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本研究旨在探討國民中學校長透明化優勢領導與學校混沌動力系統之間的關係。除探討國民中學校長透明化優勢領導、學校混沌動力系統的內涵及現況，瞭解教育人員人口變項及學校背景變項在校長透明化優勢領導及學校混沌動力系統得分的差異情形外，亦分析校長透明化優勢領導與學校混沌動力系統之相關程度，並探討校長透明化優勢領導對學校混沌動力系統的預測情形。 本研究係以台灣地區之國民中學教育人員為研究對象，以「國民中學校長透明化優勢領導與學校混沌動力系統調查問卷」為工具進行研究，內含基本資料、國民中學校長透明化優勢領導問卷及學校混沌動力系統問卷三部分，具有良好的信度、效度。正式施測有效樣本502位，分別以描述分析、t考驗、變異數分析、積差相關分析、多元逐步迴歸分析等統計方法進行分析，並得到以下數項結論： 一、國民中學教育人員在知覺「校長透明化優勢領導問卷」的總得分上，屬於中上程度，在各向度之得分中，以「誠實至上」最高，最低則是「勇於認錯」。國民中學教育人員在「學校混沌動力系統問卷」的總得分上，亦屬於中上程度，在各向度之得分中，以「回饋機制」最高，最低則是「亂中求序」。 二、教育人員人口變項與學校背景變項中，性別、年齡、服務年資、職務及區域在校長透明化優勢領導問卷上，均具有顯著差異，僅學歷無顯著差異。 三、教育人員人口變項與學校背景變項中，性別、年齡、服務年資、職務及區域在學校混沌動力系統問卷上，均具有顯著差異，僅學歷無顯著差異。 四、教育人員知覺校長透明化優勢領導問卷之得分中，低、中、高三組在整體學校混沌動力系統及學校混沌動力系統各向度上，均有顯著差異；同時，不論在整體學校混沌動力系統或各向度的得分上，高分組均顯著優於中、低分組；中分組顯著優於低分組。 五、校長透明化優勢領導及各向度，與學校混沌動力系統及各向度間呈現出顯著的正相關，亦即教育人員知覺校長透明化優勢領導行為愈高，則校長經營學校混沌動力系統之能力也愈佳。 六、在探討校長透明化優勢領導各向度中，以鼓勵讚賞、傳達警訊、信守承諾、勇於認錯、卸下防禦及沈著鎮靜等六者對學校混沌動力系統之聯合預測力最佳，尤以鼓勵讚賞最具有預測力。 最後，本研究擬根據上述研究結果進行分析討論，以形成結論及建議，並提供教育行政機關、國民中學校長及未來相關研究之參考。 / The purposes of this study were to explore relationships between principal's transparency edge leading and chaotic dynamical system in junior high school. The fist were to explore the reality for principal's transparency edge leading and chaotic dynamical system in schools. Secondary, the researcher also investigated the differences of school staff’s demographic variables and schools' background variables among principal's transparency edge leading and chaotic dynamical system in schools. Thirdly, to analyze the relationships among principal's transparency edge leading and chaotic dynamical system in schools. Finally, to explore predictive power of principal's transparency edge leading on chaotic dynamical system in schools. This study employed the survey method. The subject were 502 educational staff randomly sample from 70 junior high schools in Taiwan island. Data were analyzed using the method of descriptive and inferential statistics, included Frequencies, t-test, ANOVA, Correlation analysis, and Multiple stepwise regression analysis. The major findings were： 1. There is above average perception for principal's transparency edge leading and chaotic dynamical system in schools among the junior high school staff. 2. Significant difference existed among the gender, age, seniority, position, and district for principal's transparency edge leading. 3. Significant difference existed among the gender, age, seniority, position, and district for chaotic dynamical system in schools. 4. Significant difference existed among low, middle, and high teachers' perception of principal's transparency edge leading for chaotic dynamical system in schools. 5. Significant positive correlation between principal's transparency edge leading and chaotic dynamical system in schools. 6. In regression forecast of principal's transparency edge leading to chaotic dynamical system in schools, especially the variable of “encouragement and applause” has the biggest predictability. Based on the results of this study, to make some suggestions for educational administration, the junior high school principals and future study.

The neural net computer simulations which will be presented here are based on the acceptance of a set of assumptions that for the last twenty years have been expressed in the fields of information processing, neurophysiology and cognitive sciences. First of all, neural networks and their dynamical behaviors in terms of attractors is the natural way adopted by the brain to encode information. Any information item to be stored in the neural net should be coded in some way or another in one of the dynamical attractors of the brain and retrieved by stimulating the net so as to trap its dynamics in the desired item's basin of attraction. The second view shared by neural net researchers is to base the learning of the synaptic matrix on a local Hebbian mechanism. The last assumption is the presence of chaos and the benefit gained by its presence. Chaos, although very simply produced, inherently possesses an infinite amount of cyclic regimes that can be exploited for coding information. Moreover, the network randomly wanders around these unstable regimes in a spontaneous way, thus rapidly proposing alternative responses to external stimuli and being able to easily switch from one of these potential attractors to another in response to any coming stimulus. In this thesis, it is shown experimentally that the more information is to be stored in robust cyclic attractors, the more chaos appears as a regime in the back, erratically itinerating among brief appearances of these attractors. Chaos does not appear to be the cause but the consequence of the learning. However, it appears as an helpful consequence that widens the net's encoding capacity. To learn the information to be stored, an unsupervised Hebbian learning algorithm is introduced. By leaving the semantics of the attractors to be associated with the feeding data unprescribed, promising results have been obtained in term of storing capacity.

This dissertation investigates the application of computational intelligence methods in the analysis of nonlinear chaotic systems in the framework of many known and newly designed complex systems. Parallel comparisons are made between these methods. This provides insight into the difficult challenges facing nonlinear systems characterization and aids in developing a generalized algorithm in computing algorithmic complexity measures, Lyapunov exponents, information dimension and topological entropy. These metrics are implemented to characterize the dynamic patterns of discrete and continuous systems. These metrics make it possible to distinguish order from disorder in these systems. Steps required for computing Lyapunov exponents with a reorthonormalization method and a group theory approach are formalized. Procedures for implementing computational algorithms are designed and numerical results for each system are presented. The advance-time sampling technique is designed to overcome the scarcity of phase space samples and the buffer overflow problem in algorithmic complexity measure estimation in slow dynamics feedback-controlled systems. It is proved analytically and tested numerically that for a quasiperiodic system like a Fibonacci map, complexity grows logarithmically with the evolutionary length of the data block. It is concluded that a normalized algorithmic complexity measure can be used as a system classifier. This quantity turns out to be one for random sequences and a non-zero value less than one for chaotic sequences. For periodic and quasi-periodic responses, as data strings grow their normalized complexity approaches zero, while a faster deceasing rate is observed for periodic responses. Algorithmic complexity analysis is performed on a class of certain rate convolutional encoders. The degree of diffusion in random-like patterns is measured. Simulation evidence indicates that algorithmic complexity associated with a particular class of 1/n-rate code increases with the increase of the encoder constraint length. This occurs in parallel with the increase of error correcting capacity of the decoder. Comparing groups of rate-1/n convolutional encoders, it is observed that as the encoder rate decreases from 1/2 to 1/7, the encoded data sequence manifests smaller algorithmic complexity with a larger free distance value.

Cette thèse est une étude numérique d'un écoulement d'air dans une cavité différentiellement chauffée bidimensionnelle en présence de gravité. Pour un rapport hauteur/largeur de deux et des parois horizontales supposées adiabatiques, l'écoulement de base correspond à une recirculation autour de la cavité avec un coeur stratifié et des couches limites verticales. Les équations de Navier-Stokes sont résolues par un code de simulation numérique directe spectrale instationnaire basé sur l’hypothèse de Boussinesq couplé à un algorithme de suivi de particules avec interpolation. Le nombre de Rayleigh basé sur la différence de température est choisi comme paramètre de contrôle de l’écoulement. La transition vers le chaos au sein de cet écoulement est explorée à la fois du point de vue eulérien (développement de l’instationnarité) et lagrangien (mélange chaotique).L'approche lagrangienne considère le mélange de traceurs passifs infinitésimaux non diffusifs. L'étude se base sur l'identification d'objets invariants de la dynamiques : points fixes, orbites périodiques et leurs variétés stable/instable, connections homoclines et hétéroclines, trajectoires toroïdales. Le mélange des traceurs est partiel lorsque l'écoulement subit une première bifurcation de Hopf. La dispersion globale des traceurs résulte d'un compromis entre la présence de tores Kolmogorov-Arnold-Moser qui jouent le rôle de barrières au mélange, et d'enchevêtrements homoclines/hétéroclines responsables du chaos lagrangien. L'étude statistique des temps de retour et du taux d'homogénéisation révèle la présence de zones où la dynamique est non hyperbolique. En augmentant le nombre de Rayleigh, le mélange devient progressivement complet avant que l'écoulement ne devienne quasi-périodique en temps. L'approche eulérienne considère les divers scénarios de transition vers le chaos par l'identification numérique d'attracteurs et des bifurcations associées lorsque le nombre de Rayleigh varie. Deux routes principales se distinguent en fonction des symétries associées aux deux premières bifurcations de Hopf du système, contenant chacune plusieurs branches hystérétiques. Trente trois régimes différents sont identifiés et analysés depuis l'écoulement stationnaire jusqu'à un écoulement chaotique voire hyperchaotique. Parmi ceux-ci, des branches de tores à deux et trois fréquences incommensurables, ainsi que des régimes intermittents sont examinés. Des diagrammes de bifurcations qualitatifs et quantitatifs sont proposés pour résumer l'ensemble des dynamiques observées. / This thesis is about the numerical study of an air flow inside a two dimensionally heated cavity. The aspect ratio height/width is set to two. Boundary conditions on horizontal walls are taken as adiabatic. In this case, the base flow consists of a recirculation around the stratified core of the cavity and of boundary layers along the vertical walls. The Navier-Stokes equations are solved using a spectral direct numerical simulation code under the Boussinesq assumption coupled with a particle tracking scheme based on interpolation. The Rayleigh number, based on the temperature difference is chosen as the control parameter of the system. The transition to chaos in this flow is considered both from the Eulerian and Lagrangian point of view.The Lagrangian point of view considers the mixing of point-wise non-diffusive passive tracers. The study is based on the identification of invariant objects: fixed points, periodic orbits and their stable/unstable manifolds,homoclinic and heteroclinic connections, toroidal trajectories.The mixing of tracers is partial when the flow undergoes the first Hopf bifurcation. The complete mixing of tracers results from a compromise between Kolmogorov-Arnold-Moser's tori, which act as barriers to mixing, and homoclinic/heteroclinic tangles which are responsible for the mixing.The statistical study of return times and the homogenisation rate shows regionswhere the dynamics is non-hyperbolic. When the Rayleigh number is increased, mixing is increasingly complete before the flow becomes quasi-periodic in time.The Eulerian description considers the transition to chaos via the numerical identification of attractors and their associated bifurcations when the Rayleigh number is varied. Two main routes are found depending on the symmetries associated with the first two Hopf bifurcations of the system. A total of thirty three different regimes are identified from steady to hyperchaotic, among which two- and three-frequency tori as well as intermittent dynamics. Both quantitative and qualitative bifurcation diagrams are suggested for the system.

Redes neurais biológicas contêm bilhões de células (neurônios) agrupadas em regiões espacial e funcionalmente distintas. Elas também apresentam comportamentos complexos, tais como dinâmicas periódicas e caóticas. Na área da Inteligência Artificial, pesquisas mostram que Redes Neurais Caóticas, isto é, modelos de Redes Neurais Artificiais que operam com dinâmicas complexas, são mais eficientes do que modelos tradicionais no que diz respeito a evitar memórias espúrias. Inspirado pelo fato de que o córtex cerebral contém agrupamentos de células e motivado pela eficiência no uso de dinâmicas complexas, este projeto de pesquisa investiga o comportamento dinâmico de um modelo de Rede Neural Artificial Recorrente, como o de Hopfield, porém com a topologia sináptica reorganizada a ponto de originar agrupamentos de neurônios, tal como acontece em uma Rede Complexa quando esta apresenta uma estrutura de comunidades. O modelo de treinamento tradicional de Hopfield também é alterado para uma regra de aprendizado que posta os padrões em ciclos, gerando uma matriz de pesos assimétrica. Resultados indicam que o modelo proposto oscila entre comportamentos periódicos e caóticos, dependendo do grau de fragmentação das sinapses. Com baixo grau de fragmentação, a rede opera com dinâmica periódica, como consequência da regra de treinamento utilizada. Dinâmicas caóticas parecem surgir quando existe um alto grau de fragmentação. Mostra-se, também, que é possível obter caoticidade em uma topologia adequadamente modular, ou seja, como uma estrutura de comunidades válida. Desta forma, este projeto de pesquisa provê uma metodologia alternativa para se construir um modelo de Rede Neural Artificial que realiza tarefas de reconhecimento de padrões, explorando dinâmicas complexas por meio de uma estrutura de conexões que se mostra mais similar à topologia existente no cérebro / Biological neural networks contain billions of neurons divided in spatial and functional clusters to perform dierent tasks. It also operates with complex dynamics such as periodic and chaotic ones. It has been shown that Chaotic Neural Networks are more efficient than conventional recurrent neural networks in avoiding spurious memory. Inspired by the fact that the cerebral cortex has speficic groups of cells and motivated by the efficiency of complex behaviors, in this document we investigate the dynamics of a recurrent neural network, as the Hopfield one, but with neurons coupled in such a way to form a complex network community structure. Also, we generate an asymmetric weight matrix placing pattern cycles during learning. Our study shows that the network can operate with periodic and chaotic dynamics, depending on the degree of the connection\'s fragmentation. For low fragmentation degree, the network operates with periodic dynamic duo to the employed learning rule. Chaotic behavior seems to rise for a high fragmentation degree. We also show that the neural network can hold both chaotic dynamic and a high value of modularity measure at the same time, indicating an acceptable community structure. These findings provide an alternative way to design dynamical neural networks to perform pattern recognition tasks exploiting periodic and chaotic dynamics by using a more similar topology to the topology of the brain

Inicialmente, apresentam-se características de dispositivos eletrônicos conhecidos como PLLs (phase-locked loops). PLLs são amplamente empregados para se extrair sinais de tempo em canais de comunicação e em aplicações nas quais se deseja controle automático de freqüência. O objeto principal é estudar PLLs analógicos descritos por uma equação diferencial ordinária de terceira ordem. Assim, deduzem-se condições de estabilidade assintótica e identifica-se um regime de caos conservativo, que ocorre sob certas combinações de valores de parâmetros. Três métodos de controle não-linear/caótico são então apresentados e aplicados. Os métodos são os seguintes: o Método de Pyragas via realimentação de variável de estado; o Método de Pyragas com atraso temporal na realimentação; e o Método de Sinha, o qual efetua o controle perturbando um parâmetro do sistema. Simulações numéricas são levadas a cabo a fim de ilustrar o comportamento dinâmico do sistema quando sujeito à ação desses métodos. Este trabalho termina com um estudo de uma rede formada por uma cadeia de PLLs. Condições para soluções síncronas, periódicas e caóticas (dissipativas e conservativas) são deduzidas para tal rede. / Firstly, features of electronic devices known as PLLs (Phase-Locked Loops) are presented. PLLs are widely employed to extract time signals in communication channels and in applications where automatic control of frequency is desired. The main goal is to study analog PLLs described by a third-order nonlinear ordinary differential equation. Thus, conditions for asymptotic stability are derived and a regime of conservative chaos occurring under certain combinations of parameter values is identified. Then, three methods of control of nonlinear/ chaotic dynamics are presented and applied. The methods are the following: the Pyragas method via feedback of state variable; the Pyragas method with time delay in the feedback; and the Sinhas method, which performs the control by disturbing a parameter of the system. Numerical simulations are accomplished in order to illustrate the dynamical behavior of the system when subjected to the action of these methods. This work ends with a study of a single-chain PLL network. Conditions for synchronous, periodic and chaotic (dissipative and conservative) solutions are derived for such a network.