Brusselator Hopf Threshold
Track the local chemical feedback that crosses an oscillatory instability threshold.
Free theory articleTrack the local chemical feedback that crosses an oscillatory instability threshold.
Concept & interpretation
The Brusselator is a theoretical model for a type of autocatalytic reaction that exhibits oscillations. This module explores the stability of its fixed point as parameters are varied, specifically focusing on the Hopf bifurcation where the system transitions from a stable steady state to sustained chemical oscillations (a limit cycle).
Experiment
Use the interactive model to observe the transition through the Hopf threshold:
- Set Feed A to 1 and Feed B to 1. Observe that the Jacobian trace is -1 (negative), indicating Linear stability is Stable.
- Increase Feed B to 2. Observe that the Jacobian trace becomes exactly 0 and the Linear stability becomes Hopf boundary.
- Further increase Feed B to 3. Observe that the Jacobian trace becomes +1 (positive), and the Linear stability becomes Unstable.
- Change the Probe u to 2 and Probe v to 4 to sample the local vector field derivatives at different locations in the phase space.