Tinkerbell map

The Tinkerbell map is a discrete-time dynamical system given by:

:$x\_\{n+1\}=x\_n^2-y\_n^2+ax\_n+by\_n,$

:$y\_\{n+1\}=2x\_ny\_n+cx\_n+dy\_n,$

Some commonly quoted values of a, b, c, and d are

* a=0.3, b=0.6, c=2, d=0.27.
* a=0.9, b=-0.6013, c=2, d=0.5.

ee also

* List of chaotic maps

References

* [http://www.macalester.edu/~kaplan/preprints/bremer.pdf C.L. Bremer & D.T. Kaplan, "Markov Chain Monte Carlo Estimation of Nonlinear Dynamics from Time Series"]
* K.T. Alligood, T.D. Sauer & J.A. Yorke, "Chaos: An Introduction to Dynamical Systems", Berlin: Springer-Verlag, 1996.
* [http://www.maths.ox.ac.uk/~mcsharry/papers/dynsys18n3p191y2003mcsharry.pdf P.E. McSharry & P.R.C. Ruffino, "Asymptotic angular stability in non-linear systems: rotation numbers and winding numbers"]
* [http://chaos1.la.asu.edu/~yclai/papers/PLA_01_DLKB.pdf R.L. Davidchack, Y.-C. Lai, A. Klebanoff & E.M. Bollt, "Towards complete detection of unstable periodic orbits in chaotic systems"]