Some Examples of Rossler MPSM
Providing and good initial guess will ensure a very fast convergence to true set of cycle points on the Poincaré section. Note that the guesses I provide always start on the Poincaré section; my choice was x=0.  Take one of the cycle points on the last iteration of the MPSM routine and try it as an initial condition for your rossler flow.  You can use the cycle visualizer for this.

(*2 cycle*)
initguess={{0,3.4,3.5},{0,6.8,0.02}};
MPSA[initguess,2,3,{1,0,0},0.2,0.2,5.7];

(*3 cycle*)
initguess={{0,4.5,0.04},{0,7.0,0.1},{0,3.4,7.5}};
MPSA[initguess,3,4,{1,0,0},0.2,0.2,5.7];

(*3 cycle*)
initguess={{0,2,2},{0,8,0.1},{0,6,7.5}};
MPSA[initguess,3,6,{1,0,0},0.2,0.2,5.7];

(*4 cycle*)
initguess={{0,6.5,0},{0,5.7,2},{0,7,0.7},{0,3.5,4.7}};
MPSA[initguess,4,4,{1,0,0},0.2,0.2,5.7];

(*5 cycle*)
initguess={{0,2.28,0.058},{0,5.59,1.68},{0,7.11,0.66},{0,3.41,4.6},{0,6.2,0.05}};
MPSA[initguess,5,4,{1,0,0},0.2,0.2,5.7];

(*5 cycle*)
initguess={{0,6.28,0.058},{0,5.59,1.68},{0,7.11,0.66},{0,3.41,4.6},{0,6.2,0.05}};
MPSA[initguess,5,4,{1,0,0},0.2,0.2,5.7];