Bifurcations in a forced Wilson-Cowan neuron pair

We investigate bifurcations of periodic solutions observed in the forced Wilson-Cowan neuron pair by both the brute-force computation and the shooting method. By superimposing the results given by both methods, a detailed topological classification of periodic solutions is achieved that includes tori and chaos attractors in the parameter space is achieved. We thoroughly explore the parameter space composed of threshold values, amplitude, and angular velocity of an external forcing term. Many bifurcation curves that are invisible when using brute-force method are solved by the shooting method. We find out a typical bifurcation structure including Arnold tongue in the angular velocity and the amplitude of the external force parameter plane, and confirm its fractal structure. In addition, the emergence of periodic bursting responses depending on these patterns is explained

Nonlinear Morphoelastic Plates I: Genesis of Residual Stress

Volumetric growth of an elastic body may give rise to residual stress. Here a rigorous analysis of the residual strains and stresses generated by growth in the axisymmetric Kirchhoff plate is given. Balance equations are derived via the global constraint principle, growth is incorporated via a multiplicative decomposition of the deformation gradient, and the system is closed by a response function. The particular case of a compressible neo-Hookean material is analyzed and the existence of residually stressed states is established

Ranking species in complex ecosystems through nestedness maximization

Identifying the rank of species in a social or ecological network is a difficult task, since the rank of each species is invariably determined by complex interactions stipulated with other species. Simply put, the rank of a species is a function of the ranks of all other species through the adjacency matrix of the network. A common system of ranking is to order species in such a way that their neighbours form maximally nested sets, a problem called nested maximization problem (NMP). Here we show that the NMP can be formulated as an instance of the Quadratic Assignment Problem, one of the most important combinatorial optimization problem widely studied in computer science, economics, and operations research. We tackle the problem by Statistical Physics techniques: we derive a set of self-consistent nonlinear equations whose fixed point represents the optimal rankings of species in an arbitrary bipartite mutualistic network, which generalize the Fitness-Complexity equations widely used in the field of economic complexity. Furthermore, we present an efficient algorithm to solve the NMP that outperforms state-of-the-art network-based metrics and genetic algorithms. Eventually, our theoretical framework may be easily generalized to study the relationship between ranking and network structure beyond pairwise interactions, e.g. in higher-order networks.Comment: 28 pages; 2 figure

Complexity in the entangled bank: On the structural and dynamical properties of empirical mutualistic networks

El mutualismo, que durante largo tiempo había sido considerado un tipo de interacción fascinante pero marginalmente relevante, es reconocido hoy en día por desempeñar un papel crucial en la formación de los ecosistemas. En esta tesis analizamos la complejidad del rico entrelazado que forman estas relaciones ecológicas en los sistemas naturales, o lo que Darwin célebremente llamó el `ribazo enmarañado’, desde el punto de vista del formalismo de redes.En la primera parte de la tesis nos centramos en estudiar el origen de la arquitectura de las redes mutualistas. En detalle, a partir de la aplicación de conceptos de la teoría de la información y la física estadística, abordamos la cuestión de la emergencia de un ubicuo patrón estructural conocido como anidamiento. A través del análisis de un vasto conjunto de redes empíricas, mostramos que unas pocas asunciones mínimas sobre el número de interacciones mutualistas por especie junto con el efecto del azar son condiciones suficientes para reproducir la estructura observada –sin necesidad de suponer la intervención de fuerzas selectivas o procesos mecanicistas. En este sentido, nuestros resultados muestran que la estructura global de las comunidades mutualistas puede explicarse, en términos estadísticos, a partir de las propiedades locales del sistema. En segundo lugar, exploramos también cómo las diferentes métricas propuestas en la literatura cuantifican el anidamiento, evaluando su eficacia tanto en redes reales como sintéticas. Nuestros resultados indican que la comparación y clasificación de patrones anidados correspondientes a distintos ecosistemas es entorpecida, sustancialmente, por la existencia de dependencias respecto a otros parámetros de la red.En la segunda parte de esta tesis, continuamos profundizando en el estudio de la organización de comunidades mutualistas pero abordando un desafío distinto, concretamente el de superar el paradigma de agregación temporal de las redes. Para empezar, caracterizamos un conjunto de redes empíricas y evaluamos cómo la incorporación de información detallada sobre la variabilidad temporal modifica la descripción estática del sistema. A continuación, proponemos un grupo de modelos que permite generar, bajo diversos supuestos, configuraciones sintéticas de fenología compatibles con una red determinada. Encontramos que, si bien la idoneidad de los modelos mecanicistas para producir configuraciones realistas depende en gran medida del sistema estudiado, un modelo estadístico basado en el principio de máxima entropía se comporta generalmente bien independientemente de los detalles de la red. Basándonos en estos resultados, exploramos brevemente las consecuencias dinámicas, específicamente para la persistencia de las especies, de tener en cuenta la dimensión temporal de la red de interacciones. En particular, observamos que las especies con un período de actividad corto se enfrentan a una mayor incertidumbre frente a perturbaciones externas. Este enfoque preliminar, sin embargo, requiere investigaciones más detalladas, especialmente en el contexto del cambio climático.En conjunto, a lo largo de esta tesis analizamos cómo se puede utilizar el lenguaje de redes para estudiar la complejidad de los sistemas mutualistas naturales, evaluando por un lado la información mínima requerida para comprender el `ribazo enmarañado', y por otro lado, identificando las limitaciones de la aún predominante representación estática de los ecosistemas.<br /

NBS monograph

From Introduction Statement of Objectives: "The purpose of this publication is to provide assistance to the practicing engineer who is faced with the problem of making dynamic measurements of rapidly changing pressures.

Modulation and detection schemes based on chaotic attractors properties : application to wideband transmissions

Au cours des vingt dernières années, les systèmes de communications basés sur le chaos ont été étudiés, avec pour objectif la possibilité de générer les signaux large-bande par des circuits électroniques simples, permettant une faible complexité des circuits émetteurs-récepteurs. Cette thèse concerne l’étude de systèmes de transmissions large-bande basés sur le chaos, en utilisant certaines propriétés des attracteurs chaotiques. Tout d’abord, un système dynamique a été choisi et étudié, permettant de générer des signaux chaotiques qui possèdent des composantes périodiques. L’analyse de ces attracteurs chaotiques cycliques (CCA) met en évidence des propriétés spécifiques en lien avec leur période. Ensuite, deux schémas de modulation basés sur les CCAs sont proposés. Les détections non-cohérentes associées sont réalisées par l’observation des propriétés spécifiques des signaux rec¸us. L’évaluation des performances des systèmes basés sur les CCAs dans le cas d’un canal de bruit additif Gaussien montre des performances meilleures que celles des systèmes dits ”differential chaos shift keying (DCSK)”, en bas débit de symboles. En outre, les performances dans le cas multi-trajet sont comparables dans la bande de 2,4 GHz. ------------------------------------------------------------------------------------------------------------------------------------------- In the past twenty years, chaos-based communication systems have been studied, considering the possibility of generating wideband signals by simple electronic circuits, hence low complexity in transceiver. The aim of this thesis is to study the chaos-based wideband transmission systems relying on the properties of chaotic attractors. Firstly, a dynamical system is selected and studied, allowing to generate the chaotic signals with a periodic component. The analysis of such chaotic cyclic attractors (CCA) shows the specific properties. Then, two CCA-based modulation schemes are proposed, with the simple noncoherent detections realized by observing the specific properties of the received signals. The performance evaluation of CCA-based systems in the additive white Gaussian noise (AWGN) channel shows a better noise performance with long symbol duration, compared to the one of differentially chaos shift keying (DCSK). In addition, they have a comparable multipath performance in the 2.4 GHz ISM environmen

Agricultural Production Economics

Agricultural Production Economics (Second Edition, Amazon Createspace 2012) is a revised edition of the textbook Agricultural Production Economics published by Macmillan in 1986 (ISBN 0-02-328060-3). This is a free pdf download of the entire book. As the author, I own the copyright. Amazon markets bound print copies of the book at amazon.com at a nominal price for classroom use. The book can also be ordered through college bookstores using the following ISBN numbers: ISBN-13 978-1469960647 ISBN-10 1469960648 The format and coverage remains similar to the first edition, many small revisions and updates have been made. All graphs have been redrawn using the latest in computer imaging technology. The book contains a comprehensive treatment of the traditional agricultural production economics topics employing both detailed graphics and differential calculus. The text focuses on the neoclassical factor-product, factor-factor and product-product models, and is suitable for an advanced undergraduate or a beginning graduate-level course in static production economics. Chapters also deal with linear programming, risk and uncertainty and intertemporal resource allocation. A basic knowledge of differential calculus is assumed. Individual chapters are largely self-contained, and the book is suitable for instruction at a variety of levels depending on the specific needs of the instructor and the mathematics background of the students.https://uknowledge.uky.edu/agecon_textbooks/1000/thumbnail.jp

The extinction of subharmonic vibration under the effects of gravity on the equilibrium of motion.

The extinction of second order subharmonic vibration response of a single degree of freedom system is investigated for the case of damped centrifugal excitation. The degree of the restoring force asymmetry resulting from the effect of gravity is expressed in terms of the parameter of static deflection. The resonance under gravity effects is analysed theoretically for a wide range of physical conditions to determine the behavioural characteristics of the subharmonic components. The inherently coupled algebraic equations are obtained by the approximate energy method of Ritz-Galerkin and by the method of harmonic balance. These two methods are not bounded to any degree of non-linearity. As there is no exact solution for this investigation and because of the dissipative forces inevitably introducing the problem of stability, the actual existence of the approximate solution over the frequency band-width is ascertained. There are no real roots in the instability region. The algebraic polynomial expressions cannot be satisfied simultaneously because of the accumulative effect in an accompanying harmonic of the vibratory motion. The build-up oscillation occurs in the second order region, having a frequency the same as that of the main component of subharmonic motion. The stability criterion is derived from comparing the characteristic exponent of solution to the variational equation with damping coefficient of the system. The response characteristics are then investigated where the polynomial equations are simplified through justifying the approximation of the fundamental harmonic as the effective amplitude of the disturbing force. The results are of comparable accuracy for cases in which gravity effects do not increase the effective non-linearity with resonance. The approximation, however, is applicable whatever tha physical characteristic behaviour of the non-linearity in the region of the critical state of subharmonic extinction. The subharmonic motion in the process of analysis is shown to exist in two opposite phases, differing by pi radians. The resulting phase of periodic vibration depends upon initial conditions. The isocline graphical method is used to depict the transient motion. The effective non-linearity is determined to be governed by the influence of gravity effects on the equilibrium of moition. The pronounced subharmonics are of the order one half, and the extinction conditions for the resonance predominant over the higher orders ere investigated through expressing the limiting inequalities in terms of the system parameters. In the critical state, complete suppression of the subharmonics is achieved. The limiting condition is then examined where damping is fixed at a convenient minimum value and the corresponding optimum limit of gravity effect tolerable can be evaluated for which the amplitude of excitation has no influence on the effective non-linearity as regard to exciting the resonance. As inequality is also presented from which the limiting frequencies of the subharmonic vibration can be predicted with reasonable accuracy. In these investigations the limiting inequalities are not dependant on the resulting variables in the non linear phenomena. An experimental test-rig is designed to demonstrate the subharmonic response. The values recorded from it compare favourably with the approximated theoretical results and with the experimental results obtained from the electronic analogue computer