#!/usr/bin/env python3
# -*- encoding: utf-8 -*-

# Parameters
α = 1
β = 0.1
γ = 1.5
δ = 0.075

# Initial conditions
xₒ = 10
yₒ = 5
Zₒ = xₒ, yₒ

# Solution parameters
tₒ = 0
Δt = 0.001
T = 10

# Lotka-Volterra derivative
def f(Z, t):
    x, y = Z
    ẋ = x * (α - β*y)
    ẏ = -y * (γ - δ*x)
    return ẋ, ẏ

# Accumulate results from Euler stepper
tᵢ = tₒ
Zᵢ = Zₒ
Zₜ, t = [], []
while tᵢ <= tₒ + T:
    Zₜ.append(Zᵢ)
    t.append(tᵢ)
    Zᵢ = [Zᵢⱼ+ Δt*Żᵢⱼ for Zᵢⱼ, Żᵢⱼ in zip(Zᵢ, f(Zᵢ, tᵢ))]
    tᵢ += Δt

# Output since I don't have plotting libraries in Python 3
print('t', 'x', 'y')
for tᵢ, (xᵢ, yᵢ) in zip(t, Zₜ):
    print(tᵢ, xᵢ, yᵢ)