Dynamics of a Hénon-Lozi type map
Chaos Solitons & Fractals, Vol. 12(12), pp 2323-2341, (2001).
Aziz Alaoui, M.A.(1),
Robert, C.(2), and Grebogi, C.(3)
(1) Labo. Math., Le Havre University, France.
(2) University of California, Santa
Barbara, California 93106, U.S.A.
Mathematics and Inst. Physical Science and Technology,
Univ. Maryland, College Park, Maryland 20742, U.S.A.
We present and analyze a smooth version of the piecewise linear Lozi map. The
principal motivation for this work is to develop a map, which is better
amenable for an analytical treatment as compared to the H\'enon map and is one that still
possesses the characteristics of a H\'enon-type dynamics. This paper is a first step.
It does the comparison of the Lozi map (which is a piecewise linear version
of the H\'enon map) with the map that we introduce.
This comparison is done for fixed parameters and also through global bifurcation
by changing a parameter. If $\varepsilon$ measures the degree of
smoothness, we prove that, as $\varepsilon\goes 0$, the stability and the
existence of the fixed points is the same for both maps.
We also numerically compare the chaotic dynamics, both in the form of an attractor and
of a chaotic saddle.
For an animated view of this new
attractor click here
Ref: M.A. Aziz Alaoui,
Preprint Univ. Le Havre. (Jan. 1999)
Back to the previous page
Back to Aziz Alaoui's home page