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I have a system of two coupled equations which I have first examined without noise and have obtained a streamplot for it, to look at the trajectories. trajectories of the two coupled equations. Code for this is here:

V_x = 1;
Solve[{-Alpha1/R^2 - Subscript[V, X]*Sin[[Phi]] == 0, V_x*Cos[[Phi]]/R == 0}, {R, [Phi]}];

Manipulate[StreamPlot[{-Alpha1/R^2 - V_x*Sin[[Phi]], V_x*Cos[[Phi]]/R}, {R, 1, 10}, {[Phi], -2 \[Pi], 2 \[Pi]}], {\[Alpha]1, -1, 1}]

Now, I have added noise to the equations using Ito Process and am trying to do the same. I don't know how to go about doing so. Added noise to both R and Phi and now trying do a similar plot of Rdot vs. Phidot to see the trajectories.

\[Alpha]1 = -1; \[Phi]1 = \[Pi]/2;
Rwithnoise = ItoProcess[\[DifferentialD]R[t] == (-\[Alpha]1/R[t]^2 - V_x*Sin[[Phi]1]) dt + Sqrt[(2.451*10^-13)]*\[DifferentialD]w[t], R[t], {R, 1}, t, w \[Distributed] WienerProcess[]]
plot1 = RandomFunction[Rwithnoise, {0.0, 10.0, 0.01}]; ListLinePlot[plot1, Filling -> Axis]

Phiwithnoise = ItoProcess[\[DifferentialD]\[Phi][t] ==Sqrt[(2.451*10^-13)][DifferentialD]w[t], \[Phi][t], {\[Phi], 2 \[Pi]}, t, w \[Distributed] WienerProcess[]]
plot2 = RandomFunction[Phiwithnoise, {0.0, 10.0, 0.01}]; ListLinePlot[plot1, Filling -> Axis]

Any help is appreciated. Thanks.

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  • $\begingroup$ Result of copy-paste. It's the Vx you see in the image, which is treated to be 1. $\endgroup$ – Skidmore_TCIS Mar 18 '15 at 8:24

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