Dynamical analysis of fractional-order R?ssler and modified Lorenz systems

摘要

This Letter is devoted to the dynamical analysis of fractional-order systems, namely the R?ssler and a modified Lorenz system. The work here described compares the dynamical regimes of such fractional-order systems to that of the corresponding standard systems. It turns out that most of the chaotic attractors are topologically equivalent to those found in the original integer-order systems, although in some particular (and apparently rare) cases unusual bifurcation patterns and attractors are found.