Figure 1. Dynamic Behaviors of a Two-Node Feedback Loop in Response to a Small Perturbation from Steady-State.

(Top) Schematic of a simple feedback circuit with the nodes and edges labeled.

(Middle) We illustrate the dependence of stability on the values of a ₁₂ and a ₂₁ as they are varied from −1 to 1, with constant self-degradation terms a ₁₁ = −0.3 and a ₂₂ = −0.7. The system can be stable (green), oscillatory (blue), or unstable (red). These regions are determined by gain k = a ₁₂ a ₂₁. Shown in white are contours of constant gain k. The quadrants labeled (+) correspond to positive feedback (a ₁₂ and a ₁₁ have the same sign), while the quadrants labeled (−) correspond to negative feedback (a ₁₁ and a ₂₁ have opposite signs).

(Bottom) The stability regions vary as the values of self-degradation terms a ₁₁ and a ₁₂ change. The more stable the open-loop nodes (more negative a ₁₁ and a ₂₂), the greater the regions of closed-loop stability. However, if a ₁₁ and a ₂₂ are close in sign and magnitude, the size of the oscillatory regions increases.