Safe, explosive, and dangerous bifurcations in dissipative dynamical systems

Journal Article · Mon Jan 31 23:00:00 EST 1994 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States)

DOI:https://doi.org/10.1103/PhysRevE.49.1019· OSTI ID:5217586

Thompson, J M.T. ^[1]; Stewart, H B ^[2]; Ueda, Y ^[3]

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1. Centre for Nonlinear Dynamics and Its Applications, Civil Engineering Building, University College London, Gower Street, London WC1E6BT (United Kingdom)
2. Mathematical Sciences Group, Building 490-A, Department of Applied Science, Brookhaven National Laboratory, Upton, New York 11973 (United States)
3. Department of Electrical Engineering, Kyoto University, Kyoto 606 (Japan)

A comprehensive listing of the generic codimension-1 attractor bifurcations of dissipative dynamical systems is presented. It includes local and global bifurcations of regular and chaotic attractors. The bifurcations are classified according to the continuity or discontinuity of the attractor path, which governs the physical outcome that would be observed under a slow control sweep. Related issues of determinacy, hysteresis, basin structure, and intermittency are addressed. Recently discovered chaotic bifurcations are discussed in some detail, with particular reference to the regular or chaotic saddle-type destroyer with which an attractor may collide.

• DOE Contract Number: AC02-76CH00016
• OSTI ID: 5217586
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States), Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States) Vol. 49:2; ISSN PLEEE8; ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

661300 -- Other Aspects of Physical Science-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
ATTRACTORS
CONTROL THEORY
HYSTERESIS
MATHEMATICAL SPACE
MATHEMATICS
PHASE SPACE
SPACE
STOCHASTIC PROCESSES
TOPOLOGY