractors. Like regular attractors, their dynamics is nonchaotic; like typical chaotic attractors, they exhibit fractal phase space structure. Furthermore, SNAs are related to Anderson localization in the Schrödinger equation with a spatially quasiperiodic potential [18], and they may have a practical application in secure communication [19]. Therefore, dynamical transitions in quasiperiodically forced systems have become a topic of considerable current interest. However, their mechanisms are still much less understood than those in unforced or periodically forced systems.Here we are interested in the dynamical transition to SNAs accompanied by intermittent behavior, as reported in [12]. As a parameter passes a threshold value, a smooth torus is abruptly transformed into an intermittent SNA. Near the transition point, the intermittent dynamics on the SNA was characterized in terms of the average interburst time and the Lyapunov exponent. This route to an intermittent SNA is quite general and has been observed in a number of quasiperiodically forced period-doubling maps and flows (e.g., see [13,14]). It has been suggested [15] that the observed intermittent behavior results through interaction with an unstable orbit. However, in the previous work, such an unstable orbit was not located, and thus the bifurcation mechanism for the intermittent transition still remains unclear.In this paper, we study the underlying mechanism of the intermittency in the quasiperiodically forced logistic map M [5] which is a representative model for the quasiperiodically forced period-doubling systems:M :where x ∈ [0, 1], θ ∈ S 1 , a is the nonlinearity parameter of the logistic map, and ω and ...

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confidence: 99%

Mechanism for the intermittent route to strange nonchaotic attractors

2003

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“…Also, these exotic attractors were confirmed by an experiment consisting of a quasiperiodically forced, buckled, magnetoelastic ribbon [23], in analog simulations of a multistable potential [24], and in a neon glow discharge experiment [25]. The SNAs are also related to the Anderson localization in the Schrödinger equation with a quasiperiodic potential [26,27] and they may have a practical application in secure communication [28,29,30].…”

Section: Introductionmentioning

confidence: 63%

Experimental realization of strange nonchaotic attractors in a quasiperiodically forced electronic circuit

Thamilmaran

Senthilkumar

Venkatesan³

et al. 2006

Phys. Rev. E

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We have identified the three prominent routes, namely Heagy-Hammel, fractalization and intermittency routes, and their mechanisms for the birth of strange nonchaotic attractors (SNAs) in a quasiperiodically forced electronic system constructed using a negative conductance series LCR circuit with a diode both numerically and experimentally. The birth of SNAs by these three routes is verified from both experimental and their corresponding numerical data by maximal Lyapunov exponents, and their variance, Poincaré maps, Fourier amplitude spectrum, spectral distribution function and finite-time Lyapunov exponents. Although these three routes have been identified numerically in different dynamical systems, the experimental observation of all these mechanisms is reported for the first time to our knowledge and that too in a single second order electronic circuit.

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“…But dynamically, they do not show sensitive dependence on initial conditions as seen from negative Lyapunov exponents, that is, they are strange but nonchaotic. Following the pioneering work of Grebogi et al [4], SNAs have been extensively investigated numerically in dynamical systems, such as biological oscillators [5], driven Duffing type oscillators [6][7][8][9] and in certain maps, namely driven velocity-dependent systems [10], two dimensional maps [11], quasiperiodically forced logistic map [12][13][14], one dimensional cubic map [15][16][17], Harper map [18], map representing driven damped superconducting quantum interference device [19][20][21] and SNAs in HH-neural oscillator [22], in neon glow discharge experiment [23] and in quasiperiodically forced, buckled, magnetoelastic ribbon [24]. In some physically relevant situations, the existence of SNAs have also been demonstrated experimentally such as in electronic circuits [25][26][27], Different routes to SNAs and different scenarios for the formation of SNAs along with their distinct signatures/mechanisms have been summarized in references [27,10].…”

Section: Introductionmentioning

confidence: 99%