Lotka-Volterra model solving using Runge Kutta methods (predator-prey and competitve equations describing Gause’s “Struggle for Existence”) on Python

This project solves two Lotka-Volterra models: classic equations (predator-prey)

$$\dfrac{dN_1}{dt} = \alpha N_1 - \beta N_1 N_2$$ $$\dfrac{dN_2}{dt} = \delta N_1 N_2 - \gamma N_1$$

/bio_ode_solver/examples/lotka_volterra/lv.png:

and competitive equations describing Gause’s “Struggle for Existence”.

$$\dfrac{dN_1}{dt} = b_1 N_1 \left(1 - \dfrac{N_1 + \alpha N_2} {K_1} \right)$$ $$\dfrac{dN_2}{dt} = b_2 N_2 \left(1 - \dfrac{N_2 + \beta N_1} {K_2} \right)$$

/bio_ode_solver/examples/lotka_volterra/lv.png:

No additional packages were used for computing ODE's. Numpy is used to compute Runge-Kutta methods.