AUTONOMOUS EQUATIONS and POPULATION DYNAMICS

Population Dynamics Problems

Autonomous Equations:

y' = f(y) (no explicit t);
equilibrium solutions, stable or unstable.

Exponential Growth:

y' = ry, growth rate r.

Logistic Growth:

y' = r(1-y/K)y,
with saturation level K; equilibrium solutions
at y=0 and y=K are critical point for f(y).

Critical Threshold

growth: y' = -r(1-y/T)y,
with threshold level T.

Logistic Growth with Threshold:

y' = -r(1-y/T)(1-y/K)y.