What is the Matlab code the future state-dependent system: $\frac{du}{dt} = a*u - u(t)^3*v(t+\tau), \frac{dv}{dt} = k + u^2(t+\tau)*v^2(t)$, where $a$ and $k$ are constants?
A remark: if tau=0, the problem is a classical non-linear ODE of first order. Indeed, using a two-variable unknown z = [u;v], is reads dz/dt = f(z) and it can be solved using ode45 matlab routine for instance.
With non zero tau, the ODE is somehow non-local in time and I guess there are no standard routines to solve it. In this case, it means that an integration scheme in time should be programmed from scratch. By the way, the equations are a bit strange, since t+tau is in the future, so these do not satisfy to the causality principle (unless tau is negative). Nevertheless, to solve it, it can be interpreted as a backward in time problem, i.e. starting from the end time of the studied interval and going backward in time, so variables at t+tau are known when solving the problem at t.
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