## number of parameters for a nonlinear differential equation

Take for example a system
$\frac{dx_i}{dt}$=(x_i,t,a,b,....) i-number of state equations.
What would be the maximum number of parameters permitted for this system of non-linear differential equations?

Is it finally determined by the solution space?Is there a criteria for number of parameters in a system of differential equations?

 Recognitions: Gold Member Science Advisor Staff Emeritus Perhaps I am misundersanding your question. You can have any number of parameters in a differential equation.

 Tags nonlinear dynamcs