Predator-Prey Dynamics with Fixed Sum

The MATLAB code models the Lotka-Volterra predator-prey equations over time. It shows population dynamics of predators and prey using ode23

The MATLAB code provides a simulation of the Lotka-Volterra predator-prey model, which is a pair of first-order, non-linear differential equations frequently used to describe the dynamics of biological systems. Here's a more detailed description:

Inputs:

- Initial conditions (`y0 = [20; 20]`): The system starts with 20 predators and 20 preys.

- Time span (`t0 = 0, tfinal = 15`): The simulation is conducted from time t=0 to t=15.

Functions:

- `lotka(t, y)`: This function defines the Lotka-Volterra equations. It uses a 2x2 diagonal matrix to represent the interactions between the two species.

- `yp = diag([1 - .01*y(2), -1 + .02*y(1)])*y;`

ODE Solver:

- `ode23`: This built-in MATLAB function is used to numerically solve the system of ordinary differential equations.

Output:

- The code produces a plot that shows the populations of predators and prey as functions of time.

Visualization:

- The plot visualizes the populations of predators and preys over the defined time span.

Overall, the code is a basic but insightful computational tool for understanding the dynamics of predator-prey interactions.