Schematic Representation of the Phase Space (<i>μ,V</i>)

<p>(A) The depression <i>μ</i> is plotted on the <i>x</i>-axis, while the variable <i>V</i> is on the <i>y</i>-axis (for the schematic representation, no scale is given). The recurrent sets are the attractor points <i>P</i>₁ (the Down state), the saddle point <i>P</i>₃<b>,</b> and the attractor <i>P</i>₂ (the Up state), separated by an unstable limit cycle C (dashed line). The region inside the unstable limit cycle is the basin of attraction of <i>P</i>₂. By definition, it is the Up state. For a specific value of the parameter, an homoclinic curve can appear. The unstable branch of the separatrix starting from <i>P</i>₃ terminates inside the basin of attraction of the Down state. The noise drives the dynamics beyond the separatrices (lines with arrow converging to <i>P</i>₃) but a second transition is necessary for a stochastic trajectory to enter inside the Up state delimited by C. However a single noise transition is enough to destabilize the dynamics from the Up to the Down state.</p> <p>(B) Example of a trajectory in the phase space.