Differential Equations for Calculus 2, Pt 6: Intro to Competing Species Model (use Mathematica)
This is an introduction to a competing species model described by the nonlinear system of differential equations dx/dt = α*x - β*x*y, dy/dt = γ*y - δ*x*y. We can factor the right-hand sides to help find both the equilibrium points and the nullclines. With Wolfram Mathematica, we can draw the vector field with VectorPlot, the nullclines with ContourPlot, and the solution curves (trajectories) with SteamPlot. For the competing species model, one or the other species dies off, with a separatrix solution at the boundary between the two cases. NDSolveValue also approximates solutions.
#calculus2 #DifferentialEquations #CompetingSpecies #mathematica
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