Dans cette thèse, j'étudie la dynamique non linéaire résultant d’une compétition entre deux modes dans des systèmes lasers à boites quantiques.D’abord, je considère le cas de la compétition entre deux modes de polarisation apparaissant dans les diodes laser nanostructurées à cavité verticale et émettant par la surface (VCSELs). Il est connu que ces composants peuvent avoir une polarisation instable menant à des dynamiques riches. Récemment, un surprenant saut de mode entre deux états polarisés elliptiquement a été récemment découvert dans les VCSELs à boites quantiques. Ce comportement montre des propriétés intrigantes qui nécessitent une interprétation alternative. Dans cette thèse, je montre que ce comportement dynamique peut-être reproduit en utilisant le modèle spin-flip (SFM). En particulier je démontre et confirme expérimentalement que les sauts de modes sont en réalité des fluctuations chaotiques de faible dimension : un chaos en polarisation. Je démontre ensuite la pertinence de la dynamique chaotique observée pour les applications exploitant le chaos optique, en réalisant un générateur de nombres aléatoires à grande vitesse basé sur le chaos en polarisation.Deuxièmement, j'étudie les effet d'une rétroaction optique à délai sur les lasers à boites quantiques émettant simultanément depuis l'état fondamental et le premier état excité. Je clarifie l'impact the cette rétroaction optique ainsi que les mécanismes et bifurcations correspondantes. Je montre théoriquement qu'une rétroaction optique favorise globalement l'émission par l'état fondamental, mais aussi qu'un tel montage peut être utilisé pour commuter entre ces deux modes d'émission lorsque l'on change le taux ou le délai de la rétroaction. Enfin, je confirme ces observations expérimentalement, en rapportant des commutations entre l'état fondamental et l'état excité. / In this thesis, I study the nonlinear dynamics induced by the competition between two modes in quantum dot laser systems.First, I focus on the competition between polarization modes that takes place in quantum dot vertical-cavity surface-emitting lasers (VCSELs). It is well-known that these devices can exhibit polarization instabilities leading to rich dynamical evolution. Recently, a new peculiar random-like hopping between two non-orthogonal elliptically polarized states has been highlighted in QD VCSELs. This behavior shows intriguing features which clearly call for a different interpretation. In this thesis, I show that the dynamical behavior reported experimentally can accurately be reproduced within the spin-flip model (SFM) framework. In particular, I demonstrate and confirm experimentally that the peculiar random-like hoppings are in fact deterministic low-dimensional chaotic fluctuations, i.e. ``Polarization Chaos''. I then make a proof-of-concept demonstration of a high-speed random bit generator based on polarization chaos, hence demonstrating that the chaotic dynamics uncovered is relevant for optical chaos-based applications.Secondly, I investigate the effects of an external optical feedback on quantum dot lasers emitting simultaneously from the ground and the excited states. I bring new light on the impact of optical feedback and the corresponding mechanisms and bifurcations. I highlight theoretically that optical feedback globally favors the ground state emission, but also that it can be used to switch from one mode to the other when changing the feedback rate and/or the time-delay. In addition, I experimentally report switching between the ground and excited states when varying the external cavity length at the micrometer scale, which supports the theoretical predictions.

As part of the Large Hadron Collider high luminosity upgrade it is proposed to include crab cavities and large aperture niobium tin final focussing magnets in the lattice in order to enhance the luminosity. In this thesis the dynamics of a proposed cavity design were considered in terms of their impact upon the dynamic aperture of the machine. Taylor maps for the cavity were created and used to perform this analysis with a full assessment of their validity. A set of symplectic thin cavity models were also developed and cross checked with the Taylor maps. Finally, dynamic aperture studies were performed using these models in order to determine which components of the crab cavity dynamics are important when considering the long term stability of the beam in the LHC upgrade. It is shown that crab cavities exhibit little impact on the LHC beam stability. For the final focussing magnets a preliminary study was conducted into the importance of including their fringe fields in a model of the LHC upgrade. A technical study was carried out into developing a symplectic model which was compatible with the current magnet models use for dynamic aperture studies. A preliminary dynamic aperture study was performed with the inclusion of fringe fields for the final focussing magnets from which the fringe fields are shown to have a negative impact on the long term beam stability.

abstract: Complex dynamical systems are the kind of systems with many interacting components that usually have nonlinear dynamics. Those systems exist in a wide range of disciplines, such as physical, biological, and social fields. Those systems, due to a large amount of interacting components, tend to possess very high dimensionality. Additionally, due to the intrinsic nonlinear dynamics, they have tremendous rich system behavior, such as bifurcation, synchronization, chaos, solitons. To develop methods to predict and control those systems has always been a challenge and an active research area. My research mainly concentrates on predicting and controlling tipping points (saddle-node bifurcation) in complex ecological systems, comparing linear and nonlinear control methods in complex dynamical systems. Moreover, I use advanced artificial neural networks to predict chaotic spatiotemporal dynamical systems. Complex networked systems can exhibit a tipping point (a “point of no return”) at which a total collapse occurs. Using complex mutualistic networks in ecology as a prototype class of systems, I carry out a dimension reduction process to arrive at an effective two-dimensional (2D) system with the two dynamical variables corresponding to the average pollinator and plant abundances, respectively. I demonstrate that, using 59 empirical mutualistic networks extracted from real data, our 2D model can accurately predict the occurrence of a tipping point even in the presence of stochastic disturbances. I also develop an ecologically feasible strategy to manage/control the tipping point by maintaining the abundance of a particular pollinator species at a constant level, which essentially removes the hysteresis associated with tipping points. Besides, I also find that the nodal importance ranking for nonlinear and linear control exhibits opposite trends: for the former, large degree nodes are more important but for the latter, the importance scale is tilted towards the small-degree nodes, suggesting strongly irrelevance of linear controllability to these systems. Focusing on a class of recurrent neural networks - reservoir computing systems that have recently been exploited for model-free prediction of nonlinear dynamical systems, I uncover a surprising phenomenon: the emergence of an interval in the spectral radius of the neural network in which the prediction error is minimized. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2020

I study dusty plasma produced by electrostatically confining melamine formaldehyde microparticles in a radio-frequency glow discharge plasma. Dusty plasma is a mixture of particles of solid matter (dust), electrons, ions, and neutral gas atoms. The dust particles have a very high charge and a mass compared to the electrons and ions in the ambient plasma. As a consequence, a dusty plasma exhibits collective phenomena such as dust acoustic waves, crystallization, and melting. The discrete nature of dust particles gives rise to compressibility. In this thesis I report findings of four tasks that were performed to investigate dust acoustic waves, compressibility, and melting. First, the nonlinear phenomenon of synchronization was characterized experimentally for the dust acoustic wave propagating in a dust cloud with many layers. I find four synchronized states, with frequencies that are multiples of 1, 2, 3, and 1/2 of the driving frequency. Comparing to phenomena that are typical of the van der Pol paradigm, I find that synchronization of the dust acoustic wave exhibits the signature of the suppression mechanism but not that of the phaselocking mechanism. Additionally, I find that the synchronization of the dust acoustic wave exhibits three characteristics that differ from the van der Pol paradigm: a threshold amplitude that can be seen in the Arnold tongue diagram, a branching of the 1:1 harmonic tongue at its lower extremity, and a nonharmonic state. Second, to assess which physical processes are important for a dust acoustic instability, I derived dispersion relations that encompass more physical processes than commonly done. I investigated how various physical processes affect a dust acoustic wave by solving these dispersion relations using parameters from a typical dust acoustic wave experiment. I find that the growth rate diminishes for large ion currents. I also find that the compressibility, a measure of the coupling between the dust particles, have a strong effect on the wave propagation. Comparing the kinetic vs. hydrodynamic descriptions for ions, I find that under typical laboratory conditions the inverse Landau damping and the ion-neutral collisions contribute about equally to the dust acoustic instability. Third, I performed dust acoustic wave experiments to resolve a previously unremarked discrepancy in the literature regarding the sign of the compressibility of a strongly-coupled dust component in a dusty plasma. According to theories compressibility is negative, whereas experiments suggest that it is positive. I find that the compressibility is positive. This conclusion was reached after allowing for a wide range of experimental uncertainties and model dependent systematic errors. Finally, the polygon construction method of Glaser and Clark was used to characterize crystallization and melting in a single-layer dusty plasma. Using particle positions measured in a previous dusty plasma experiment, I identified geometrical defects, which are polygons with four or more sides. These geometrical defects are found to proliferate during melting. I also identify a possibility of latent heat involvement in melting and crystallization processes of a dusty plasma.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第22069号 / 工博第4650号 / 新制||工||1725(附属図書館) / 京都大学大学院工学研究科電気工学専攻 / (主査)教授 引原 隆士, 教授 松尾 哲司, 准教授 三谷 友彦 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

This thesis presents a generalized approach for the fully digital design and implementation of chaos generators through the numerical solution of chaotic ordinary differential equations. In particular, implementations use the Euler approximation with a fixed-point twos complement number representation system for optimal hardware and performance. In general, digital design enables significant benefits in terms of power, area, throughput, reliability, repeatability and portability over analog implementations of chaos due to lower process, voltage and temperature sensitivities and easy compatibility with other digital systems such as microprocessors, digital signal processing units, communication systems and encryption systems. Furthermore, this thesis introduces the idea of implementing multidimensional chaotic systems rather than 1-D chaotic maps to enable wider throughputs and multiplier-free architectures that provide significant performance and area benefits. This work focuses efforts on the well-understood family of autonomous 3rd order "jerk" chaotic systems. The effect of implementation precision, internal delay cycles and external delay cycles on the chaotic response are assessed. Multiplexing of parameters is implemented to enable switching between chaotic and periodic modes of operation. Enhanced chaos generators that exploit long-term divergence in two identical systems of different precision are also explored. Digital design is shown to enable real-time controllability of 1D multiscroll systems and 4th order hyperchaotic systems, essentially creating non-autonomous chaos that has thus far been difficult to implement in the analog domain. Seven different systems are mathematically assessed for chaotic properties, implemented at the register transfer level in Verilog HDL and experimentally verified on a Xilinx Virtex 4 FPGA. The statistical properties of the output are rigorously studied using the NIST SP. 800-22 statistical testing suite. The output is adapted for pseudo random number generation by truncating statistically defective bits. Finally, a novel post-processing technique using the Fibonacci series is proposed and implemented with a non-autonomous driven hyperchaotic system to provide pseudo random number generators with high nonlinear complexity and controllable period length that enables full utilization of all branches of the chaotic output as statistically secure pseudo random output.

Indiana University-Purdue University Indianapolis (IUPUI) / This research investigates characteristics of PT (parity-time) symmetry breaking in a system of two optically-coupled, time-delayed semiconductor lasers. A theoretical rate equation model for the lasers' electric fields is presented and then reduced to a 2x2 Hamiltonian model, which, in the absence of time-delay, is PT-symmetric. The important parameters we control are the temporal separation of the lasers, the frequency detuning, and the coupling strength. The detuning is experimentally controlled by varying the lasers' temperatures, and intensity vs. detuning behavior are examined, specifically how the PT-transition and the period and amplitude of sideband intensity oscillations change with coupling and delay. Experiments are compared to analytic predictions and numerical results, and all are found to be in good agreement. Eigenvalues, eigenvectors, and exceptional points of the reduced Hamiltonian model are numerically and analytically investigated, specifically how nonzero delay affects existing exceptional points.

<div>Lattices composed of bistable elements are of great significance across various fields of science and engineering due to their ability to support a class of solitary waves, called transition waves. Common with all solitary waves, transition waves carry highly concentrated energy with minimal degradation and thus have many useful engineering applications, such as extreme waveguides, bandgap transmission, vibration absorption, and energy harvesting. The rich dynamics arising from the strong nonlinearities of the constitutive bistable microstructures still have much to be unveiled for the practical implementation of the transition waves in real-world engineering structures. Especially, the quasi-particle characteristics of the transition waves can potentially address the performance limits posed by the unit cell size in linear metamaterials.</div><div><br></div><div>In this thesis, we first present an input-independent generation of transition waves in the lattices of asymmetric bistable unit cells when snap-through transitions occur at any site within the lattice. The resulting responses are invariant across the lattice except near the boundaries. These characteristics imply useful applications in broadband energy harvesting, exploiting the highly concentrated energy of the transition waves. We further observe that the inherent lattice discreteness induces dominantly monochromatic oscillatory tail following the main transition wave. This radiated energy of the tail can always be efficiently harvested through resonant transduction regardless of the input excitations. This type of bistable lattice transforms any input disturbance into an output form that can be conveniently transduced; thus, energy harvesting becomes an inherent metamaterial property of the bistable lattice.</div><div><br></div><div>To enhance the responses further for improved energy harvesting capability, we introduce engineered defects in the form of a mass impurity, inhomogeneous inter-site stiffness, and their combinations, achieving localization of energy at desired sites. Remarkably, we also observe a long-lived breather-like mode for the first time in this type of lattice. To enhance the tail motions globally across the lattice, we investigate the responses in a set of bistable lattices with the same mass and elastic densities but with different lattice spacing distances (or lattice discreteness). From the available tail energy, we observe a significant increase in the harvesting capability with the increased lattice discreteness.</div><div><br></div><div>Next, the effect of functional grading on the onsite and inter-site stiffnesses are investigated to augment the control of the transition waves in the bistable lattices. The unidirectionality still remains in the direction of decreasing stiffness, while a boomerang-like wave reversal occurs in the direction of increasing stiffness. Both the compression and rarefaction transition waves are allowed to propagate, enabling continuous transmission of the transition waves without complex resetting mechanisms, thus expanding the bistable lattices' functionality for practical applications.</div><div><br></div><div>The observed input-independent dynamics of the one-dimensional bistable lattices can be extended to higher-dimensional metastructures by allowing macrostructural flexibility. Metabeams composed of spring-joined bistable elements are subjected to in-plane sinusoidal input at the microstructural level, and the out-of-plane responses at the macrosctructural level are measured. As long as transition waves are triggered within the metabeam, the most dominant output frequency occurs near the natural frequency of the macroscopic structure regardless of the input excitations initiating the transition waves, yielding energy transfer between uncorrelated frequencies.</div><div><br></div><div>Finally, high-fidelity in-house numerical solvers are developed for the massively parallelized computation of the problems involving generic bistable architectures, addressing the problem size limit. The improved numerical solution accuracy and computational performance, compared to those of commercial solvers, provide great potential to discover new dynamics by drastically expanding the accessible analysis regimes.</div><div><br></div><div>The experiments, simulations, and theoretical contributions in this thesis illustrate the possibilities afforded by strongly nonlinear phenomena to tailor the dynamics of materials systems. Importantly, the presented results show mechanisms to affect global dynamic properties unconstrained by the unit cell size, thereby offering new routes to extreme dynamics beyond current metamaterial architectures.</div>

Networks that self-organize in response to information are one of the most central studies in complex systems theory. A new time series analysis tool for studying self-organizing systems is developed and demonstrated. This method is applied to interacting complex swarms to explore the connection between information transport and group size, providing evidence for Dunbar's numbers having a foundation in network dynamics. A complex network model of information spread is developed. This network infodemic model uses reinforcement learning to simulate connection and opinion adaptation resulting from interaction between units. The model is applied to study polarized populations and echo chamber formation, exploring strategies for network resilience and weakening. The model is straightforward to extend to multilayer networks and networks generated from real world data. By unifying explanation and prediction, the network infodemic model offers a timely step toward understanding global collective behavior.

<p>QC 20101126</p>