Topological Entropy in the Synchronization of Piecewise Linear and Monotone Maps: Coupled Duffing Oscillators

Caneco, Acilina; Rocha, J. Leonel; Grácio, Clara

doi:10.1142/s0218127409025183

Cited by 12 publications

(8 citation statements)

References 23 publications

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“…In a previous work we have found in the parameter plane ) , (   regions U and B where the first return Poincaré map behaves like a unimodal map and like a bimodal map respectively, see [4]. We computed the kneading sequences, the kneading determinant and the topological entropy for some values of the parameters ) , (   , see [2] and [4]. The synchronization will occur when y x  .…”

Section: Duffing Applicationmentioning

confidence: 99%

Symbolic dynamics and chaotic synchronization

2011

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Chaotic communications schemes based on synchronization aim to provide security over the conventional communication schemes. Symbolic dynamics based on synchronization methods has provided high quality synchronization [5]. Symbolic dynamics is a rigorous way to investigate chaotic behavior with finite precision and can be used combined with information theory [13]. In previous works we have studied the kneading theory analysis of the Duffing equation [3] and the symbolic dynamics and chaotic synchronization in coupled Duffing oscillators [2] and [4]. In this work we consider the complete synchronization of two identical coupled unimodal and bimodal maps. We relate the synchronization with the symbolic dynamics, namely, defining a distance between the kneading sequences generated by the map iterates in its critical points and defining n-symbolic synchronization. We establish the synchronization in terms of the topological entropy of two unidirectional or bidirectional coupled piecewise linear unimodal and bimodal maps. We also give numerical simulations with coupled Duffing oscillators that exhibit numerical evidence of the n-symbolic synchronization.

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Section: Duffing Applicationmentioning

confidence: 99%

Symbolic dynamics and chaotic synchronization

2011

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“…In particular, period-doubling bifurcations, which generally happen in Arnold's tongues for strong amplitude of the driving signal, are noteworthy because in the limit of their sequence a chaotic behavior occurs. The structure of the bifurcation diagrams, the possible synchronization regimes, and the connection between desynchronization and chaos are reported elsewhere, together with the study of chaos in terms of the topological entropy [13][14][15][16][17].…”

Section:  mentioning

confidence: 99%

“…These systems are well modeled by the van der Pol equation and exhibit a variety of dynamical phenomena observed in forced oscillators of van der Pol type [13][14][15]. In particular, mode locking and periodic pulling, bifurcations between quasi-periodic and frequency entrained states have been observed, as well as perioddoubling bifurcations as a route to deterministic chaos [12], for which the study of chaotic dynamics and the derivation of lower bounds on their topological entropy is yet an attractive problem [13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Evaluating the Spectrum of Unlocked Injection Frequency Dividers in Pulling Mode

Buonomo¹,

Schiavo²

2013

Entropy

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Abstract:We study the phenomenon of periodic pulling which occurs in certain integrated microcircuits of relevant interest in applications, namely the injection-locked frequency dividers (ILFDs). They are modelled as second-order driven oscillators working in the subharmonic (secondary) resonance regime, i.e., when the self-oscillating frequency is close (resonant) to an integer submultiple n of the driving frequency. Under the assumption of weak injection, we find the spectrum of the system's oscillatory response in the unlocked mode through closed-form expressions, showing that such spectrum is double-sided and asymmetric, unlike the single-sided spectrum of systems with primary resonance (n1). An analytical expression for the amplitude modulation of the oscillatory response is also presented. Numerical results are presented to support theoretical relations derived.

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“…e application of entropy measures is useful in many branches of science and disciplines. Several examples from different areas where different entropy concepts were used, e.g., topological entropy, Kolmogorov-Sinai entropy, topological order, can be found in the following references proposed by Caneco et al [10], Rocha and Aleixo [11], and Rocha and Carvalho [12].…”

Section: Introductionmentioning

confidence: 99%

Characterizations and Entropy Measures of the Exponentiated Generalized Frechet Geometric Distribution

Saud

Rafique

Ijaz

et al. 2022

Advances in Mathematical Physics

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Some characterizations and entropy measures of the Exponentiated Generalized Fréchet Geometric (EGFG) distribution are studied in this paper. Firstly, characterizations of the EGFG distribution based on five different approaches are discussed. The submodels for the EGFG distribution with their characterization expressions formed on the ratio of two truncated moments are also presented. Secondly, four different entropy measures are considered and expressed analytically via the incomplete gamma function. The behavior of all these entropy measures is discussed by performing a numerical study.

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Topological Entropy in the Synchronization of Piecewise Linear and Monotone Maps: Coupled Duffing Oscillators

Cited by 12 publications

References 23 publications

Symbolic dynamics and chaotic synchronization

Symbolic dynamics and chaotic synchronization

Evaluating the Spectrum of Unlocked Injection Frequency Dividers in Pulling Mode

Characterizations and Entropy Measures of the Exponentiated Generalized Frechet Geometric Distribution

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