We investigate the instability of two-layer Phillips model in this paper, which is a prototypical geophysical fluid model. Using the results of Guo and Strauss et al, we obtained linear instability implies nonlinear instability provided the linearized system has an exponentially growing solution.
This paper is concerned with the bifurcation of a complex Swift-Hohenberg equation. The attractor bifurcation of the complex Swift-Hohenberg equation on a one- dimensional domain (0, L) is investigated. It is shown that the n-dimensional complex Swift-Hohenberg equation bifurcates from the trivial solution to an attractor under the Dirichlet boundary condition on a general domain and under a periodic boundary condi- tion when the bifurcation parameter crosses some critical values. The stability property of the bifurcation attractor is analyzed.
