Consider a system of differential equations where both are both continuous partial derivatives. Let's call them $F$ and $G$. Is there a proof suggesting that if there exists a solution that is a limit cycle of the system (call it $l(t)$), the system must then have an equilibrium solution?
2026-02-23 05:40:39.1771825239
Is there a proof for this limit cycle equilibrium
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There is a theorem that a closed trajectory always encloses at least one equilibrium point. See e.g. Boyce and diPrima, theorem 9.7.1.