Double Hopf bifurcation induces coexistence of periodic oscillations in a diffusive Ginzburg-Landau model

Publication date: Available online 16 January 2019Source: Physics Letters AAuthor(s): Yanfei Du, Ben Niu, Yuxiao Guo, Jianquan LiAbstractWe perform bifurcation analysis in a complex Ginzburg-Landau system with delayed feedback under the homogeneous Neumann boundary condition. We calculate the amplitude death region, and it turns out that the boundary of the amplitude death region consists of two Hopf bifurcation curves with wave number zero. The existence conditions for double Hopf bifurcations are established. Taking the feedback strength and time delay as bifurcation parameters, normal forms truncated to the third order at double Hopf singularity are derived, and the unfolding near the critical points is given. The bifurcation diagram near the double Hopf bifurcation is drawn in the two-parameter plane. The phenomena of amplitude death, the existence of stable bifurcating periodic solutions, and the coexistence of two stable periodic solutions with fast oscillation and slow oscillation respectively are simulated.

Source: Physics Letters A - January 17, 2019 Category: Physics Source Type: research