<<EquationTrekker`

r´=μr-(r^3);

EquationTrekker[{x'[t]==-y[t]+x[t](α-(x[t]^2+y[t]^2)),y'[t]==x[t]+y[t](α+(x[t]^2+y[t]^2)-(x[t]^2+y[t]^2)^2)}, {x,y}, {t,0, 1000},
PlotRange->{{-2,2},{-2,2}},
TrekParameters->{α-> 0}];

r´=μr+(r^3)-(r^5);

EquationTrekker[{x'[t]==-y[t]+x[t](α+(x[t]^2+y[t]^2)-(x[t]^2+y[t]^2)^2),y'[t]==x[t]+y[t](α+(x[t]^2+y[t]^2)-(x[t]^2+y[t]^2)^2)}, {x,y}, {t,0, 1000},
PlotRange->{{-2,2},{-2,2}},
TrekParameters->{α-> 0}];

EquationTrekker[{x'[t]==-y[t]+x[t](α+(x[t]^2+y[t]^2)-(x[t]^2+y[t]^2)^2),y'[t]==x[t]+y[t](α+(x[t]^2+y[t]^2)-(x[t]^2+y[t]^2)^2)}, {x,y}, {t,0, 1000},
PlotRange->{{-2,2},{-2,2}},
TrekParameters->{α-> -0.25}];

x´=μx-y+(xy^2) ; y´=x+μy+(y^3);

Clear[x,y]

EquationTrekker[{x'[t]==α x[t]-y[t]+x[t] y[t]^2,y'[t]==x[t]+α y[t]+y[t]^3}, {x,y}, {t,0, 1000},
PlotRange->{{-2,2},{-2,2}},
TrekParameters->{α-> 0}];

x'=y ; y'=μy+x-(x^2)+xy

EquationTrekker[{x'[t]==y[t],y'[t]==α y[t]+x[t]-((x[t])^2)+x[t] y[t]}, {x,y}, {t,0, 1000},
PlotRange->{{-2,2},{-2,2}},
TrekParameters->{α-> -2}];