Consider the following code:
In[1]:= Subscript[a, 11] = 1.0
Out[1]= 1.
In[2]:= Subscript[a, 12] = 0.0015
Out[2]= 0.0015
In[3]:= Subscript[a, 13] = 0.0055
Out[3]= 0.0055
In[4]:= Subscript[a, 21] = 0.5
Out[4]= 0.5
In[5]:= Subscript[a, 22] = 0.00025
Out[5]= 0.00025
In[6]:= Subscript[a, 23] = 0.0055
Out[6]= 0.0055
In[7]:= Subscript[d, 1] = 0.23
Out[7]= 0.23
In[8]:= Subscript[d, 2] = 0.45
Out[8]= 0.45
In[9]:= j =
NDSolveValue[{D[u[x, \[Psi]], \[Psi], \[Psi]] == 0,
u[x, -1] == u[x, 1] == u[-1, \[Psi]] == u[1, \[Psi]] == 0},
u, {x, -1, 1}, {\[Psi], -1, 1}]
Out[9]= InterpolatingFunction[{{-1., 1.}, {-1., 1.}}, <>]
In[10]:= k =
NDSolveValue[{D[u[y, \[Psi]], \[Psi], \[Psi]] == 0,
u[y, -1] == u[y, 1] == u[-1, \[Psi]] == u[1, \[Psi]] == 0},
u, {y, -1, 1}, {\[Psi], -1, 1}]
Out[10]= InterpolatingFunction[{{-1., 1.}, {-1., 1.}}, <>]
In[12]:= Equationp =
NDSolve[{x'[t] ==
Subscript[a, 11] x[t] - Subscript[a, 12] x[t]^2 -
Subscript[a, 13] x[t] y[t] + Subscript[d, 1] j[t],
y'[t] == -Subscript[a, 21] y[t] - Subscript[a, 22] y[t]^2 +
Subscript[a, 23] x[t] y[t] + Subscript[d, 2] k[t], x[0] == 10,
y[0] == 5, \[Psi][0] == 5, D[u[x, \[Psi]], \[Psi]] == 10,
D[u[y, \[Psi]], \[Psi]] == 5}, {x, y, \[Psi]}, {\[Psi], 0,
2 \[Pi]}, {t, 0, 25}]
During evaluation of In[12]:= NDSolve::dsfun: [Psi] cannot be used as a function.
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