(*limit cycle, p.979*)
miu=0.1
b=1
omega=1
s1=NDSolve[{r'[t]==miu*r[t]-(r[t])^3,theta'[t]==omega+b*(r[t])^2,r[0]==2.5,theta[0]==0.},{r,theta},{t,0,10.}]
s2=NDSolve[{r'[t]==miu*r[t]-(r[t])^3,theta'[t]==omega+b*(r[t])^2,r[0]==0.1,theta[0]==0.},{r,theta},{t,0,10.}]
ParametricPlot[Evaluate[{{r[t]*Sin[theta[t]],r[t]*Cos[theta[t]]}/.s1,{r[t]*Sin[theta[t]],r[t]*Cos[theta[t]]}/.s2}],{t,0,10.},PlotStyle->{{GrayLevel[0.],Thickness[0.015]},{GrayLevel[0.],Thickness[0.015],Dashed,RGBColor[1.,0.,0.]}}]
miu=0.1
b=1
omega=1
s1=NDSolve[{r'[t]==miu*r[t]-(r[t])^3,theta'[t]==omega+b*(r[t])^2,r[0]==2.5,theta[0]==0.},{r,theta},{t,0,15.}]
s2=NDSolve[{r'[t]==miu*r[t]-(r[t])^3,theta'[t]==omega+b*(r[t])^2,r[0]==0.1,theta[0]==0.},{r,theta},{t,0,15.}]
ParametricPlot[Evaluate[{{r[t]*Sin[theta[t]],r[t]*Cos[theta[t]]}/.s1,{r[t]*Sin[theta[t]],r[t]*Cos[theta[t]]}/.s2}],{t,0,15.},PlotStyle->{{GrayLevel[0.],Thickness[0.015]},{GrayLevel[0.],Thickness[0.015],Dashed,RGBColor[1.,0.,0.]}}]
miu=0.1
b=1
omega=1
s1=NDSolve[{r'[t]==miu*r[t]-(r[t])^3,theta'[t]==omega+b*(r[t])^2,r[0]==2.5,theta[0]==0.},{r,theta},{t,0,20.}]
s2=NDSolve[{r'[t]==miu*r[t]-(r[t])^3,theta'[t]==omega+b*(r[t])^2,r[0]==0.1,theta[0]==0.},{r,theta},{t,0,20.}]
ParametricPlot[Evaluate[{{r[t]*Sin[theta[t]],r[t]*Cos[theta[t]]}/.s1,{r[t]*Sin[theta[t]],r[t]*Cos[theta[t]]}/.s2}],{t,0,20.},PlotStyle->{{GrayLevel[0.],Thickness[0.015]},{GrayLevel[0.],Thickness[0.015],Dashed,RGBColor[1.,0.,0.]}}]
miu=0.1
b=1
omega=1
s1=NDSolve[{r'[t]==miu*r[t]-(r[t])^3,theta'[t]==omega+b*(r[t])^2,r[0]==2.5,theta[0]==0.},{r,theta},{t,0,30.}]
s2=NDSolve[{r'[t]==miu*r[t]-(r[t])^3,theta'[t]==omega+b*(r[t])^2,r[0]==0.1,theta[0]==0.},{r,theta},{t,0,30.}]
ParametricPlot[Evaluate[{{r[t]*Sin[theta[t]],r[t]*Cos[theta[t]]}/.s1,{r[t]*Sin[theta[t]],r[t]*Cos[theta[t]]}/.s2}],{t,0,30.},PlotStyle->{{GrayLevel[0.],Thickness[0.015]},{GrayLevel[0.],Thickness[0.015],Dashed,RGBColor[1.,0.,0.]}}]