scholarly journals Numerical study of complex dynamics and extreme events within noise-like pulses from an erbium figure-eight laser

2019 ◽  
Vol 27 (26) ◽  
pp. 37196 ◽  
Author(s):  
J. P. Lauterio-Cruz ◽  
H. E. Ibarra-Villalon ◽  
O. Pottiez ◽  
Y. E. Bracamontes-Rodriguez ◽  
O. S. Torres-Muñoz ◽  
...  
Keyword(s):  
Extreme Events ◽  
Complex Dynamics ◽  
Numerical Study

Causality and information transfer in systems with extreme events

2020 ◽  
Author(s):  
Milan Palus
Keyword(s):  
Information Theory ◽  
Extreme Events ◽  
Information Transfer ◽  
Complex Dynamics ◽  
Probability Distributions ◽  
Mathematical Formulation ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Theoretic Approach ◽  
Heavy Tailed

<p>The mathematical formulation of causality in measurable terms of predictability was given by the father of cybernetics N. Wiener [1] and formulated for time series by C.W.J. Granger [2]. The Granger causality is based on the evaluation of predictability in bivariate autoregressive models. This concept has been generalized for nonlinear systems using methods rooted in information theory [3,4]. The information-theoretic approach, defining causality as information transfer, has been successful in many applications and generalized to multivariate data and causal networks [e.g., 5]. This approach, rooted in the information theory of Shannon, usually ignores two important properties of complex systems, such as the Earth climate: the systems evolve on multiple time scales and their variables have heavy-tailed probability distributions. While the multiscale character of complex dynamics, such as air temperature variability, can be studied within the Shannonian framework [6, 7], the entropy concepts of Rényi and Tsallis have been proposed to cope with variables with heavy-tailed probability distributions. We will discuss how such non-Shannonian entropy concepts can be applied in inference of causality in systems with heavy-tailed probability distributions and extreme events, using examples from the climate system.</p><p>This study was supported by the Czech Science Foundation, project GA19-16066S.</p><p> </p><p> [1] N. Wiener, in: E. F. Beckenbach (Editor), Modern Mathematics for Engineers (McGraw-Hill, New York, 1956)</p><p>[2] C.W.J. Granger, Econometrica 37 (1969) 424</p><p>[3] K. Hlaváčková-Schindler et al., Phys. Rep. 441 (2007)  1</p><p>[4] M. Paluš, M. Vejmelka, Phys. Rev. E 75 (2007) 056211</p><p>[5] J. Runge et al., Nature Communications 6 (2015) 8502</p><p>[6] M. Paluš, Phys. Rev. Lett. 112 (2014) 078702</p><p> [7] N. Jajcay, J. Hlinka, S. Kravtsov, A. A. Tsonis, M. Paluš, Geophys. Res. Lett. 43(2) (2016) 902–909</p>

Bifurcation Behavior of a Supercavitating Vehicle

2006 ◽  
Author(s):  
Guojian Lin ◽  
Balakumar Balachandran ◽  
Eyad H. Abed
Keyword(s):  
Complex Dynamics ◽  
Numerical Study ◽  
Period Doubling ◽  
Linear Feedback ◽  
Hopf Bifurcations ◽  
Linear Feedback Control ◽  
Chaotic Motions ◽  
Supercavitating Vehicle ◽  
Bifurcation Behavior ◽  
Period Doubling Bifurcations

In this effort, a numerical study of the bifurcation behavior of a supercavitating vehicle is conducted. The nonsmoothness of this system is due to the planing force acting on the vehicle. With a focus on dive-plane dynamics, bifurcations with respect to a quasi-static variation of the cavitation number are studied. The system is found to exhibit rich and complex dynamics including nonsmooth bifurcations such as the grazing bifurcation and smooth bifurcations such as Hopf bifurcations, cyclic-fold bifurcations, and period-doubling bifurcations, chaotic attractors, transient chaotic motions, and crises. The tailslap phenomenon of the supercavitating vehicle is identified as a consequence of the Hopf bifurcation followed by a grazing event. It is shown that the occurrence of these bifurcations can be delayed or triggered earlier by using dynamic linear feedback control aided by washout filters.

Numerical study of extreme events in a laser diode with phase-conjugate optical feedback

2015 ◽  
Vol 91 (4) ◽  
Author(s):  
Émeric Mercier ◽  
Armelle Even ◽  
Elodie Mirisola ◽  
Delphine Wolfersberger ◽  
Marc Sciamanna
Keyword(s):  
Laser Diode ◽  
Extreme Events ◽  
Optical Feedback ◽  
Numerical Study ◽  
Phase Conjugate

scholarly journals BIFURCATION AND CHAOS IN A COMPLEX MODEL OF DISSIPATIVE MEDIUM

2004 ◽  
Vol 14 (10) ◽  
pp. 3409-3447 ◽  
Author(s):  
MARIUS-F. DANCA ◽  
GUANRONG CHEN
Keyword(s):  
Numerical Methods ◽  
Numerical Method ◽  
Complex Dynamics ◽  
Numerical Study ◽  
Complex Model ◽  
Dissipative Medium ◽  
Bifurcation And Chaos ◽  
New Findings

In this paper, we carefully reexamine the chaotic RF model, first studied by Rabinovich and Fabrikant [1979], and have found many new and rich complex dynamics of the model that were mostly not reported before. The chaotic RF model has proved to be a great challenge to classical numerical methods, in the sense that most classical numerical methods have not been very successful in the study of complex dynamics of this special RF model. Therefore, in this paper, we present and apply a special numerical method, the Local Iterative Linearization (LIL) method, along with a special Turbo Pascal code based on this accurate LIL algorithm, for a careful numerical study of this complex RF model. Many interesting new findings are summarized and reported in this paper.

scholarly journals Alternation of Defects and Phase Turbulence Induces Extreme Events in an Extended Microcavity Laser

Entropy ◽  
2018 ◽  
Vol 20 (10) ◽  
pp. 789 ◽  
Author(s):  
Sylvain Barbay ◽  
Saliya Coulibaly ◽  
Marcel Clerc
Keyword(s):  
Extreme Events ◽  
Complex Dynamics ◽  
Dynamical Behavior ◽  
High Amplitude ◽  
Equation Model ◽  
Spatiotemporal Chaos ◽  
Ginzburg Landau ◽  
Microcavity Laser ◽  
Secondary Bifurcation ◽  
Secondary Instabilities

Out-of-equilibrium systems exhibit complex spatiotemporal behaviors when they present a secondary bifurcation to an oscillatory instability. Here, we investigate the complex dynamics shown by a pulsing regime in an extended, one-dimensional semiconductor microcavity laser whose cavity is composed by integrated gain and saturable absorber media. This system is known to give rise experimentally and theoretically to extreme events characterized by rare and high amplitude optical pulses following the onset of spatiotemporal chaos. Based on a theoretical model, we reveal a dynamical behavior characterized by the chaotic alternation of phase and amplitude turbulence. The highest amplitude pulses, i.e., the extreme events, are observed in the phase turbulence zones. This chaotic alternation behavior between different turbulent regimes is at contrast to what is usually observed in a generic amplitude equation model such as the Ginzburg–Landau model. Hence, these regimes provide some insight into the poorly known properties of the complex spatiotemporal dynamics exhibited by secondary instabilities of an Andronov–Hopf bifurcation.

Modeling Social and Geopolitical Disasters as Extreme Events: A Case Study Considering the Complex Dynamics of International Armed Conflicts

2019 ◽  
pp. 233-254
Author(s):  
Reinaldo Roberto Rosa ◽  
Joshi Neelakshi ◽  
Gabriel Augusto L. L. Pinheiro ◽  
Paulo Henrique Barchi ◽  
Elcio Hideiti Shiguemori
Keyword(s):  
Extreme Events ◽  
Complex Dynamics ◽  
Armed Conflicts

Stability of Quantum Computing in the Presence of Imperfections

2003 ◽  
Vol 17 (22n24) ◽  
pp. 3932-3946 ◽  
Author(s):  
G. Benenti ◽  
G. Casati ◽  
S. Montangero
Keyword(s):  
Quantum Chaos ◽  
Complex Dynamics ◽  
Quantum Computer ◽  
Numerical Study ◽  
Random Noise ◽  
Quantum Algorithm ◽  
Computer Hardware ◽  
Space Structures ◽  
Occupation Numbers ◽  
Dirac Distribution

We model an isolated quantum computer as a two-dimensional lattice of qubits (spin halves) with fluctuations in individual qubit energies and residual short-range inter-qubit couplings. We show that above a critical inter-qubit coupling strength, quantum chaos sets in and this results in the interaction induced dynamical thermalization and occupation numbers well described by the Fermi–Dirac distribution. This thermalization destroys the noninteracting qubit structure and sets serious requirements for the quantum computer operability. We then construct a quantum algorithm which uses qubits in an optimal way and efficiently simulates a physical model with rich and complex dynamics. The numerical study of the effect of static imperfections in the quantum computer hardware shows that the main elements of the phase space structures are accurately reproduced up to a time scale which is polynomial in the number of qubits. The errors generated by these imperfections are more significant than the errors of random noise in gate operations.

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