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Bifurcations and bursting in the Epileptor

Fig 3

Epileptor’s fixed points and bursting trajectory.

A: Fixed points manifold for x₁. For x₁ < 0, there are two solutions, while for x₁ ≥ 0 we have one fixed point when and two solutions for smaller values. The lower branch of fixed points is the rest or interictal state. The upper branch is stable for values of and unstable otherwise. SN⁺ occurs for , SN⁻ for , SN⁰ for μ = −1 and the Hopf curve for . B: Trajectory of the Epileptor’s fast subsystem (x₁, x₂) plotted against the parameter μ. It can be observed the hysteresis-loop caused by the two SN curves.

doi: https://doi.org/10.1371/journal.pcbi.1011903.g003