I am trying to plot the phase portrait of the following differential equation $$ \begin{cases} \dot{R}= aR+bJ\vert1-J\vert+f(t)\\ \dot{J}= cR\vert1-R\vert+dJ, \end{cases} \quad f(t)=5\sin(\pi t). $$
for $a=-7,\,b=-2,\,c=1,\,d=1$. The plot should look something like
but using the code
s[a_, b_] := a*R[t] + b*J[t]*Abs[1 - J[t]] + 5 Sin[\[Pi]*t];
h[c_, d_] := c*R[t]*Abs[1 - R[t]] + d*J[t];
StreamPlot[{s[-7, -2], h[1, 1]}, {R[t], 0, 5}, {J[t], 0, 5}]
does not give the desired result.
Setting the paramters to be a = −1.1, b = −2, c = 1, and d = 1 should give chaotic behavior, as shown below