Dynamical analysis of fractional-order Rössler and modified Lorenz systems

• The fractional order q acts as a bifurcation parameter.
• In most of the cases, q<1q<1 (q>1q>1) reduces (increases) the complexity of the dynamics.
• Most of the solutions to fractional-order systems are topologically equivalent to solution of the original system with a displacement in the parameter space.
• Rarely, solutions are found not to correspond to any solution of the original system, but “numerical instabilities” are suspected in these cases.

This Letter is devoted to the dynamical analysis of fractional-order systems, namely the Rössler 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.