Complexity and synchronization in chaotic fiber-optic systems

Chlouverakis, K.E.; Argyris, Apostolos; Bogris, Adonis; Syvridis, Dimitris

doi:10.1016/j.physd.2007.09.023

Cited by 13 publications

(8 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A numerical test with the Lorenz model [14] confirmed that the third direction of the V frame is not only always nearly orthogonal to the flow [20], but also always nearly parallel to the third direction of the W frame, with deviations of the order of the deviations within the V frame. How fast does an arbitrarily chosen frame approach the locally unique frame directions, described by a transient time τtransient?…”

Section: The Rateitschak and Klages (Rk) Constraint Frame Wmentioning

confidence: 88%

See 1 more Smart Citation

Symmetric Jacobian for local Lyapunov exponents and Lyapunov stability analysis revisited

Waldner

Klages

2012

Chaos, Solitons & Fractals

View full text Add to dashboard Cite

The stability analysis introduced by Lyapunov and extended by Oseledec is an excellent tool to describe the character of nonlinear n-dimensional flows by n global exponents if these flows are stable in time. However, there are two main shortcomings: (a) The local exponents fail to indicate the origin of instability where trajectories start to diverge. Instead, their time evolution contains a much stronger chaos than the trajectories, which is only eliminated by integrating over a long time. Therefore, shorter time intervals cannot be characterized correctly, which would be essential to analyse changes of chaotic character as in transients. (b) Moreover, although Oseledec uses an n dimensional sphere around a point x to be transformed into an n dimensional ellipse in first order, this local ellipse has yet not been evaluated. The aim of this contribution is to eliminate these two shortcomings. Problem (a) disappears if the Oseledec method is replaced by a frame with a 'constraint' as performed by Rateitschak and Klages (RK) [Phys. Rev. E 65 036209 (2002)]. The reasons why this method is better will be illustrated by comparing different systems. In order to analyze shorter time intervals, integrals between consecutive Poincaré points will be evaluated. The local problems (b) will be solved analytically by introducing the symmetric 'Jacobian deformation ellipsoid' and its orthogonal submatrix, which enable to search in the full phase space for extreme local separation exponents. These are close to the RK exponents but need no time integration of the RK frame. Finally, four sets of local exponents are compared: Oseledec frame, RK frame, Jacobian deformation ellipsoid and its orthogonal submatrix.

show abstract

Section: The Rateitschak and Klages (Rk) Constraint Frame Wmentioning

confidence: 88%

“…Hence, it seems worthwhile to quantitatively compare both methods. There are ways to test the complexity of their local exponents, see Chlouverakis et al [20]. However, the local exponents themselves are merely tools to analyse the chaos of a given nonlinear dynamics.…”

Section: Purpose Of the Methodsmentioning

confidence: 99%

Symmetric Jacobian for local Lyapunov exponents and Lyapunov stability analysis revisited

Waldner

Klages

2012

Chaos, Solitons & Fractals

View full text Add to dashboard Cite

show abstract

“…We first present the results for H S for different embedding dimensions (4 ≤ D ≤ 7) with a τ e value that typically allows for a proper reconstruction of the chaotic attractor. This optimal reconstruction lag, denoted hereafter as τ rec e , is estimated from the autocorrelation function at the next point where it drops to 1−e −1 ≈ 0.63 of its initial value [36], [37]. Estimated values for τ rec e as a function of the injected current and feedback strength are detailed in Table II.…”

Section: A Permutation Entropy Approachmentioning

confidence: 99%

Characterizing the Hyperchaotic Dynamics of a Semiconductor Laser Subject to Optical Feedback Via Permutation Entropy

Zunino

Rosso

Soriano

2011

IEEE J. Select. Topics Quantum Electron.

View full text Add to dashboard Cite

The time evolution of the output of a semiconductor laser subject to delayed optical feedback can exhibit highdimensional chaotic fluctuations. In this contribution, our aim is to quantify the degree of unpredictability of this hyperchaotic time evolution. To that end, we estimate permutation entropy, a novel information-theory-derived quantifier particularly robust in a noisy environment. The permutation entropy is defined as a functional of a symbolic probability distribution, evaluated using the Bandt-Pompe recipe to assign a probability distribution function to the time series generated by the chaotic system. This measure quantifies the diversity of orderings present in the associated time series. In order to evaluate the performance of this novel quantifier, we compare with the results obtained by using a more standard chaos quantifier, namely the Kolmogorov-Sinai entropy. Here, we present numerical results showing that the permutation entropy, evaluated at specific timescales involved in the chaotic regime of the semiconductor laser subject to optical feedback, give valuable information about the degree of unpredictability of the chaotic laser dynamics. The influence of additive observational noise on the proposed tool is also investigated.

show abstract

“…For a detailed description of this method, see [21,23,[25][26][27]. For the zero-biased GAS (subsection b) chaos data analysis is performed in Fig.…”

mentioning

confidence: 99%

“…The filter is not able to destroy or create information by itself but is able to provide the correct geometrical morphology of the attractor by mitigating the spuriously increased dimension aright. For periodic cases and stable solutions, but also for chaotic cases that are amply contaminated with noise of comparable amplitude [27], K 2 is affected since noise mimics a chaotic attractor that actually is a noisy one (K 2 and D 2 ! 1) but with limited bandwidth (therefore K 2 and D 2 have finite spurious values).…”

mentioning

confidence: 99%

Photonic Integrated Device for Chaos Applications in Communications

et al. 2008

Self Cite

View full text Add to dashboard Cite

A novel photonic monolithic integrated device consisting of a distributed feedback laser, a passive resonator, and active elements that control the optical feedback properties has been designed, fabricated, and evaluated as a compact potential chaotic emitter in optical communications. Under diverse operating parameters, the device behaves in different modes providing stable solutions, periodic states, and broadband chaotic dynamics. Chaos data analysis is performed in order to quantify the complexity and chaoticity of the experimental reconstructed attractors by applying nonlinear noise filtering.

show abstract

Complexity and synchronization in chaotic fiber-optic systems

Cited by 13 publications

References 23 publications

Symmetric Jacobian for local Lyapunov exponents and Lyapunov stability analysis revisited

Symmetric Jacobian for local Lyapunov exponents and Lyapunov stability analysis revisited

Characterizing the Hyperchaotic Dynamics of a Semiconductor Laser Subject to Optical Feedback Via Permutation Entropy

Photonic Integrated Device for Chaos Applications in Communications

Contact Info

Product

Resources

About