I am trying to simulate the oscillator with an RLC circuit with the initial condition V(V1) = 0 and D(V(V1)) = 0. Since LTspice does not allow initial condition with time derivatives, I set the initial current of the inductor to be -6A. (Initial resistance is 1/3 ohm, and initial current through the capacitor is zero.) The node V(V1) does show a limit cycle behavior, but the amplitude(around 1.2V) is different from the numerical result in Mathematica(2V). I have set all serial and parallel resistance/inductance/capacitance to be zero for the components. Any suggestions on what could be wrong? Thanks in advance for any advice!
Also, if I change the resistance in my Mathematica file to be 1/(3*V(V1)*V(V1)-1) instead of 1/(1*V(V1)*V(V1)-1), the voltage response is exactly the same as the result in LTspice. (The first plot in the picture below is when I change the expression of the resistance, and the second plot shows the overlap with LTspice result.)
On the other hand, all voltage responses scale proportionally as expected. For instance, when the resistance in Mathematica is 1/(V(V1)*V(V1)-4), the amplitude doubles and becomes 4V. The amplitude in LTspice also doubles to be around 2.4V when resistance is 1/(V(V1)*V(V1)-4).