Stability And Bifurcations Of Systems With Hysteresis And Multistable Systems
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Stability and Bifurcations of Systems with Hysteresis and Multistable Systems
Multistability is one of the complex phenomena that can be observed in the systems characterized by the slow and fast motions (the slow-fast systems). Hysteresis phenomena is closely related to multistability, since systems with hysteresis naturally appear as the limit of the slow-fast systems. This thesis attempts to develop methods of bifurcation analysis of such systems in application to the problems that stem from hydrology and laser physics. It consists of 3 parts, two of them consider the dynamics of systems with hysteresis and the third part is related to the multistable slow-fast systems. In the first part of the thesis the differential equations coupled with the input-output memory relation defined by the Preisach operator are considered. The differential equation relates an instant value of the rate of change of the output of the Preisach operator with an instant value of its input. An algorithm for the linearization of the evolution operator of the system is proposed, and it is applied to define the characteristic multiplier of periodic solutions, which determines their stability. Examples of the system considered include models of terrestrial hydrology. In the second part of the thesis the process of cyclic wetting and drying of soils due to changing weather conditions is considered in more detail. The presence of hysteresis in relationship between the pressure of matric potential and the water content in the soil is well documented. It suggests that there is substantial dissipation of energy associated with intermittent wetting and drying of the soil, which can be released in the form of heat. A combination of analytic and numerical methods is proposed to evaluate the energy dissipation rate due to soil-moisture hysteresis, and how it is affected by the variation of rain parameters. The last part focuses on dynamics of slow-fast systems, which are used to model the electric field propagation in semiconductor lasers. The bifurcation mechanisms of the development and break up of different operation regimes in a passively mode-locked monolithic semiconductor laser are studied by solving numerically partial differential equations for amplitudes of two counter-propagating waves and carrier densities in gain and absorber sections.
Chaotic Systems with Multistability and Hidden Attractors
This book presents a collection of new articles written by world-leading experts and active researchers to present their recent finding and progress in the new area of chaotic systems and dynamics, regarding emerging subjects of unconventional chaotic systems and their complex dynamics.It guide readers directly to the research front of the new scientific studies. This book is unique of its kind in the current literature, presenting broad scientific research topics including multistability and hidden attractors in unconventional chaotic systems, such as chaotic systems without equilibria, with only stable equilibria, with a curve or a surface of equilibria. The book describes many novel phenomena observed from chaotic systems, such as non-Shilnikov type chaos, coexistence of different types of attractors, and spontaneous symmetry breaking in chaotic systems. The book presents state-of-the-art scientific research progress in the field with both theoretical advances and potential applications. This book is suitable for all researchers and professionals in the areas of nonlinear dynamics and complex systems, including research professionals, physicists, applied mathematicians, computer scientists and, in particular, graduate students in related fields.
Introduction to Systems Biology
Author: Sangdun Choi
language: en
Publisher: Springer Science & Business Media
Release Date: 2008-05-17
Introduction to Systems Biology is an introductory text for undergraduate and graduate students who are interested in comprehensive biological systems. The authors provide a broad overview of the field using key examples and typical approaches to experimental design. The volume begins with an introduction to systems biology and then details experimental omics tools. Other sections introduce the reader to challenging computational approaches to help understand biological dynamic systems. The final sections of the volume provide ideas for theoretical and modeling optimization in systemic biological researches, presenting most algorithms as implementations, including an up-to-date full range of bioinformatic programs and available successful applications. Informative and cutting-edge, this volume presents a clear and intuitive illustration of the biological systemic approaches and introduces ideal computational methods for research. Introduction to Systems Biology is an indispensable resource, providing a first glimpse into the state-of-the-art in systems biology.