sol=NDSolve[{x''[t]+0.1(3x[t]^2-1)x'[t]+x[t]==0,x[0]==0,x'[0]==-0.1},x,{t,0,100}]

Animate[ParametricPlot[Evaluate[{x[t],x'[t]}/.sol],{t,0,k},
PlotRange->{{-1.7,1.5},{-1.8,1.8}},PlotPoints->1000],
{k,0,100}]

sol2=NDSolve[{x'[t]==y[t]-x[t]^3+x[t],y'[t]==-0.5x[t],x[0]==0.2,y[0]==-0.1},
{x,y},{t,0,100}]

Animate[ParametricPlot[Evaluate[{x[t],y[t]}/. sol2],{t,0,k},
PlotRange->{{-2,2},{-2,2}}],{k,0,30}]

sol3=NDSolve[{x'[t]==a(y[t]-x[t]),y'[t]==b x[t]-y[t]-x[t]z[t],
z'[t]==x[t]y[t]-c z[t],
x[0]==0.5,y[0]==0.5,z[0]==0.5}/.{a-> 10,b->33,c->6},{x,y,z},{t,0,100}]

ParametricPlot3D[Evaluate[{x[t],y[t],z[t]}/.sol3],{t,0,45}]

Animate[ParametricPlot3D[Evaluate[{x[t],y[t],z[t]}/.sol3],{t,0,k},
AspectRatio->1,Axes->None, PlotRange->All,PlotPoints->4000],{k,0.1,100,1}]