# Matlab Code For Nonlinear Equation System [closed]

Help me please. How can i solve that below equation system ?

$dx/dt=a*x-b*v*x$

$dy/dt=a*y+b*v*x-k*y$

$dv/dt=k*L*y-b*v*x-m*v$

## closed as off-topic by Michael Grant, Claude Leibovici, JonMark Perry, kingW3, Behrouz MalekiJan 4 '17 at 12:53

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is not about mathematics, within the scope defined in the help center." – Michael Grant, Claude Leibovici, JonMark Perry, kingW3, Behrouz Maleki
If this question can be reworded to fit the rules in the help center, please edit the question.

• You will easily find examples of similar problems on stackoverflow, stackoverflow.com/questions/tagged/…. If you ask your question there, show that you read these examples and the Matlab documentation and post code that shows your understanding. – LutzL Jan 3 '17 at 9:18
• Hmm, another user who asks questions, receives answers but cannot be bothered to accept them. I simply avoid them. – Alex M. Jan 4 '17 at 11:49

Borrowing code from the stackoverflow question https://stackoverflow.com/questions/17013941/implementation-hyperchaotic-lorenz-in-matlab, one could implement this system and its solution as (untested)

function Y=bacteriophage(a,b,k,L,m,T,x0,y0,v0)
[T,Y]=ode45(system,T,[x0; y0; v0]);
function out=system(t,state)
x = state(1); y=state(2), v=state(3)
out= [
a∗x-b∗v∗x;
a∗y+b∗v∗x-k∗y;
k∗L∗y-b∗v∗x-m∗v
];
end;
end;

a = 0.1121*exp(0.0634); %replication coefficient of bacteria
b = 1*10^(-6); % the transmission coefficient
k = 0.706;     % the lysis rate coefficient
L = 50;        % the burst size
m = 4.8;       % the decay rate of free phage
x0= 1.9*10^4; % initial condition for x(t)
y0= 5.4*10^3; % initial condition for y(t)
v0= 7.4*10^4; % initial condition for v(t)
T = 0:0.001:3;
Y=bacteriophage(a,b,k,L,m,T,x0,y0,v0)


Matlab have full support to solve ODE's. You can find the documentation here.

Basically, you will need to create a function defining this system of equations and pass a function handler to ode45 or any other ODE solver. You can find a more detailed explanaition at the links I have indicated.