Research on Chaos Control
I have carried out research in this topic in collaboration with Dr.
J. Güémez (from the Universidad de Cantabria). We introduced
a new method that works by applying perturbations to the variables of the
chaotic system. These perturbations can yield a transition of the system
to regular behavior, if the parameters are judiciously chosen. The following
papers contain our results in this field:
- J. Güémez and M.A. Matías, Control of
chaos in unidimensional maps, Physics Letters A 181,
29-32 (1993).
- M.A. Matías and J. Güémez, Stabilization of chaos
by proportional pulses in the system variables, Physical Review Letters,
72, 1455-1458 (1994).
- J. Güémez, J.M. Gutiérrez, A. Iglesias, and M.A.
Matías, Stabilization of periodic and quasiperiodic motion in
chaotic systems through changes in the system variables, Physics Letters
A, 190, 429-433 (1994).
- J. Güémez, J.M. Gutiérrez, A. Iglesias, and M.A.
Matías, Suppression of chaos through changes in the system variables:
transient chaos and crises, Physica D, 79, 164-173 (1994).
- M.A. Matías and J. Güémez, Chaos suppression
in flows using proportional pulses in the system variables, Physical
Review E, 54, 198-209 (1996).
- J.M. Gutiérrez, A. Iglesias, J. Güémez, and M.A.
Matías, Suppression of chaos through changes in the system variables
through Poincaré and Lorenz maps, International Journal of Bifurcation
and Chaos, 6, 1351-1362 (1996).
- A. Iglesias, J.M. Gutiérrez, J. Güémez, and M.A.
Matías, Chaos Suppression through changes in the system variables
and numerical rounding errors, Chaos, Solitons, and Fractals 7,
1305-1316 (1996).
Nonlinear Physics Group at Salamanca