# Lotka volterra model for 3 species (1 prey - 2 predators)

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José Manuel on 23 Nov 2023
Edited: José Manuel on 27 Nov 2023
How can i adapt the following code and function to solve a three species lotka volterra model?
clc
clear clc
t0 = 0; %Condiciones iniciales.
tfinal = 15; %Condiciones finales.
y0 = [60.28; 2.043051]; %Poblaciones iniciales de depredadores y presas.
[t,y] = ode45(@lotka,[t0 tfinal],y0); %%Resuelve la ecuación de Lotka-Volterra
% con los parámetros anteriores gracias a la función "ode45 “ – (Fórmula Runge-Kutta (4,5)).
%Primer Gráfica.
nexttile % Graficar en una sola ventana.
plot(t,y) % Graficar función Lotka-Volterra.
title('Poblaciones de depredadores y presas a lo largo del tiempo')
xlabel('Tiempo t')
ylabel('Población')
%Segunda Gráfica.
nexttile % Graficar en una sola ventana.
plot(y(:,1),y(:,2))
title('Retrato de fase')
xlabel('Población Presa')
function yp = lotka(t,y)
%LOTKA Lotka-Volterra predator-prey model.
yp = diag([1 - .01*y(2), -1 + .02*y(1)])*y;

Sam Chak on 24 Nov 2023
This isn't strictly a MATLAB-related question, but I believe animal behaviorists might be able to advise you. Alternatively, from a critical thinking perspective, you could consider modifying the Lotka-Volterra equations for a 2-predator-1-prey model.
In a particular phase, the prey population attains a level of abundance that initiates the growth of the predator communities. Over time, the heightened presence of predators induces a decline in the prey population. Subsequently, this reduction in prey numbers contributes to a decrease in the populations of the predators. Eventually, this cyclical pattern recurs.
tspan = [0 20];
y0 = [5; 3; 2];
[t, y] = ode45(@lotka, tspan, y0);
plot(t, y), grid on, ylim([0 6])
legend('Prey', 'Predator 1', 'Predator 2', 'location', 'SE')
xlabel('t')
title('Numbers of prey & predators for the Lotka-Volterra model')
%% Modified Lotka-Volterra 2-predator-1-prey model
function dydt = lotka(t, y)
dydt = zeros(3, 1);
% Parameters
a = 2.4; % maximum prey per capita growth rate
b1 = 0.6; % effect of the presence of predator 1 on the prey's growth rate
b2 = 0.6; % effect of the presence of predator 2 on the prey's growth rate
c1 = 0.8; % predator 1 per capita death rate
c2 = 0.8; % predator 2 per capita death rate
d1 = 0.3; % effect of the presence of preys on the predator 1's growth rate
d2 = 0.3; % effect of the presence of preys on the predator 2's growth rate
% Lotka-Volterra equations for 2 predators and 1 prey
dydt(1) = a*y(1) - b1*y(1)*y(2) - b2*y(1)*y(3); % Prey
dydt(2) = - c1*y(2) + d1*y(1)*y(2); % Predator 1
dydt(3) = - c2*y(3) + d2*y(1)*y(3); % Predator 2
end

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