$\dot x = r - x - e^{-x}$

Show[Plot[x + Exp[-x],{x,-1,0},PlotRange-{{-1,1},{-1,1}}],
     Plot[x + Exp[-x],{x,0,1},PlotRange-{{-1,1},{-1,1}},
PlotStyle->Dashing[{0.1,0.1,.01}]]]