Help with NDSolve inside Manipulate

Questions
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1

Guys please can you help me and tell me how to correct my code? I attached the file. i want to solve a system of 3 odes.

2 
step[k_, a_] := k HeavisidePi[t/a - 1/2]

Manipulate[
 Plot[Evaluate[{u[t], w[t], v[t]} /. 
    NDSolve[ {u'[t] == 
       step[10, 20] + \[Lambda]1*u[t]^2/(1 + u[t]^2) - Log2/120*u[t] -
         v[t]*\[Alpha]*u[t], 
      w'[t] == \[Lambda]1*u[t]^2/(1 + u[t]^2) - Log2/120*w[t], 
      v'[t] == \[Lambda]1*1/(1 + w[t]^2)*step[10, 20] + \[Beta] - 
        Log2/30*v[t], u[0] == w[0] == v[0] == 0}, {u, w, v}, {t, 0, 
      100}]], {t, 0, 100}], {{\[Alpha], 0, TraditionalForm[auxin]}, 0,
   10},
 {{\[Beta], 0, TraditionalForm[b]}, 0, 10},
 {{\[Lambda]1, 0, TraditionalForm[lamda1]}, 0, 10}]
3

The main problem is that Log2 is a function, not a number. I substituted Log[2] for it and moved the diff. eq. outside Manipulate to avoid recalculating the solution many times.

step[k_, a_] := k HeavisidePi[t/a - 1/2];
psol = ParametricNDSolveValue[{
    u'[t] == step[10, 20] + \[Lambda]1*u[t]^2/(1 + u[t]^2) - Log[2]/120*u[t] - v[t]*\[Alpha]*u[t],
    w'[t] == \[Lambda]1*u[t]^2/(1 + u[t]^2) - Log[2]/120*w[t],
    v'[t] == \[Lambda]1*1/(1 + w[t]^2)*step[10, 20] + \[Beta] - Log[2]/30*v[t],
    u[0] == w[0] == v[0] == 0},
   {u[t], w[t], v[t]},
   {t, 0, 100},
   {\[Alpha], \[Beta], \[Lambda]1}];


Manipulate[
 Plot[Evaluate@psol[\[Alpha], \[Beta], \[Lambda]1], {t, 0, 100}],
 {{\[Alpha], 0, TraditionalForm[auxin]}, 0, 10},
 {{\[Beta], 0, TraditionalForm[b]}, 0, 10},
 {{\[Lambda]1, 0, TraditionalForm[lamda1]}, 0, 10}]
4

oh ,yes. now it’s working. thank you very much!