J. Godelle & C. Letellier
Symbolic sequence statistical analysis for free liquid jets,
Physical Review E, 62 (6), 7973-7981, 2000.
O. Ménard, C. Letellier, J. Maquet & G. Gouesbet
Map modeling by using rational functions,
Physical Review E, 62 (5), 6325-6331, 2000.
O. Ménard, C. Letellier, J. Maquet, L. Le Sceller & G. Gouesbet
Analysis of a non synchronized sinusoidally driven dynamical system,
International Journal of Bifurcation & Chaos, 10 (7), 1759-1772, 2000.
A nonautonomous system, i.e. a system driven by an external force, is usually considered as being phase synchronized with this force. In such a case, the dynamical behavior is conveniently studied in an extended phase space Rm which is the product of the phase space Rm of the undriven system by an extra dimension associated with the external force. The analysis is then performed by taking advantage of the known period of the external force to defi-ne a Poincaré section relying on a stroboscopic sampling. Nevertheless, it may so happen that the phase synchronization does not occur. It is then more convenient to consider the nonautonomous system as an autonomous system incorporating the subsystem generating the driving force. In the case of a sinusoidal driving force, the phase space is Rm+2 instead of the usual extended phase space Rm x S1. It is also demonstrated that a global model may then be obtained by using m+ 2 dynamical variables with two variables associated with the driving force. The obtained model characterizes an autonomous system in contrast with a classical input/output model obtained when the driving force is considered as an input.
C. Letellier, S. Meunier-Guttin-Cluzel & G. Gouesbet
Topological invariants in period-doubling cascades,
Journal of Physics A, 33, 1809-1825, 2000.
C. Lainscsek, C. Letellier, J. Kadtke, G. Gouesbet & F. Schurrer
Equivariance identification using delay differential equations,
Physics Letters A, 265 (4), 264-273, 2000.