Solving using ODE45 and Euler's Method in MATLAB

% Model a 10 year period with each discrete time interval = 0.001 years

% L=Lion, D=Deer, G=Grass, H=Hunters

% initial values of populations ==> L=25,D=100,G=400

% constant values : Lamda1=0.005 Lamda2=0.5 Lamda3=0.15 C1=0.0035

% C2 through C7=0.005

% Mu1=0.002 Mu2=0.2

% Forcing Functions: H=H0(1+sin(w1*t)) R=R0(1+cos(w2*t))

% with constants w1=w2=2, H0=5, R0=15

% lion grows from eating deer

% deer grows from eating grass

% grass growth depends on rainfall (R)

% ***************************************************

% Modeling the lion population:

% Lamda1*L = natural birth rate of lions

% Lamda1=a constant prediction rate

% L=total number of lions

% Mu1*L = natural death rate of lions

% u1= constant prediction rate

% C1*LD = increased birth rate

% C1=relationship constant

% C2LH = enhanced death rate of lions due to hunters

% C2=a relationship constant

% dL/dy =Lamda1*L+C1*LD-Mu1*L-C2*LH

% ****************************************************

% Modeling the deer population:

% Lamda2*D = natural birth rate of deer

% D= total number of deer

% Mu2*D = natural deatj rate of deer

% C3*DG = increased birth rate due to grass

% C4*DL = enhanced death due to lions

% C5*DH = enhanced death due to hunters

% dD/dt =Lamda2*D+C3*DG-Mu2*D-C4*DL-C5*DH

% *****************************************************

% Modeling the grass population

% Lamda3*G= Natural growth rate of grass

% G = total amount of grass

% C6*GR = increased growth of grass due to rain

% C7*DG = elimination of grass due to the deer

% dG/dt=Lamda3*G+C6*GR-C7*DG

% *****************************************************