Differential Equation - Finding Steady States
Posted on February 2, 2019
Tags: physics
\[ \frac{dN}{dt} = r_B N ( 1 - \frac{N}{K_B} ) - p(N)\]
\(N\) is population size \(r_B\) is Linear Birth rate \(K_B\) is carrying capacity related to amount of food \(p(N)\) is predation by predators
0.0.1 Dimensional analysis
Design a dimensionless function for p(N)
design variables
0.0.2 Finding the stable state
Plot the D(f(x)) vs f(x) assume f(x) = population at time x
Where the graph crosses 0 are the stable states. Showing there is no change in population.
This means for every time x, we need to make a plot.
