Nonlinear Differential Equation Frequency response

Hi dear all, I have difficulty to obtain the frequency response of 2 nonlinear differential equations. As you know, for linear ODEs, we obtain the state space easily and then the frequency response is easily obtained by using the tf function of the sys and then the bode plot. However, for the nonlinear system, the state-space can not be obtained or at least, using the x_dot=Ax+B, A is not obtained with some numbers inside because it is nonlinear.

So, I can only solve the equations in time domain using ode45 and not able to transfer the system to frequency domain using tf(sys).

I was wondering if anyone can come up with a solution about this at the earliest convenience of time? Thanks in advance

[Star Strider]

You most likely have to linearize your nonlinear system first. This involves taking the Jacobian of your nonlinear ‘A’ matrix. See your linear or nonlinear control textbooks for a detailed explanation.