Predator-prey systems
General · Mathematics
Study notes
Q: Rabbits x, foxes y: dx/dt = 2x-0.1xy, dy/dt = -3y+0.05xy. Find equilibrium. Set zero: x(2-0.1y) = 0, y(-3+0.05x) = 0. Nontrivial: 2-0.1y = 0: y = 20. -3+0.05x = 0: x = 60. Equilibrium: (60 rabbits, 20 foxes)! Orbits cycle around it (neutral center!)! More rabbits → more foxes → fewer rabbits...! (Predator-prey: nature's cycles!)