# Finding Oscillations

I am looking to find oscillations for my work and I'm wondering if there is a specific technique to finding it? Currently I am moving the parameters to find some sort of oscillation, however I'm not finding consistent steady oscillation. If anyone is able to help point me in the correct direction that would help. Below is what I am working on in the answers area, my code works but I'm not sure what I should look to move specifically to find the stable oscillation. Thanks in advance.

sol=ParametricNDSolveValue[{x'[t] ==c1+ (g1*((y[t]^3)/(a+y[t]^3))*(b/(b+x[t]^3)))-k1*x[t],y'[t]==c2+(g2*(d/(d+x[t]^3)))-k2* y[t]  ,x[0] == y[0] ==0},{x, y},{t, 0,500},{g1,g2,a,b,c1,c2,k1,k2,d}] Manipulate[Plot[Evaluate[#[t]&/@sol[g1,g2,a,b,c1,c2,k1,k2,d]],{t,0,100},PlotLegends->{x,y}],{{g1,20},0,50},{{g2,20.1},0,50}, {{a,3},0,20},{{b,0.3},0,50},{{c1,0.21},0,5},{{c2,0.3},0,5},{{k1,1.46},0,5},{{k2,0.5},0,5},{{d,0.19},0,50}]


When you copy in the code, you just need to press enter in front of the word "Manipulate" to drop it down onto a separate line (as shown in the picture), and then it will run.

• Note, you have a typo in your code, a space is missing: "k1x[t]" should read: "k1 x[t]" Nov 23, 2022 at 19:51
• What code? Please include a working example. Nov 23, 2022 at 20:43
• I have attached an image to explain, sorry. Nov 23, 2022 at 20:50
• Please directly post the Mathematica code which can be copy and run,not the picture. Nov 23, 2022 at 23:08
• Thanks for letting me know, I have added the code. I'm new to using the program so wasn't too sure how to do it initially Nov 24, 2022 at 10:00

Runnable Code!

sol = ParametricNDSolveValue[{x'[t] ==
c1 + (g1*((y[t]^3)/(a + y[t]^3)) (b/(b + x[t]^3))) - k1*x[t],
y'[t] == c2 + (g2*(d/(d + x[t]^3))) - k2*y[t],
x[0] == y[0] == 0}, {x, y}, {t, 0, 500}, {g1, g2, a, b, c1, c2, k1,
k2, d}]

Manipulate[
Plot[Evaluate[#[t] & /@ sol[g1, g2, a, b, c1, c2, k1, k2, d]], {t, 0,
50}, PlotLegends -> {x, y}], {{g1, 20}, 0, 50}, {{g2, 20.1}, 0,
50}, {{a, 3}, 0, 20}, {{b, 0.3}, 0, 50}, {{c1, 0.21}, 0,
5}, {{c2, 0.3}, 0, 5}, {{k1, 1.46}, 0, 5}, {{k2, 0.5}, 0,
5}, {{d, 0.19}, 0, 50}]