Bifurcation from Discrete Rotating Waves
نویسندگان
چکیده
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. The approach centers around the analysis of diffeomorphisms that are equivariant with respect to distinct group actions in the domain and the range. 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.
منابع مشابه
Transition from Rotating Waves to Modulated Rotating Waves on the Sphere
In this article, we study parameter-dependent systems of reaction-diffusion equations on the sphere, which are equivariant under the group SO(3) of all rigid rotations on a sphere. Two main types of spatial-temporal patterns that can appear in such systems are rotating waves (equilibrium in a co-rotating frame) and modulated rotating waves (periodic solution in a corotating frame). The transiti...
متن کاملReversible Relative Periodic Orbits
We study the bundle structure near reversible relative periodic orbits in reversible equivariant systems. In particular we show that the vector eld on the bundle forms a skew product system, by which the study of bifurcation from reversible relative periodic solutions reduces to the analysis of bifurcation from reversible discrete rotating waves. We also discuss possibilities for drifts along g...
متن کاملA Hamiltonian Analogue of the Meandering Transition
In this paper a Hamiltonian analogue of the well-known meandering transition from rotating waves to modulated rotating and modulated travelling waves in systems with the Euclidean symmetry of the plane is presented. In non-Hamiltonian systems, for example in spiral wave dynamics, this transition is a Hopf bifurcation in a corotating frame, as external parameters are varied, and modulated travel...
متن کاملSpiral Meandering
The complex, so called meandering, dynamics of spiral waves in excitable media is examined from the point of view of bifurcation theory. A computational bifurcation analysis is made of spiral dynamics. It is shown that spiral meandering is organized in parameter space around a codimension-two point where a Hopf bifurcation from rotating waves interacts with symmetries on the plane. A simple mod...
متن کاملRotating and modulated rotating waves in transitions of an enclosed swirling flow
The transitions of the flow in an enclosed cylinder driven by the constant rotation of an endwall, from steady axisymmetric flow to aperiodic flow characterized by intermittent bursting dynamics where all the spatial and spatio-temporal symmetries have been broken, is studied numerically. The problem is controlled by two parameters, the Reynolds number and the cylinder aspect ratio. We vary the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1998