Dòng Nội dung
1
A survey of nonlinear dynamics : "chaos theory" / R. L. Ingraham
Singapore : World Scientific, 1992
107 pages. : illustrations ; 22 cm.
Ký hiệu phân loại (DDC): 531.113
This is a concise introduction to nonlinear dynamics (or "chaos theory"). Among the topics covered are pde dynamics and Galerkin approximations, critical phenomena and renormalization group approach to critical exponents. Various levels and meanings of chaos are summarized.
 Số bản sách: (1) Tài liệu số: (0)
2
Bifurcations and chaos in piecewise-smooth dynamical systems /Zhanybai T. Zhusubaliyev, Erik Mosekilde
Singapore : World Scientific, 2003
xii, 363 pages. : illustrations ; 27 cm.
Ký hiệu phân loại (DDC): 515.3
Technical problems often lead to differential equations with piecewise-smooth right-hand sides. Problems in mechanical engineering, for instance, violate the requirements of smoothness if they involve collisions, finite clearances, or stick-slip phenomena. Systems of this type can display a large variety of complicated bifurcation scenarios that still lack a detailed description.This book presents some of the fascinating new phenomena that one can observe in piecewise-smooth dynamical systems. The practical significance of these phenomena is demonstrated through a series of well-documented and realistic applications to switching power converters, relay systems, and different types of pulse-width modulated control systems. Other examples are derived from mechanical engineering, digital electronics, and economic business-cycle theory.The topics considered in the book include abrupt transitions associated with modified period-doubling, saddle-node and Hopf bifurcations, the interplay between classical bifurcations and border-collision bifurcations, truncated bifurcation scenarios, period-tripling and -quadrupling bifurcations, multiple-choice bifurcations, new types of direct transitions to chaos, and torus destruction in nonsmooth systems.In spite of its orientation towards engineering problems, the book addresses theoretical and numerical problems in sufficient detail to be of interest to nonlinear scientists in general.
 Số bản sách: (4) Tài liệu số: (0)
3
Frequency-domain approach to Hopf bifurcation analysis : continuous time-delayed systems / Franco Sebastián Gentile, Jorge L. Moiola, G. Chen
Singapore : World Scientific, 2020
xiv, 378 pages. : illustrations ; 25 cm.
Ký hiệu phân loại (DDC): 515.352
This book is devoted to the study of an effective frequency-domain approach, based on systems control theory, to compute and analyze several types of standard bifurcation conditions for general continuous-time nonlinear dynamical systems. A very rich pictorial gallery of local bifurcation diagrams for such nonlinear systems under simultaneous variations of several system parameters is presented. Some higher-order harmonic balance approximation formulas are derived for analyzing the oscillatory dynamics in small neighborhoods of certain types of Hopf and degenerate Hopf bifurcations. The frequency-domain approach is then extended to the large class of delay-differential equations, where the time delays can be either discrete or distributed. For the case of discrete delays, two alternatives are presented, depending on the structure of the underlying dynamical system, where the more general setting is then extended to the case of distributed time-delayed systems. Some representative examples in engineering and biology are discussed
 Số bản sách: (1) Tài liệu số: (0)
4
Perturbation methods, instability, catastrophe, and chaos / C F Chan Man Fong ; D De Kee
Singapore ; River Edge, N.J : World Scientific, 1999
260 p. : illustrations ; 29 cm.
Ký hiệu phân loại (DDC): 515.35
This text introduces perturbation and qualitative methods for differential equations for students with only a basic knowledge of calculus and ordinary linear differential equations. Theorems are applied to solve examples and ideas are introduced via concepts familiar to the reader.
 Số bản sách: (10) Tài liệu số: (0)