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Steady State & Plotting Trajectories in MATLAB

Please see attached files regarding specifics. This problem has two parts (written & programming).

The Brusselator is a simple model for oscillatory chemical systems such as the Belousov-Zhabotinski reaction. The time evolution of the concentration of two chemical species, x and y, is described by the ODE's: AND ,
Where A>0, B>0 are constants.

[A]. Find the single steady state of this model (do this portion on paper and attach to solution).

[B]. Write a program (MATLAB) to compute x(t) and y(t) for a given initial condition x(0)≥0 and y(0) ≥0. Plot a few trajectories in the xy plane, and mark the location of the steady state. Investigate cases where B/(1+A2) is less than, greater that, and equal to one.

Please make "x vs t" and "y vs x" plots for three scenarios:

A=0.5, B=1, x_initial=0.1, y_initial=2
A=1, B=3, x_initial=1, y_initial=1
A=2, B=5, x_initial=1, y_initial=1

In all scenarios please use Nstep=10000 and tau=0.01.

Attachments

Solution Preview

[A] The equations governing the two concentrations can be re-written as

dy/dt = Bx - x^2y (1)

and

dx/dt = A - x - dy/dt. (2)

The equilibrium exists at

dx/dt = dy/dt = 0 ...

Solution Summary

This Solution is given in .m files.

$2.19