Finding the equilibrium points and the lapsed time between those points on phase paths ?
Hiqmet Kamberaj
Maybe you can tell more about your system; I guess that x is a phase space variable function of time t and ''x means d^2x/dt^2 (second derivative with time). Moreover, is your system closed or open system?
From mathematical point of view, you can replace your system by this equivalent system of differential equations of first order:
dx/dt = v
dv/dt = x^2-x
where the solution x(t) will depend on the initial conditions:
x(t0) and v(t0)
You can also use any numerical integrator to solve the about equations. (For example, Runge-Kutta numerical method.)
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