Chapter 14 - Ecosystems

[argunaykut]

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[acallegar]

Hi, for the students asking about exercise 14.10

the relevant equations are (14.23) (system of dx/dt and dy/dt)
and (14.24) (equilibrium points; the first one is non-trivial)

--- a possible choice for the simulation parameters [they appear in equation (14.23)]

r1 = 0.01;
r2 = 0.02;
K1 = 140;
K2 = 150;
a12 = 0.5;
a21 = 0.7;

One way to solve 14.10 is:
plot the phase space, plot the equilibrium point, plot a few trajectories. Ex, see the figure below:

The different colors represent different trajectories (they start from different initial x,y values).

See below for the time dependence of the trajectories x(t) and y(t)

black trajectory:

blue trajectory:

[acallegar]

Hi, for the students asking about exercise 14.7

The finite difference equation for the explicit Euler is:

you take equation (14.15) and write
dx = x_(n+1) - x_(n)

and get
x_(n+1) = x_(n) + dt * (r * x_(n) - alpha * x_(n)^2)