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1

Wiesenfeld, Kurt, and Indu Satija. "Noise tolerance of frequency-locked dynamics." Physical Review B 36, no. 5 (August 15, 1987): 2483–92. http://dx.doi.org/10.1103/physrevb.36.2483.

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2

Ponzo, Peter J., and Nelson Wax. "The dynamics of phase-locked loops." Journal of the Franklin Institute 328, no. 2-3 (January 1991): 179–88. http://dx.doi.org/10.1016/0016-0032(91)90028-2.

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3

Tsyrulnikova L.A. and Safin A.R. "Controllable neuromorphic dynamics of the phase locked loop." Technical Physics Letters 48, no. 14 (2022): 34. http://dx.doi.org/10.21883/tpl.2022.14.52060.18891.

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We consider the neuromorphic dynamics of a filter-free phase locked loop with a phase modulation of a reference oscillator. The transition from pulsed single-spike dynamics to the bursting dynamics can be easily controlled by changing the depth and frequency of phase modulation, as well as the gain factor along the ring of the phase locked loop. The possibility of implementing neuromorphic calculations of the "OR" type in the scheme of three phase locked loops mutually coupled through a common loop filter (control circuit) is shown. The presented results can be used in designing hardware-implementable neuromorphic networks with increased frequency stability, resistant to noise effects. Keywords: neuromorphic dynamics, phase locked loop, logical operations.
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4

Slepneva, S., B. Kelleher, B. O’Shaughnessy, S. P. Hegarty, A. G. Vladimirov, and G. Huyet. "Dynamics of Fourier domain mode-locked lasers." Optics Express 21, no. 16 (August 6, 2013): 19240. http://dx.doi.org/10.1364/oe.21.019240.

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5

Riès, Stéphanie, Niels Janssen, Borís Burle, and F. Xavier Alario. "Response-Locked Brain Dynamics of Word Production." PLoS ONE 8, no. 3 (March 12, 2013): e58197. http://dx.doi.org/10.1371/journal.pone.0058197.

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6

Wang, S. S., and H. G. Winful. "Dynamics of phase‐locked semiconductor laser arrays." Applied Physics Letters 52, no. 21 (May 23, 1988): 1774–76. http://dx.doi.org/10.1063/1.99622.

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7

Curran, Paul F., Chuang Bi, and Orla Feely. "Dynamics of charge-pump phase-locked loops." International Journal of Circuit Theory and Applications 41, no. 11 (April 19, 2012): 1109–35. http://dx.doi.org/10.1002/cta.1814.

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8

Matrosov, Valerij, and Dmitry Kasatkin. "Particularities of dynamics of three cascade-coupled phase-locked loops." Izvestiya VUZ. Applied Nonlinear Dynamics 12, no. 1-2 (June 20, 2004): 159–68. http://dx.doi.org/10.18500/0869-6632-2004-12-1-159-168.

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Results of investigations of dynamic modes of three phase-locked loops are presented. The influence of coupling parameters and initial frequency mismatch on synchronous and quasi-synchronous modes is studied. Domains of quasi-synchronous oscillations of controlled oscillators are allocated in the parameter space. The comparative analysis of dynamics of ensembles, consisting of two and three oscillators is carried out.
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9

Buonomo, Antonio, and Alessandro Lo Schiavo. "Nonlinear dynamics of divide-by-two injection-locked frequency dividers in locked operation mode." International Journal of Circuit Theory and Applications 42, no. 8 (January 11, 2013): 794–807. http://dx.doi.org/10.1002/cta.1888.

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10

Merlis, Timothy M., and Tapio Schneider. "Atmospheric Dynamics of Earth-Like Tidally Locked Aquaplanets." Journal of Advances in Modeling Earth Systems 2, no. 4 (April 2010): n/a. http://dx.doi.org/10.3894/james.2010.2.13.

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11

Zeng Heping, 曾和平, and 彭俊松 Peng Junsong. "Time-Varying Dynamics of Mode-Locked Fiber Lasers." Acta Optica Sinica 41, no. 1 (2021): 0114005. http://dx.doi.org/10.3788/aos202141.0114005.

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12

Wu, Hsiao-Hua, Chi-Rong Huang, and Jian-Tzung Huang. "Spatiotemporal dynamics of a passively mode-locked Nd:GdVO4laser." Optics Express 15, no. 5 (2007): 2391. http://dx.doi.org/10.1364/oe.15.002391.

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13

Helbing, F. W., G. Steinmeyer, U. Keller, R. S. Windeler, J. Stenger, and H. R. Telle. "Carrier-envelope offset dynamics of mode-locked lasers." Optics Letters 27, no. 3 (February 1, 2002): 194. http://dx.doi.org/10.1364/ol.27.000194.

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14

Bernstein, G. M., M. A. Liberman, and A. J. Lichtenberg. "Nonlinear dynamics of a digital phase locked loop." IEEE Transactions on Communications 37, no. 10 (1989): 1062–70. http://dx.doi.org/10.1109/26.41161.

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15

Teplinsky, A., O. Feely, and A. Rogers. "Phase-jitter dynamics of digital phase-locked loops." IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 46, no. 5 (May 1999): 545–58. http://dx.doi.org/10.1109/81.762920.

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16

Geddes, John B., Willie J. Firth, and Kelly Black. "Pulse Dynamics in an Actively Mode-Locked Laser." SIAM Journal on Applied Dynamical Systems 2, no. 4 (January 2003): 647–71. http://dx.doi.org/10.1137/s1111111102416599.

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17

Matrosov, Valery V., Mikhail A. Mishchenko, and Vladimir D. Shalfeev. "Neuron-like dynamics of a phase-locked loop." European Physical Journal Special Topics 222, no. 10 (October 2013): 2399–405. http://dx.doi.org/10.1140/epjst/e2013-02024-9.

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18

Gkortsas, V. M., C. Wang, L. Kuznetsova, L. Diehl, A. Gordon, C. Jirauschek, M. A. Belkin, A. Belyanin, F. Capasso, and F. X. Kärtner. "Dynamics of actively mode-locked Quantum Cascade Lasers." Optics Express 18, no. 13 (June 10, 2010): 13616. http://dx.doi.org/10.1364/oe.18.013616.

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19

Sørensen, M. P., K. A. Shore, T. Geisler, P. L. Christiansen, J. Mørk, and J. Mark. "Dynamics of additive-pulse mode-locked fibre lasers." Optics Communications 90, no. 1-3 (June 1992): 65–69. http://dx.doi.org/10.1016/0030-4018(92)90329-p.

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20

Shirokov, Yu V., and L. N. Kazakov. "Nonlinear dynamics of phase-locked discrete coupled systems." Radiophysics and Quantum Electronics 38, no. 3-4 (1996): 141–46. http://dx.doi.org/10.1007/bf01037887.

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21

Jones, D. J., L. M. Zhang, J. E. Carroll, and D. D. Marcenac. "Dynamics of monolithic passively mode-locked semiconductor lasers." IEEE Journal of Quantum Electronics 31, no. 6 (June 1995): 1051–58. http://dx.doi.org/10.1109/3.387042.

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22

Zhang, Zexin, Jinrong Tian, Youshuo Cui, Yunfeng Wu, and Yanrong Song. "Dynamics of multi-state in a simplified mode-locked Yb-doped fiber laser." Chinese Optics Letters 20, no. 8 (2022): 081402. http://dx.doi.org/10.3788/col202220.081402.

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23

Wang, Jiazhu, Liang Jin, Shangzhi Xie, Renyan Wang, He Zhang, Yingtian Xu, Xin Zhao, Yan Li, and Xiaohui Ma. "Vector dynamics of ultrafast cylindrical vector beams in a mode-locked fiber laser." Chinese Optics Letters 19, no. 11 (2021): 111903. http://dx.doi.org/10.3788/col202119.111903.

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24

Qu, Kun, Qiuluan Chen, Katarzyna A. Ciazynska, Banghui Liu, Xixi Zhang, Jingjing Wang, Yujie He, et al. "Engineered disulfide reveals structural dynamics of locked SARS-CoV-2 spike." PLOS Pathogens 18, no. 7 (July 29, 2022): e1010583. http://dx.doi.org/10.1371/journal.ppat.1010583.

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The spike (S) protein of SARS-CoV-2 has been observed in three distinct pre-fusion conformations: locked, closed and open. Of these, the function of the locked conformation remains poorly understood. Here we engineered a SARS-CoV-2 S protein construct “S-R/x3” to arrest SARS-CoV-2 spikes in the locked conformation by a disulfide bond. Using this construct we determined high-resolution structures confirming that the x3 disulfide bond has the ability to stabilize the otherwise transient locked conformations. Structural analyses reveal that wild-type SARS-CoV-2 spike can adopt two distinct locked-1 and locked-2 conformations. For the D614G spike, based on which all variants of concern were evolved, only the locked-2 conformation was observed. Analysis of the structures suggests that rigidified domain D in the locked conformations interacts with the hinge to domain C and thereby restrains RBD movement. Structural change in domain D correlates with spike conformational change. We propose that the locked-1 and locked-2 conformations of S are present in the acidic high-lipid cellular compartments during virus assembly and egress. In this model, release of the virion into the neutral pH extracellular space would favour transition to the closed or open conformations. The dynamics of this transition can be altered by mutations that modulate domain D structure, as is the case for the D614G mutation, leading to changes in viral fitness. The S-R/x3 construct provides a tool for the further structural and functional characterization of the locked conformations of S, as well as how sequence changes might alter S assembly and regulation of receptor binding domain dynamics.
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25

Archundia-Berra, Luis C., and Peter J. Delfyett. "External cavity multiwavelength semiconductor mode-locked lasers gain dynamics." Optics Express 14, no. 20 (2006): 9223. http://dx.doi.org/10.1364/oe.14.009223.

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26

Alemohammad, Milad, Yifei Li, and Peter Herczfeld. "Design and Dynamics of Multiloop Optical Frequency Locked Loop." Journal of Lightwave Technology 31, no. 22 (November 2013): 3453–59. http://dx.doi.org/10.1109/jlt.2013.2283470.

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27

VIEIRA, MARIA DE SOUSA, ALLAN J. LICHTENBERG, and MICHAEL A. LIEBERMAN. "NONLINEAR DYNAMICS OF DIGITAL PHASE-LOCKED LOOPS WITH DELAY." International Journal of Bifurcation and Chaos 04, no. 03 (June 1994): 715–26. http://dx.doi.org/10.1142/s0218127494000514.

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We investigate numerically and analytically the nonlinear dynamics of a system consisting of two self-synchronizing pulse-coupled nonlinear oscillators with delay. The particular system considered consists of connected digital phase-locked loops. We find mapping equations that govern the system and determine the synchronization properties. We study the bifurcation diagrams, which show regions of periodic, quasiperiodic and chaotic behavior, with unusual bifurcation diagrams, depending on the delay. We show that depending on the parameter that is varied, the delay will have a synchronizing or desynchronizing effect on the locked state. The stability of the system is studied by determining the Liapunov exponents, indicating marked differences compared to coupled systems without delay.
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28

Ablowitz, Mark J., Theodoros P. Horikis, Sean D. Nixon, and Yi Zhu. "Asymptotic Analysis of Pulse Dynamics in Mode-Locked Lasers." Studies in Applied Mathematics 122, no. 4 (May 2009): 411–25. http://dx.doi.org/10.1111/j.1467-9590.2009.00441.x.

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29

Bale, Brandon G., Khanh Kieu, J. Nathan Kutz, and Frank Wise. "Transition dynamics for multi-pulsing in mode-locked lasers." Optics Express 17, no. 25 (December 2, 2009): 23137. http://dx.doi.org/10.1364/oe.17.023137.

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30

Salerno, M., N. Gro/nbech-Jensen, and M. R. Samuelsen. "Relaxation towards phase-locked dynamics in long Josephson junctions." Physical Review B 51, no. 21 (June 1, 1995): 15613–16. http://dx.doi.org/10.1103/physrevb.51.15613.

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31

Ell, R., W. Seitz, U. Morgner, T. R. Schibli, and F. X. Kärtner. "Carrier-envelope phase dynamics of synchronized mode-locked lasers." Optics Communications 220, no. 1-3 (May 2003): 211–14. http://dx.doi.org/10.1016/s0030-4018(03)01362-2.

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32

New, G. H. C., and D. Wood. "Dynamics of Gain-switched and Mode-locked Semiconductor Lasers." Journal of Modern Optics 38, no. 4 (April 1991): 785–99. http://dx.doi.org/10.1080/09500349114550771.

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33

Forysiak, W., and J. V. Moloney. "Dynamics of synchronously pumped mode-locked color-center lasers." Physical Review A 45, no. 5 (March 1, 1992): 3275–88. http://dx.doi.org/10.1103/physreva.45.3275.

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34

Dellunde, J., M. C. Torrent, J. M. Sancho, and M. San Miguel. "Frequency dynamics of gain-switched injection-locked semiconductor lasers." IEEE Journal of Quantum Electronics 33, no. 9 (1997): 1537–42. http://dx.doi.org/10.1109/3.622634.

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35

Delfyett, P. J., A. Dienes, J. P. Heritage, M. Y. Hong, and Y. H. Chang. "Femtosecond hybrid mode-locked semiconductor laser and amplifier dynamics." Applied Physics B Laser and Optics 58, no. 3 (March 1994): 183–95. http://dx.doi.org/10.1007/bf01081311.

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36

Feng, Ni, Renlai Zhou, Sen Wang, Rui Zhang, and K. Nakkeeran. "Progressive pulse dynamics in a mode-locked fiber laser." Optics & Laser Technology 168 (January 2024): 109827. http://dx.doi.org/10.1016/j.optlastec.2023.109827.

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37

Zhang, Wei Tong, Zhi Qiang Li, and Wen Ming Zhu. "A Novel Frequency Locked Loop Based on Stochastic Resonance." Applied Mechanics and Materials 347-350 (August 2013): 1763–67. http://dx.doi.org/10.4028/www.scientific.net/amm.347-350.1763.

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Frequency locked loop (FLL) plays an important role in carrier synchronization because of its excellent dynamic performance. However, it performs inadequately in low signal-to-noise ratio (SNR). In this paper, the principle of stochastic resonance (SR) is briefly introduced and a SR processor is proposed. Based on traditional FLL, the SR processor is added before frequency discriminator in order to weaken the effect that thermal noise brings to FLL. The paper investigates the processing effect of SR. Simulation results show that the performance of improved FLL is greatly improved. It can tolerate rather high dynamics and tracking accuracy of frequency achieve 0.2Hz even with CNR as low as 25 dBHz, which verified the validity of above ideas.
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38

VASYLENKO, ANNA, and ORLA FEELY. "DYNAMICS OF PHASE-LOCKED LOOP WITH FM INPUT AND LOW MODULATING FREQUENCY." International Journal of Bifurcation and Chaos 12, no. 07 (July 2002): 1633–42. http://dx.doi.org/10.1142/s0218127402005376.

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Phase-locked loops are important engineering systems whose dynamics are incompletely understood. In this paper we investigate the dynamics of a first-order phase-locked loop with a frequency-modulated input signal of low modulating frequency. The system displays interesting bifurcations not observed at higher modulating frequencies and exhibits a range of behavior, including chaos, quasiperiodic motion and strange nonchaotic attractors.
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39

Rabajante, Jomar F., Jerrold M. Tubay, Hiromu Ito, Takashi Uehara, Satoshi Kakishima, Satoru Morita, Jin Yoshimura, and Dieter Ebert. "Host-parasite Red Queen dynamics with phase-locked rare genotypes." Science Advances 2, no. 3 (March 2016): e1501548. http://dx.doi.org/10.1126/sciadv.1501548.

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Interactions between hosts and parasites have been hypothesized to cause winnerless coevolution, called Red Queen dynamics. The canonical Red Queen dynamics assume that all interacting genotypes of hosts and parasites undergo cyclic changes in abundance through negative frequency-dependent selection, which means that any genotype could become frequent at some stage. However, this prediction cannot explain why many rare genotypes stay rare in natural host-parasite systems. To investigate this, we build a mathematical model involving multihost and multiparasite genotypes. In a deterministic and controlled environment, Red Queen dynamics occur between two genotypes undergoing cyclic dominance changes, whereas the rest of the genotypes remain subordinate for long periods of time in phase-locked synchronized dynamics with low amplitude. However, introduction of stochastic noise in the model might allow the subordinate cyclic host and parasite types to replace dominant cyclic types as new players in the Red Queen dynamics. The factors that influence such evolutionary switching are interhost competition, specificity of parasitism, and degree of stochastic noise. Our model can explain, for the first time, the persistence of rare, hardly cycling genotypes in populations (for example, marine microbial communities) undergoing host-parasite coevolution.
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40

LOURENÇO, CARLOS. "ATTENTION-LOCKED COMPUTATION WITH CHAOTIC NEURAL NETS." International Journal of Bifurcation and Chaos 14, no. 02 (February 2004): 737–60. http://dx.doi.org/10.1142/s0218127404009442.

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We review a neural network model based on chaotic dynamics [Babloyantz & Lourenço, 1994, 1996] and provide a detailed discussion of its biological and computational relevance. Chaos can be viewed as a "reservoir" containing an infinite number of unstable periodic orbits. In our approach, the periodic orbits are used as coding devices. By considering a large enough number of them, one can in principle expand the information processing capacity of small or moderate-size networks. The system is most of the time in an undetermined state characterized by a chaotic attractor. Depending on the type of an external stimulus, the dynamics is stabilized into one of the available periodic orbits, and the system is then ready to process information. This corresponds to the system being driven into an "attentive" state. We show that, apart from static pattern processing, the model is capable of dealing with moving stimuli. We especially consider in this paper the case of transient visual stimuli, which has a clear biological relevance. The advantages of chaos over more regular regimes are discussed.
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41

Boscolo, Sonia, Sergey V. Sergeyev, Chengbo Mou, Veronika Tsatourian, Sergei Turitsyn, Christophe Finot, Vitaly Mikhailov, Bryan Rabin, and Paul S. Westbrook. "Nonlinear pulse shaping and polarization dynamics in mode-locked fiber lasers." International Journal of Modern Physics B 28, no. 12 (April 7, 2014): 1442011. http://dx.doi.org/10.1142/s0217979214420119.

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We review our recent progress on the study of new nonlinear mechanisms of pulse shaping in passively mode-locked fiber lasers. These include a mode-locking regime featuring pulses with a triangular distribution of the intensity, and spectral compression arising from nonlinear pulse propagation. We also report on our recent experimental studies unveiling new types of vector solitons with processing states of polarization for multi-pulse and tightly bound-state soliton (soliton molecule) operations in a carbon nanotube (CNT) mode-locked fiber laser with anomalous dispersion cavity.
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42

VILIBIĆ, I., V. ČIKEŠ KEČ, B. ZORICA, J. ŠEPIĆ, S. MATIJEVIĆ, and T. DŽOIĆ. "Hydrographic conditions driving sardine and anchovy populations in a land-locked sea." Mediterranean Marine Science 17, no. 1 (January 20, 2016): 1. http://dx.doi.org/10.12681/mms.1120.

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The aim of this paper is to establish a relationship between long-term variability in sardine and anchovy populations in the Adriatic Sea and ocean dynamics and processes that occur over interannual and decadal timescales in the Adriatic-Ionian basin. Basis for such analysis are annual time series of sardine and anchovy landings and recruits at age 0 and annual time series of environmental parameters observed at a representative Adriatic station between 1975 and 2010. Pearson correlations and robust Dynamic Factor Analysis (DFA) were applied to quantify the connections between fisheries and environmental parameters. Variations and trends in fisheries series were best explained by changes in near-bottom temperature and salinity, being an appropriate proxy for tracking changes in water masses' dynamics and hydrographic conditions in the basin. It seems that a prolonged period of decreasing sardine population was characterized by low oxygen availability and environmental conditions in the deep Adriatic waters, triggered by an extraordinary basin-wide event called the Eastern Mediterranean Transient. A collapse in anchovy population has been observed after an exceptional cooling event followed by dense water formation.
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43

Antonelli, Cristian, Jeff Chen, and Franz X. Kartner. "Intracavity pulse dynamics and stability for passively mode-locked lasers." Optics Express 15, no. 10 (2007): 5919. http://dx.doi.org/10.1364/oe.15.005919.

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44

Wellmann, Barbara, David J. Spence, and David W. Coutts. "Dynamics of solid-state lasers pumped by mode-locked lasers." Optics Express 23, no. 4 (February 12, 2015): 4441. http://dx.doi.org/10.1364/oe.23.004441.

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45

Habruseva, T., G. Huyet, and S. P. Hegarty. "Dynamics of Quantum-Dot Mode-Locked Lasers With Optical Injection." IEEE Journal of Selected Topics in Quantum Electronics 17, no. 5 (September 2011): 1272–79. http://dx.doi.org/10.1109/jstqe.2011.2123875.

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46

Bosia, G., and E. Lazzaro. "Dynamics of rotating tearing modes under phase locked feedback control." Nuclear Fusion 31, no. 6 (June 1, 1991): 1003–14. http://dx.doi.org/10.1088/0029-5515/31/6/001.

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47

Teplinsky, A., and O. Feely. "Phase-jitter dynamics of digital phase-locked loops: Part II." IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 47, no. 4 (April 2000): 458–73. http://dx.doi.org/10.1109/81.841848.

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48

Simos, Iraklis Hercules, and Christos Simos. "Synchronization Dynamics of Mutually Injected Passively Mode-Locked Semiconductor Lasers." IEEE Journal of Quantum Electronics 54, no. 6 (December 2018): 1–7. http://dx.doi.org/10.1109/jqe.2018.2874085.

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49

Sivaramakrishnan, Sudarshan, and Herbert G. Winful. "Subharmonic anti-phase dynamics in coupled mode-locked semiconductor lasers." Optics Letters 42, no. 23 (November 27, 2017): 4905. http://dx.doi.org/10.1364/ol.42.004905.

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50

Mercier, J., and M. McCall. "Stability and dynamics of an injection-locked semiconductor laser array." Optics Communications 138, no. 1-3 (May 1997): 200–210. http://dx.doi.org/10.1016/s0030-4018(97)00012-6.

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