Generations and mechanisms of multi-stripe chaotic attractors of fractional order dynamic system

In this paper, the generations of multi-stripe chaotic attractors of fractional order system are considered. The original fractional order chaotic attractors can be turned into a pattern with multiple “parallel” or “ rectangular” stripes by employing certain simple periodic nonlinear functions. The relationships between the parameters relate to the periodic functions and the shape of the generated attractors are analyzed. Theoretical investigations about the underlying mechanisms of the parallel striped attractors of fractional order system are presented, with the fractional order Lorenz, Rössler and Chua’s systems as examples. Moreover, the periodic doubling striped route to chaos of fractional order Rössler system and maximum Lyaponov exponent calculations are also given.