Hi, I am working on a problem where the differential equation \mathbf{x}'(t)=F(\mathbf{x}(t)) admits a periodic solution. For example: \begin{cases} x'(t) = -y(t) \\ y'(t)=x(t)\end{cases},\qquad x(0)=1,\ y(0)=0. The solution in this case is (x(t),y(t))= (\cos(t),\sin(t)) which has a period of 2…

Looking at your equations, you can see that your system is linear, conservative, and leads to periodic orbits. One way to find the natural frequencies, and therefore periods of periodic solutions is to linearize the underlying system of equations (which is straightforward here, but I’ll show how to…

Differential equation with periodic orbit: Can Diffeq.jl determine the period?

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ChrisRackauckas December 26, 2023, 8:58pm 8

That’s worth an issue. I presume it just was tested with parameters each time.

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Differential equation with periodic orbit: Can Diffeq.jl determine the period?

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