Dynamical systems model for the dynamics of mood.

<p><b>A</b>) A schematic showing the mood change as a function of the state variable <i>M</i> without external inputs and noise (<i>I = ε = 0</i>). The arrows at 1, 2, 3, 4 indicate the direction of change in those states. The points labeled with <i>b, c,</i> and <i>d</i> are fix points. At these points, the value of the change is zero (dM/dt = 0). Therefore, when there is no noise, the state will not change once it has reached a fix point. The fix points <i>b</i> and <i>d</i> are stable, meaning that the system will return to these states if slightly perturbed. The fix point <i>c</i> is unstable and has different properties, the system will move further away from point <i>c</i> even if the system is only slightly perturbed. In that case, the system will evolve until it reaches one of the stable fixed points. If , the system will move towards the fix point <i>d</i>. The system will evolve towards the other fix point <i>b</i>, if . Therefore, the fix point <i>c</i> separates the basins of attraction of the two stable fix points. Samples of the evolution of <i>M</i> over time <b>B</b>) without noise, <b>C</b>) with a moderate level of noise and <b>D</b>) with high level of noise. Note, that with high level of noise the system exhibits stochastic transition between positive and negative values.