Phase Portrait for ODE Not Turning Out As Expected

I am running local analyses on the critical points of the system of ODE below:

eq1 = -s1 + (1 - x1)*(1 - s1)*(a0*a4)/(1 - s1 + a1); eq2 = (1 - x1)*(a8 + a9 - (a0*(1 - s1))/(1 - s1 + a1)); eq3 = -s2 - (1 - x1)*(1 - s1)*(a0*a5)/(1 - s1 + a1) + (1 - x2)*(1 - s2)*(a2*a6)/(1 - s2 + a3 + a7*(1 - s2)^2); eq4 = (1 - x2)*(a8 + a10 - (a2*(1 - s2))/(1 - s2 + a3 + a7*(1 - s2)^2)); 

There are 6 critical points, and two of them (CP3 and CP6) are supposed to be asymptotically stable. I got nice plots ie phase portraits and time series for the first two critical points, but CP3 onwards are giving me grief. I either get a plot where the trajectories do not scale nicely or I get plots where there are empty areas where there should be trajectories.

I tried increasing the plot range in case there’s a bigger pattern I’m not capturing… I tried decreasing the plot range in case my plot weren’t “local” enough… I also tried different ways to define my vectors and arrows.

I'm not sure if the problem is because the ODE system itself is not behaving or because my code needs to be fixed. Here's the current version of my code:

params = {a0 -> 20.97055105, a1 -> 0.021621597, a2 -> 1.963662112, a3 -> 1.217960436, a4 -> 0.01100415, a5 -> 0.016340502, a6 -> 32.71694378, a7 -> 2.907136946, a8 -> 0.148074792, a9 -> 1.599070101, a10 -> 0.069124399,a11 -> 137.1688473}; rule = Solve[{eq1, eq2, eq3, eq4} == 0, {s1, s2, x1, x2}]; cplst = {{s1, x1}, {s2, x2}} /. rule /. params; cp03 = cplst[[3]] (*{{0.998034892335493, -50.911108178852665}, {-1.6050719877417985, 1.0173161380903484}} *) {{s1valcp3, x1valcp3}, {s2valcp3, x2valcp3}} = cp03; (* Phase Portrait for (s1,x1) *) s1rangecp3 = {0.95, 1.05};(* Centered around s1=1 *) x1rangecp3 = {-50.95, -50.85}; (* Centered around x1=-51 *) (* Define vector field*) vecField = {eq1, eq2} /. params; (* Plot phase portrait *) StreamPlot[vecField, {s1, s1rangecp3[[1]], s1rangecp3[[2]]}, {x1, x1rangecp3[[1]], x1rangecp3[[2]]}, StreamPoints -> Fine, StreamStyle -> Arrowheads[0.015], StreamColorFunction -> Function[{x, y, vx, vy}, ColorData["Rainbow"][Rescale[Sqrt[vx^2 + vy^2], {0, 5}]]], StreamColorFunctionScaling -> False, PlotLabel -> Style["Critical Point 3: (s1, x1) Phase Portrait", 14, Bold], Epilog -> {Red, PointSize[Large], Point[{s1valcp3, x1valcp3}]}, FrameLabel -> {"s1", "x1"}, ImageSize -> Large] 

I got a slightly better phase portrait after editing my code but I'm still not seeing asymptotically stable behavior. How can I fix this?

Thanks in advance.