4. System Stability:
-\delta_1 D + \delta_2 J - \delta_3 U = 0 \quad \Rightarrow \quad S^* = \frac{\delta_2 J - \delta_3 U}{\delta_1}
These equilibrium values (Ar, Ap, D,S) define the steady-state configuration of voter compliance, legislative behavior, democratic degradation, and overall system stability, given fixed levels of monetary incentive, perceived justice, and social norms.
2. Conditions for Bifurcation
Bifurcations occur when small changes in system parameters cause a qualitative shift in equilibrium behavior. In TDD, bifurcations are critical points where the political system transitions between:
Authoritarian drift: high voter compliance, elevated legislative arrogance, and passive acceptance of degradation (S>0)
Anarchic or unstable outcomes: low compliance, active resistance, or social unrest (S<0)
Key conditions for bifurcation can be derived from the Jacobian matrix of the coupled system:
J =Â
\begin{bmatrix}
\frac{\partial \dot{A_r}}{\partial A_r} & \frac{\partial \dot{A_r}}{\partial A_p} & \frac{\partial \dot{A_r}}{\partial D} & \frac{\partial \dot{A_r}}{\partial S} \\
