Answer Happy

Linearisation. Solve Exercise 6.15 from the textbook. Linearise
about zero disturbance.
6.15 (Transcriptional regulation) Consider the dynamics of a genetic circuit that implements self-repression: the protein produced by a gene is a repressor for that gene, thus restricting its own production. Using the models presented in Exam- ple 3.18, the dynamics for the system can be written as a dm dt + во — дт — и, 1+ kp2 dp — Кт — -γη, dt (6.42) where u is a disturbance term that affects RNA transcription and m, p > 0. Find the equilibrium points for the system and use the linearized dynamics around each equilibrium point to determine the local stability of the equilibrium point and the step response of the system to a disturbance.