Fig. 3. Bifurcation analysis for the coupled Aβ aggregation-inflammation with respect to inflammation- and coupling-related parameters.

a Contour maps representing temporal changes in Aβ monomer concentration in dependence on three parameters: $k_{\mathit{infl}}$ (outer x-axis), $\mathit{steep}$ (outer y-axis), and $\mathit{infl\_ref}$ (inner y-axis). Changes in these three parameters lead to distinct kinetic behaviors. As an example, a slice of contour maps at $\mathit{steep}=50$ and $\mathit{infl\_ref}=0.005$, demonstrates how changes in the $k_{\mathit{infl}}$ parameter affects oscillatory changes in Aβ monomer concentration (bottom of the panel). b Changes in the steady-state (relative) amplitude (primary axis, blue) and period (secondary axis, orange) of oscillations caused by variation in $k_{\mathit{infl}}$ parameter (at $\mathit{steep}=50$ and $\mathit{infl\_ref}=0.005$). When $k_{\mathit{infl}}$ increases, a transition from large-amplitude slow oscillation to small-amplitude fast oscillation is observed. Oscillations with very small amplitudes represent damped oscillations, in which the calculated spacing between peaks (period) can frequently become irregular and unreliable.