Global Bifurcation of Periodic Solutions with Symmetry by Bernold Fiedler download in ePub, pdf, iPad
Moreover, we discuss how our theory justifies certain heuristic assumptions underlying previous approaches towards period preserving and period doubling bifurcation from periodic solutions. Applied Partial Differential Equations by J. The approach centers around the analysis of diffeomorphisms that are equivariant with respect to distinct group actions in the domain and the range. Discrete rotating waves are periodic solutions that have discrete spatiotemporal symmetries in addition to their purely spatial symmetries. We present a systematic approach to the study of local bifurcation from discrete rotating waves.
In one-parameter flows, Hopf bifurcation serves as a starting point for global paths of periodic orbits. We show that only the structure skew-symmetry of the feedback can be used to explain the instability, and manipulation of the structure mistuning can be used to suppress the instability.
However, these methods only delineate the possibilities in a modelindependent fashion. We describe how turning points, period doubling bifurcations and Hopf points along the branch of periodic solutions can be handled. Furthermore equivariant Hopf points and generic secondary bifurcations of periodic orbits with Zm -symmetry are treated. Mathematical tools contain bifurcation idea, transversality idea, and prevalent approximations.
In this paper, we discuss some recent developments in the understanding of generic bifurcation from periodic solutions with spatiotemporal symmetries. The main goal of this paper is a global continuation theorem for homoclinic solutions of autonomous ordinary differential equations with two real parameters. Our results are valid for dynamical systems with finite symmetry group, and more generally for bifurcations from isolated discrete rotating waves in dynamical systems with compact symmetry group. We tested the code with standard examples, e.
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