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| DYNAMIC BIFURCATION OF NONLINEAR EVOLUTION EQUATIONS |
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Citation： |
MA Tian,WANG Shouhong.DYNAMIC BIFURCATION OF NONLINEAR EVOLUTION EQUATIONS[J].Chinese Annals of Mathematics B,2005,26(2):185~206 |
| Page view： 1280
Net amount： 883 |
Authors： |
MA Tian; WANG Shouhong |
Foundation： |
Project supported by the Office of Naval Research, the National Science Foundation, and the National
Natural Science Foundation of China (No.19971062). |
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| Abstract： |
The authors introduce a notion of dynamic bifurcation for nonlinear evolution equations,
which can be called attractor bifurcation. It is proved that as the control parameter
crosses certain critical value, the system bifurcates from a trivial steady state
solution to an attractor with dimension between m and m + 1, where m + 1 is the
number of eigenvalues crossing the imaginary axis. The attractor bifurcation theory
presented in this article generalizes the existing steady state bifurcations and the Hopf
bifurcations. It provides a unified point of view on dynamic bifurcation and can be
applied to many problems in physics and mechanics. |
Keywords： |
Attractor bifurcation, Steady state bifurcation, Dynamic bifurcation,
Hopf bifurcation, Nonlinear evolution equation |
Classification： |
37L, 35B32, 35K, 35Q, 47H |
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