Use numerical methods to solve ordinary differential equations.

du/dt = au - buv
dv/dt = -cv + dbuv

with the following notations:

• u: number of preys (for example, rabbits)
• v: number of predators (for example, foxes)
• a, b, c, d are constant parameters defining the behavior of the population:
  • a: the natural growing rate of rabbits, when there's no fox
  • b: the natural dying rate of rabbits, due to predation
  • c: the natural dying rate of fox, when there's no rabbit
  • d: the factor describing how many caught rabbits let create a new fox

• Python

  • scipy.integrate.odeint
  • scipy.integrate.ode
  • scipy.integrate.solve_ivp

• Julia

  • Sundials.jl
  • ODE.jl
  • SciPyDiffEq.jl

• R

  • deSolve
  • diffeqr

• MATLAB

  • ode45

MIT