Nonlinear Sciences – Chaotic Dynamics
Scientific paper
1994-02-22
Nonlinear Sciences
Chaotic Dynamics
56 pages, Int. Journal of Bifurcation and Chaos, vol. 3, no. 4, 803-42, 1993. Uudecode to obtain bog.tar.Z, uncompress bog.tar
Scientific paper
We investigate the bifurcations and basins of attraction in the Bogdanov map, a planar quadratic map which is conjugate to the H\'enon area-preserving map in its conservative limit. It undergoes a Hopf bifurcation as dissipation is added, and exhibits the panoply of mode locking, Arnold tongues, and chaos as an invariant circle grows out, finally to be destroyed in the homoclinic tangency of the manifolds of a remote saddle point. The Bogdanov map is the Euler map of a two-dimensional system of ordinary differential equations first considered by Bogdanov and Arnold in their study of the versal unfolding of the double-zero-eigenvalue singularity, and equivalently of a vector field invariant under rotation of the plane by an angle $2\pi$. It is a useful system in which to observe the effect of dissipative perturbations on Hamiltonian structure. In addition, we argue that the Bogdanov map provides a good approximation to the dynamics of the Poincar\'e maps of periodically forced oscillators.
Arrowsmith David K.
Cartwright Julyan H. E.
Lansbury Alexis N.
Place Colin M.
No associations
LandOfFree
The Bogdanov Map: Bifurcations, Mode Locking, and Chaos in a Dissipative System does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Bogdanov Map: Bifurcations, Mode Locking, and Chaos in a Dissipative System, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Bogdanov Map: Bifurcations, Mode Locking, and Chaos in a Dissipative System will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-123998