Minimum transition values and the dynamics of subcritical bifurcation

Journal Article · Tue Apr 01 04:00:00 EST 1986 · SIAM J. Appl. Math.; (United States)

DOI:https://doi.org/10.1137/0146014· OSTI ID:5738657

Tu, S; Reiss, E L

Perturbation and asymptotic methods are presented for analyzing a class of subcritical bifurcation problems whose solutions possess minimum transition values. These minimum transition values are determined. In addition, the dynamics of the transitions from the basic state to the larger amplitude bifurcation states are obtained. The effects of imperfections on the response of the systems are also investigated. The method is presented for two model problems. However, it is valid for a wide class of problems in elastic and hydrodynamic stability, in reaction-diffusion systems and in other applications. In the first problem the authors obtain subcritical steady bifurcation states for a one-dimensional nonlinear diffusion problem. In the second problem they consider the subcritical Hopf bifurcation of periodic solutions for a higher order van der Pol-Duffing oscillator.

• Research Organization: Dept. of Engineering Sciences and Applied Mathematics, Northwestern Univ., Evanston, IL 60201
• OSTI ID: 5738657
• Journal Information: SIAM J. Appl. Math.; (United States), Journal Name: SIAM J. Appl. Math.; (United States) Vol. 46:2; ISSN SMJMA
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420800* -- Engineering-- Electronic Circuits & Devices-- (-1989)
AMPLITUDES
ASYMPTOTIC SOLUTIONS
DIFFUSION
ELASTICITY
ELECTRONIC EQUIPMENT
EQUIPMENT
FLUID MECHANICS
HYDRODYNAMICS
MECHANICAL PROPERTIES
MECHANICS
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
ONE-DIMENSIONAL CALCULATIONS
OSCILLATORS
PERTURBATION THEORY
STABILITY
STEADY-STATE CONDITIONS
TENSILE PROPERTIES