Author : Jorge L. Moiola
Publisher :
Page : 12 pages
File Size : 10,89 MB
Release : 1998
Category :
ISBN :
Hopf Bifurcations and Degeneracies in Chua's Circuit
Jorge L. Moiola
[PDF] Hopf Bifurcations And Degeneracies In Chuas Circuit eBook
Hopf Bifurcations And Degeneracies In Chuas Circuit Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Hopf Bifurcations And Degeneracies In Chuas Circuit book. This book definitely worth reading, it is an incredibly well-written.
2-d Quadratic Maps And 3-d Ode Systems: A Rigorous Approach
Zeraoulia Elhadj
Author : Zeraoulia Elhadj
Publisher : World Scientific
Page : 357 pages
File Size : 27,15 MB
Release : 2010-07-08
Category : Science
ISBN : 9814464791
This book is based on research on the rigorous proof of chaos and bifurcations in 2-D quadratic maps, especially the invertible case such as the Hénon map, and in 3-D ODE's, especially piecewise linear systems such as the Chua's circuit. In addition, the book covers some recent works in the field of general 2-D quadratic maps, especially their classification into equivalence classes, and finding regions for chaos, hyperchaos, and non-chaos in the space of bifurcation parameters.Following the main introduction to the rigorous tools used to prove chaos and bifurcations in the two representative systems, is the study of the invertible case of the 2-D quadratic map, where previous works are oriented toward Hénon mapping. 2-D quadratic maps are then classified into 30 maps with well-known formulas. Two proofs on the regions for chaos, hyperchaos, and non-chaos in the space of the bifurcation parameters are presented using a technique based on the second-derivative test and bounds for Lyapunov exponents. Also included is the proof of chaos in the piecewise linear Chua's system using two methods, the first of which is based on the construction of Poincaré map, and the second is based on a computer-assisted proof. Finally, a rigorous analysis is provided on the bifurcational phenomena in the piecewise linear Chua's system using both an analytical 2-D mapping and a 1-D approximated Poincaré mapping in addition to other analytical methods.
Analysis and Control of Nonlinear Systems with Stationary Sets
Jinzhi Wang
Author : Jinzhi Wang
Publisher : World Scientific
Page : 334 pages
File Size : 22,11 MB
Release : 2009
Category : Mathematics
ISBN : 981281471X
This book presents the analysis as well as methods based on the global properties of systems with stationary sets in a unified time-domain and frequency-domain framework. The focus is on multi-input and multi-output systems, compared to previous publications which considered only single-input and single-output systems. The control methods presented in this book will be valuable for research on nonlinear systems with stationary sets.
Hopf Bifurcation Analysis: A Frequency Domain Approach
Guanrong Chen
Author : Guanrong Chen
Publisher : World Scientific
Page : 346 pages
File Size : 45,23 MB
Release : 1996-04-09
Category : Science
ISBN : 9814499102
This book is devoted to the frequency domain approach, for both regular and degenerate Hopf bifurcation analyses. Besides showing that the time and frequency domain approaches are in fact equivalent, the fact that many significant results and computational formulas obtained in the studies of regular and degenerate Hopf bifurcations from the time domain approach can be translated and reformulated into the corresponding frequency domain setting, and be reconfirmed and rediscovered by using the frequency domain methods, is also explained. The description of how the frequency domain approach can be used to obtain several types of standard bifurcation conditions for general nonlinear dynamical systems is given as well as is demonstrated a very rich pictorial gallery of local bifurcation diagrams for nonlinear systems under simultaneous variations of several system parameters. In conjunction with this graphical analysis of local bifurcation diagrams, the defining and nondegeneracy conditions for several degenerate Hopf bifurcations is presented. With a great deal of algebraic computation, some higher-order harmonic balance approximation formulas are derived, for analyzing the dynamical behavior in small neighborhoods of certain types of degenerate Hopf bifurcations that involve multiple limit cycles and multiple limit points of periodic solutions. In addition, applications in chemical, mechanical and electrical engineering as well as in biology are discussed. This book is designed and written in a style of research monographs rather than classroom textbooks, so that the most recent contributions to the field can be included with references.
Nonlinear Systems, Vol. 1
Victoriano Carmona
Author : Victoriano Carmona
Publisher : Springer
Page : 428 pages
File Size : 32,15 MB
Release : 2018-09-15
Category : Science
ISBN : 3319667661
This book is part of a two volume set which presents the analysis of nonlinear phenomena as a long-standing challenge for research in basic and applied science as well as engineering. It discusses nonlinear differential and differential equations, bifurcation theory for periodic orbits and global connections. The integrability and reversibility of planar vector fields and theoretical analysis of classic physical models are sketched. This first volume concentrates on the mathematical theory and computational techniques that are essential for the study of nonlinear science, a second volume deals with real-world nonlinear phenomena in condensed matter, biology and optics.
Bifurcations in Continuous Piecewise Linear Differential Systems
Enrique Ponce
Author : Enrique Ponce
Publisher : Springer Nature
Page : 317 pages
File Size : 30,90 MB
Release : 2022-12-10
Category : Mathematics
ISBN : 3031211359
The book is devoted to the qualitative study of differential equations defined by piecewise linear (PWL) vector fields, mainly continuous, and presenting two or three regions of linearity. The study focuses on the more common bifurcations that PWL differential systems can undergo, with emphasis on those leading to limit cycles. Similarities and differences with respect to their smooth counterparts are considered and highlighted. Regarding the dimensionality of the addressed problems, some general results in arbitrary dimensions are included. The manuscript mainly addresses specific aspects in PWL differential systems of dimensions 2 and 3, which are sufficinet for the analysis of basic electronic oscillators. The work is divided into three parts. The first part motivates the study of PWL differential systems as the natural next step towards dynamic complexity when starting from linear differential systems. The nomenclature and some general results for PWL systems in arbitrary dimensions are introduced. In particular, a minimal representation of PWL systems, called canonical form, is presented, as well as the closing equations, which are fundamental tools for the subsequent study of periodic orbits. The second part contains some results on PWL systems in dimension 2, both continuous and discontinuous, and both with two or three regions of linearity. In particular, the focus-center-limit cycle bifurcation and the Hopf-like bifurcation are completely described. The results obtained are then applied to the study of different electronic devices. In the third part, several results on PWL differential systems in dimension 3 are presented. In particular, the focus-center-limit cycle bifurcation is studied in systems with two and three linear regions, in the latter case with symmetry. Finally, the piecewise linear version of the Hopf-pitchfork bifurcation is introduced. The analysis also includes the study of degenerate situations. Again, the above results are applied to the study of different electronic oscillators.
Definitive Analysis of Hopf Bifurcations in the Centrifugal Governor
Hailu Teju
Author : Hailu Teju
Publisher :
Page : 84 pages
File Size : 20,63 MB
Release : 2007
Category :
ISBN : 9781109993714
A steam engine with Watt's centrifugal governor was formerly analyzed by Vyshnegradskii ([Vys76], 1876). A simplified version of Vyshnegradskii's analysis was then presented by Pontryagin ([Pon62], 1962) in his book on ordinary differential equations. A more complete analysis of the classical (non-degenerate) Hopf bifurcations of the centrifugal governor was given by Hassard ([Has79], 1979), and by Hassard, Kazarinoff and Wan ([HKW81], 1981) in their book on Theory and Applications of Hopf bifurcation. In this thesis we analyze the degenerate Hopf bifurcations of the centrifugal governor by studying the recognition problems for (topological) normal forms, as well as the recognition problems for (singularity theoretic) normal forms and universal unfoldings along a certain curve in the parameter space of the centrifugal governor. We also show that the centrifugal governor, in fact, undergoes a doubly degenerate (or codimension three) Hopf bifurcation and we locate this doubly degenerate Hopf bifurcation point.
Bifurcation Control
Guanrong Chen
Author : Guanrong Chen
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 26,52 MB
Release : 2003-08-26
Category : Technology & Engineering
ISBN : 9783540403418
Bifurcation control refers to the task of designing a controller that can modify the bifurcation properties of a given nonlinear system, so as to achieve some desirable dynamical behaviors. There exists no similar control theory-oriented book available in the market that is devoted to the subject of bifurcation control, written by control engineers for control engineers. World-renowned leading experts in the field provide their state-of-the-art survey about the extensive research that has been done over the last few years in this subject. The book is not only aimed at active researchers in the field of bifurcation control and its applications, but also at a general audience in related fields.
Hopf Bifurcation Analysis
Jorge L. Moiola
Author : Jorge L. Moiola
Publisher : World Scientific
Page : 354 pages
File Size : 10,93 MB
Release : 1996
Category : Mathematics
ISBN : 9789810226282
This book is devoted to the frequency domain approach, for both regular and degenerate Hopf bifurcation analyses. Besides showing that the time and frequency domain approaches are in fact equivalent, the fact that many significant results and computational formulas obtained in the studies of regular and degenerate Hopf bifurcations from the time domain approach can be translated and reformulated into the corresponding frequency domain setting, and be reconfirmed and rediscovered by using the frequency domain methods, is also explained. The description of how the frequency domain approach can be used to obtain several types of standard bifurcation conditions for general nonlinear dynamical systems is given as well as is demonstrated a very rich pictorial gallery of local bifurcation diagrams for nonlinear systems under simultaneous variations of several system parameters. In conjunction with this graphical analysis of local bifurcation diagrams, the defining and nondegeneracy conditions for several degenerate Hopf bifurcations is presented. With a great deal of algebraic computation, some higher-order harmonic balance approximation formulas are derived, for analyzing the dynamical behavior in small neighborhoods of certain types of degenerate Hopf bifurcations that involve multiple limit cycles and multiple limit points of periodic solutions. In addition, applications in chemical, mechanical and electrical engineering as well as in biology are discussed. This book is designed and written in a style of research monographs rather than classroom textbooks, so that the most recent contributions to the field can be included with references.
Numerical Continuation Methods for Dynamical Systems
Bernd Krauskopf
Author : Bernd Krauskopf
Publisher : Springer
Page : 399 pages
File Size : 50,18 MB
Release : 2007-11-06
Category : Science
ISBN : 1402063563
Path following in combination with boundary value problem solvers has emerged as a continuing and strong influence in the development of dynamical systems theory and its application. It is widely acknowledged that the software package AUTO - developed by Eusebius J. Doedel about thirty years ago and further expanded and developed ever since - plays a central role in the brief history of numerical continuation. This book has been compiled on the occasion of Sebius Doedel's 60th birthday. Bringing together for the first time a large amount of material in a single, accessible source, it is hoped that the book will become the natural entry point for researchers in diverse disciplines who wish to learn what numerical continuation techniques can achieve. The book opens with a foreword by Herbert B. Keller and lecture notes by Sebius Doedel himself that introduce the basic concepts of numerical bifurcation analysis. The other chapters by leading experts discuss continuation for various types of systems and objects and showcase examples of how numerical bifurcation analysis can be used in concrete applications. Topics that are treated include: interactive continuation tools, higher-dimensional continuation, the computation of invariant manifolds, and continuation techniques for slow-fast systems, for symmetric Hamiltonian systems, for spatially extended systems and for systems with delay. Three chapters review physical applications: the dynamics of a SQUID, global bifurcations in laser systems, and dynamics and bifurcations in electronic circuits.