The separatrix is clearly visible by numerically solving for trajectories backwards in time. The separatrix itself is the stable manifold for the saddle point in the middle. Trajectories to the left of the separatrix converge to the left stable equilibrium, and similarly for the right. In the FitzHugh–Nagumo model, when the linear nullcline pierces the cubic nullcline at the left, middle, and right branch once each, the system has a separatrix. , we can easily see the separatrix and the two basins of attraction by solving for the trajectories backwards in time. Example: simple pendulum Ĭonsider the differential equation describing the motion of a simple pendulum:ĭ 2 θ d t 2 + g ℓ sin θ = 0. In mathematics, a separatrix is the boundary separating two modes of behaviour in a differential equation. JSTOR ( September 2012) ( Learn how and when to remove this template message).Unsourced material may be challenged and removed.įind sources: 'Separatrix' mathematics – news Please help improve this article by adding citations to reliable sources.
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