Evolution of 125,000 states in a 3D-Prey-Predator model!
This simulation visualizes the trajectories of 125k initial conditions in the state space of a prey-predator model with an additional differential equation describing the rate of change of the prey's fodder. This can be thought of as the fodder growing as grass and being eaten by the prey, but also decaying. Thus, the model is now more complex than the previous video with only prey and predators: • Exploring a Predator-Prey Model | Visualiz...
The numerical integration was performed according to the Euler scheme with a time step of 0.005 in the course of 5k iterations. The coloring of the states depends in the first two clips on the distance of the initial conditions to the center of the equilibrium and in the last two clips on the distance to the line where all states have B = 2 and C = 2
By integrating with the Euler method, numerical artifacts are created and the popualtions do not oscillate constantly but diverge which gives a cool viseulen effect
00:00 0.1 to 1, 125k states
00:41 0.1 to 2, 125k states
01:23 0.1 to 4, 125k states
02:05 0.1 to 4, 216k states
This simualtion was done in Matlab.