Bifurcation of Nonlinear Equations: II. Dynamic Bifurcation
Copyright policy )Bifurcation of Nonlinear Equations: II. Dynamic Bifurcation
[Part 1 appeared ibid., 155--178 (1994; Zbl 1095.47027), see the preceding review.] The authors study dynamic bifurcation when the eigenvalue of the linearized problem has algebraic multiplicity one or two. As in the first part of the work for steady state bifurcations, their key idea is to analyze precisely the effect of the higher-order nondegenerate nonlinear terms. The obtained results provide a complete characterization of the bifurcation and the stability of bifurcated solutions for the indicated two cases. Bifurcated attractors are classified. An application to a system of nonlinear parabolic equations is given.
- DePaul University United States
- Sichuan University China (People's Republic of)
Bifurcations in context of PDEs, Bifurcation theory for ordinary differential equations, dynamic bifurcation, Applications of operator theory to differential and integral equations, periodic solutions, Nonlinear differential equations in abstract spaces, attractor bifurcation, Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems, stability of bifurcating solutions, Variational problems in abstract bifurcation theory in infinite-dimensional spaces, Attractors, Abstract bifurcation theory involving nonlinear operators, Periodic solutions to ordinary differential equations
Bifurcations in context of PDEs, Bifurcation theory for ordinary differential equations, dynamic bifurcation, Applications of operator theory to differential and integral equations, periodic solutions, Nonlinear differential equations in abstract spaces, attractor bifurcation, Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems, stability of bifurcating solutions, Variational problems in abstract bifurcation theory in infinite-dimensional spaces, Attractors, Abstract bifurcation theory involving nonlinear operators, Periodic solutions to ordinary differential equations
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