The synchronization of chaotic systems

The goal of therapy for bradycardia or tachycardia is to rapidly identify and treat patients who are hemodynamically unstable or symptomatic due to the arrhythmia. Drugs or, when appropriate, pacing may be used to control unstable or symptomatic bradycardia. Cardioversion or drugs or both may be used to control unstable or symptomatic tachycardia. ACLS providers should closely monitor stable patients pending expert consultation and should be prepared to aggressively treat those with evidence of decompensation.

/pdf/part-8-adult-advanced-cardiovascular-life-support-2010-344vtppnij.pdf

Part 8: Adult Advanced Cardiovascular Life Support 2010 American Heart Association Guidelines for Cardiopulmonary Resuscitation and Emergency Cardiovascular Care

Wave propagation and group velocity

http://www.ens-lyon.fr/DI/wp-content/uploads/2009/07/LopesBetrouni.pdf

Fractal and multifractal analysis: a review.

We report degenerate four-wave mixing (DFWM) of visible radiation in borosilicate glasses doped with crystallites of the mixed semiconductor CdSxSe1−x. These semiconductor-doped glasses—available commercially in the form of colored glass filters—exhibit third-order nonlinearities of ~10−9–10−8 esu for DFWM with short (~10-nsec) laser pulses at various visible wavelengths. Our studies on the temporal decay of the transient gratings indicate that the nonlinearity is not thermal in origin but may be attributed to the generation of a short-lived electron–hole plasma. In contrast with DFWM experiments in other semiconductors invoking gratings of optically generated carriers (or other mobile particles), we report unique diffusion-independent decay of the gratings in these glasses; this is deduced from the dependence of the intensity and polarization of the DFWM signal on the polarization combinations of the input beams. Finally, we report detailed data on the aberration-correction properties of these isotropic glasses.

Degenerate four-wave mixing in semiconductor-doped glasses

For time series exhibiting strong periodicities, standard (linear) surrogate methods are not useful. We describe a new algorithm that can test against the null hypothesis of a periodic orbit with uncorrelated noise. We demonstrate the application of this method to artificial data and experimental time series, including human electrocardiogram recordings during sinus rhythm and ventricular tachycardia.

https://ira.lib.polyu.edu.hk/bitstream/10397/4856/1/Small_Surrogate_Pseudoperiodic_Time.pdf

Surrogate Test for Pseudoperiodic Time Series Data

1. Introduction.- 1.1 A Heuristic Approach to Instabilities.- 1.2 About This Book.- References.- I Instabilities and Chaos in Active Systems.- 2. Instabilities and Chaos in Single-Mode Homogeneous Line Lasers.- 2.1 Background.- 2.2 Transient Decay Toward a Stable State.- 2.3 Deterministic Chaos.- 2.3.1 Historical Aspects.- 2.3.2 Dynamical Aspects.- 2.3.3 Information Aspects.- 2.3.4 Role of Transients: The Hyperchaos.- 2.4 The Modulated Laser.- 2.5 The Laser with Injected Signal (LIS).- 2.6 Instabilities in a Laser with Feedback.- 2.7 The Bidirectional Ring Laser.- 2.8 Conclusion.- 2.A Appendix: A Simple-Minded Approach to Laser Equations.- 2.A.1 The Laser Equations.- 2.A.2 Adiabatic Elimination of Polarization - Modulation and Injection.- 2.A.3 Linear Stability Analysis of Class B Solutions.- 2.A.4 Laser with Injected Signal (LIS).- 2.A.5 The Bidirectional Class B Ring Laser.- References.- 3. Experimental Measurements of Transitions to Pulsations and Chaos in a Single Mode, Unidirectional Ring Laser with an Inhomogeneously-Broadened Medium.- 3.1 Background.- 3.2 The Single-Mode, Inhomogeneously-Broadened, Unidirectional Ring Laser.- 3.2.1 Background.- 3.2.2 Experimental Set-Up.- 3.2.3 Thresholds for Transitions from Stable to Pulsed Behavior.- 3.2.4 Changes in the Pulsation Pattern Above the Second Threshold.- 3.2.5 Confirming and Characterizing the Chaos.- 3.3 Discussion.- References.- 4. Single- and Multi-Mode Operation of a Laser with an Injected Signal.- 4.1 Background Information.- 4.2 Equations of Motion and the Steady-State Configuration.- 4.3 Linear Stability Analysis in the Mean-Field Limit.- 4.4 Adiabatic Elimination of the Atomic Variables.- 4.5 Dynamical Behavior of the Single-Mode Model.- 4.6 Power Spectra and Lyapunov Exponents.- 4.A Appendix: Derivation of (4.14).- 4.B Appendix: List of the Coefficients of (4.29).- 4.C Appendix: List of Coefficients in (4.31).- References.- 5. Experimental Observations of Single Mode Laser Instabilities in Optically Pumped Molecular Lasers.- 5.1 Background.- 5.2 Optically Pumped Far Infrared Lasers.- 5.2.1 Resonant Pumping.- 5.2.2 Detuned Pumping.- 5.2.3 Single-Mode Laser Instability in Near Resonantly Pumped Mid-Infrared Systems.- 5.3 Conclusion.- References.- 6. Quantum Treatment of Amplified Spontaneous Emission in High-Gain Free-Electron Lasers.- 6.1 Introduction.- 6.2 The Quantum Hamiltonian Model.- 6.3 Classical Limit and Classical Treatment of Amplified Spontaneous Emission.- 6.4 The Basic Equations of the Linear Quantum Regime.- 6.5 Analysis on Resonance and for Sufficiently Long Times.- 6.6 "Harmonic Oscillator" Limit.- 6.7 "Classical" Limit.- 6. A Appendix.- References.- Additional References with Titles.- II Instabilities and Chaos in Passive Systems.- 7. Global Bifurcations and Turbulence in a Passive Optical Resonator.- 7.1 Background Material.- 7.2 Model and Theory.- 7.3 Bifurcation and Global Phase Portraits.- 7.4 The Plane-Wave Map.- 7.4.1 The Newhouse Sink Phenomena.- 7.4.2 Boundary Crisis.- 7.5 Gaussian Beams (2D Problem).- 7.5.1 Stability of the Plane-Wave Map to Transverse Spatial Perturbations.- 7.5.2 Solitary Waves as Fixed Points of the Infinite Dimensional Map.- 7.5.3 Many Routes to Optical Turbulence.- 7.6 Gaussian Beams (3D Problem).- 7.7 Summary.- References.- 8. Experimental Verification of Regenerative Pulsations and Chaos.- 8.1 Regenerative Pulsations.- 8.2 Ikeda Instabilities.- 8.2.1 Experimental Setup.- 8.2.2 Review of Period Doubling.- 8.2.3 Universality.- 8.2.4 Nature of Transitions.- 8.2.5 Effects of Noise.- 8.2.6 Other Waveforms/Alternate Paths.- 8.2.7 Test for Chaos in High-Speed Optical Systems.- 8.3 Instabilities in Sodium Vapor.- 8.3.1 Optically Thick.- 8.3.2 Optically Thin.- 8.4 Issues for Fast Chaotic Systems.- References.- 9. Instabilities and Routes to Chaos in Passive All-Optical Resonators Containing Molecular Gases.- 9.1 Background.- 9.2 Theory of Instabilities in Passive Nonlinear Resonators.- 9.2.1 The Basic Model.- 9.2.2 Physical Interpretation of the Ikeda Instability.- 9.2.3 Fabry-Perot Resonators.- 9.2.4 Universality.- 9.2.5 Trapping Bifurcation Points.- 9.3 Nonlinear Absorption Characteristics of Molecules.- 9.3.1 Ammonia.- 9.3.2 Sulphur Hexafluoride.- 9.3.3 Molecular Energy-Level Scheme.- 9.4 Optical Bistability and Instability Generation in Optical Resonators.- 9.4.1 Ring Resonator.- 9.4.2 Fabry-Perot Resonator.- 9.4.3 Fabry-Perot Resonator with Sulphur Hexafluoride.- 9.5 Conclusion.- References.- 10. Transmission Properties of a Sodium-Filled Fabry-Perot Resonator.- 10.1 Background.- 10.2 Experimental Set-Up.- 10.3 Discussion.- 10.3.1 Optical Bistability by Zeeman Pumping.- 10.3.2 Optical Tristability.- 10.3.3 Multistability.- 10.3.4 Self-Pulsing.- References.

http://www.gbv.de/dms/ilmenau/toc/042069173.PDF

Instabilities and Chaos in Quantum Optics, II

The effect of temperature variation along a high-power fiber amplifier on the stimulated Brillouin scattering (SBS) threshold is considered theoretically. We show that for an end-pumped rare-earth-doped double-clad fiber the inhomogeneous distribution of temperature, which is caused by the absorption of pump radiation, may result in total suppression of SBS even for output powers well above 200 W.

Suppression of stimulated Brillouin scattering in high-power single-frequency fiber amplifiers.

We describe an efficient algorithm which computes the Gaussian kernel correlation integral from noisy time series; this is subsequently used to estimate the underlying correlation dimension and noise level in the noisy data. The algorithm first decomposes the integral core into two separate calculations, reducing computing time from ${O(N}^{2}\ifmmode\times\else\texttimes\fi{}{N}_{b})$ to ${O(N}^{2}{+N}_{b}^{2}).$ With other further improvements, this algorithm can speed up the calculation of the Gaussian kernel correlation integral by a factor of $\ensuremath{\gamma}\ensuremath{\sim}(2--{10)N}_{b}.$ We use typical examples to demonstrate the use of the improved Gaussian kernel algorithm.

Robert G. Harrison

Papers

Surrogate Test for Pseudoperiodic Time Series Data

Instabilities and Chaos in Quantum Optics, II

Suppression of stimulated Brillouin scattering in high-power single-frequency fiber amplifiers.

Efficient implementation of the gaussian kernel algorithm in estimating invariants and noise level from noisy time series data

Evidence of chaotic stimulated Brillouin scattering in optical fibers.