Visualizer for MPSM Rossler Results
Just put one of your estimated cycle points in for an initial condition (red text).

(*parameters*)
a=b=0.2;
c=5.7;

(*state equations: Rossler Flow*)
dxdt=x'[t]==-y[t]-z[t];
dydt=y'[t]==x[t]+a*y[t];
dzdt=z'[t]==b+z[t]*(x[t]-c);

(*enter one of the cycle points you found with the MPSM alg*)
{x1,x2,x3}={-5.798444864026705`*^-17,6.302598854074691`,1.1551009587648406`};
sect={};

runtime=40;
sect={};
sol=NDSolve[
{dxdt,
dydt,
dzdt,
x[0]==x1,
y[0]==x2,
z[0]==x3},
{x,y,z},
{t,0,runtime},
MaxSteps->Infinity,
MaxStepSize->0.01,
Method->{"EventLocator",
"Event"->x[t],Direction->-1,
EventAction:>{AppendTo[sect,{x[t],y[t],z[t]}]}}
];

ParametricPlot3D[{x[t],y[t],z[t]}/.sol,{t,0,runtime},BoxRatios->1,PlotRange->All]