Format:
Online-Ressource (XI, 697p. 228 illus., 5 illus. in color, digital)
ISBN:
9783642224614
,
1280802936
,
9783642224607
,
9787040319576
,
9781280802935
Series Statement:
SpringerLink
Content:
Introduction -- Introduction to Flow Passability -- Singularity and Flow Passability -- Flow Barriers and Switchability -- Transport Laws and Multi-valued Vector Fields -- Switchability and Attractivity of Domain Flows -- Dynamics and Singularity of Boundary Flows -- Edge Dynamics and Switching Complexity -- Dynamical System Interactions.
Content:
“Discontinuous Dynamical Systems” presents a theory of dynamics and flow switchability in discontinuous dynamical systems, which can be as the mathematical foundation for a new dynamics of dynamical system networks. The book includes a theory for flow barriers and passability to boundaries in discontinuous dynamical systems that will completely change traditional concepts and ideas in the field of dynamical systems. Edge dynamics and switching complexity of flows in discontinuous dynamical systems are explored in the book and provide the mathematical basis for developing the attractive network channels in dynamical systems. The theory of bouncing flows to boundaries, edges and vertexes in discontinuous dynamical systems with multi-valued vector fields is described in the book as a “billiard” theory of dynamical system networks. The theory of dynamical system interactions in discontinued dynamical systems can be used as a general principle in dynamical system networks, which is applied to dynamical system synchronization. The book represents a valuable reference work for university professors and researchers in applied mathematics, physics, mechanics, and control. Dr. Albert C.J. Luo is an internationally respected professor in nonlinear dynamics and mechanics, and he works at Southern Illinois University Edwardsville, USA.
Note:
Description based upon print version of record
,
Title Page; Copyright Page; Preface; Table of Contents; Chapter 1 Introduction; 1.1. A brief history; 1.2. Book layout; References; Chapter 2 Introduction to Flow Passability; 2.1. Domain accessibility; 2.2. Discontinuous dynamical systems; 2.3. Flow passability; 2.4. Grazing flows; 2.5. Switching bifurcations of passable flows; 2.6. Switching bifurcations of non-passable flows; 2.7. An application: A frictional oscillator; 2.7.1. Grazing phenomena; 2.7.2. Sliding motion; References; Chapter 3 Singularity and Flow Passability; 3.1. Real and imaginary flows
,
3.2. G-functions and vector field decomposition3.3. Passable flows; 3.4. Non-passable flows; 3.5. Grazing flows; 3.6. Flow switching bifurcations; 3.7. First integral quantity increments; 3.8. An example; 3.8.1. Conditions for sliding and grazing; 3.8.2. Periodic motions; 3.9. Concluding remarks; References; Chapter 4 Flow Barriers and Switchability; 4.1. Flow barriers for passable flows; 4.1.1. Coming flow barriers; 4.1.2. Leaving flow barriers; 4.1.3. Passable flows with both flow barriers; 4.2. Flow barriers for sink flows; 4.3. Flow barriers for source flows; 4.3.1. Boundary flow barriers
,
4.3.2. Leaving flows barriers4.4. Sink flows with flow barriers; 4.5. An application; 4.5.1. Switchability conditions; 4.5.2. Illustrations; 4.6. Concluding remarks; References; Chapter 5 Transport Laws and Multi-valued Vector Fields; 5.1. Discontinuity classification; 5.2. Singular sets on boundary; 5.3. Forbidden boundary and boundary channels; 5.3.1. Forbidden boundary; 5.3.2. Boundary channels; 5.4. Domain and boundary classifications; 5.4.1. Domain classification; 5.4.2. Boundary classifications; 5.5. Transport laws; 5.6. Multi-valued vector fields and bouncing flows
,
5.6.1. Bouncing flows5.6.2. Extended passable flows; 5.7 A controlled piecewise linear system; 5.7.1. Passable and bouncing conditions; 5.7.2. Illustrations; References; Chapter 6 Switchability and Attractivity of Domain Flows; 6.1. Dynamical systems on edges; 6.2. Edge classification and mirror domains; 6.3. Domain flow properties to convex edges; 6.4. Domain flow switchability to convex edges; 6.5. Transverse grazing passability to concave edges; 6.6. Domains flow attractivity; 6.6.1. Attractivity to boundary; 6.6.2. Attractivity to edge; 6.7. Multi-valued vector fields switching at edges
,
6.7.1. Bouncing domain flows at edges6.7.2. Extended passable domain flows to edges; References; Chapter 7 Dynamics and Singularity of Boundary Flows; 7.1. Boundary flow properties; 7.2. Boundary flow switchability; 7.3. Switchability of boundary and domain flows; 7.4. Boundary flow attractility; 7.5. Boundary dynamics with multi-valued vector fields; 7.5.1. Bouncing boundary flows; 7.5.2. Extended passable boundary flows; References; Chapter 8 Edge Dynamics and Switching Complexity; 8.1. Edge flows; 8.2. Edge flow switchability; 8.3. Edge flow attractivity
,
8.4. Edge dynamics with multi-valued vector fields
Additional Edition:
ISBN 9783642224607
Additional Edition:
Buchausg. u.d.T. Luo, Albert C. J., 1964 - Discontinuous dynamical systems Beijing : Higher Education Press, 2012 ISBN 9787040319576
Additional Edition:
ISBN 3642224601
Additional Edition:
ISBN 9783642224607
Language:
English
Subjects:
Mathematics
Keywords:
Dynamisches System
;
Diskontinuierlicher Vorgang
;
Dynamisches System
;
Diskontinuierlicher Vorgang
DOI:
10.1007/978-3-642-22461-4
URL:
Volltext
(lizenzpflichtig)
Author information:
Luo, Albert C. J. 1964-
