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Figure 9 | The Journal of Mathematical Neuroscience

Figure 9

From: From invasion to extinction in heterogeneous neural fields

Figure 9

Phase portrait of constant energy trajectories. Phase portrait of constant energy trajectories for the Hamiltonian system given by Equations 6.12 and 6.13 with F (q) = tanh(q) and g(q) = βqs. Parameters are W0 = 1.2 and β = 1. Zero-energy trajectories are indicated by thick curves. The stable and unstable fixed points of the mean-field dynamics are denoted by Q + and Q - . (a) s = 1/2: There exists a nonzero fluctuational fixed point P that is connected to Q + via a zero-energy heteroclinic connection. The curve Q+P is the optimal path from the metastable state to the absorbing state. (b) s = 1/4: There is no longer a fluctuational fixed point P , so the optimal path is a direct heteroclinic connection between Q + and Q - .

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