Consider the following simple competition model An1 aAn cAn

Consider the following simple competition model:

A(n+1)= a*A(n) - c*A(n)*B(n)

B(n+1)= b*B(n) - d*A(n)*B(n)

where a,b,c,d are positive constants. Find all fixed points.

Determine the stability of the fixed points for the specific case a = 1.2, b= 1.3, c= 0.001 and d= 0.002

Solution

forr stability

A(n+1) = A(n)

B(n+1) = B(n)

A(n+1)= a*A(n) - c*A(n)*B(n)

A(n)= a*A(n) - c*A(n)*B(n)

1 = a - c*B(n)

B(n) = (a-1)/c

= 300

-------------------

B(n+1)= b*B(n) - d*A(n)*B(n)

B(n)= b*B(n) - d*A(n)*B(n)

A(n) = (b-1)/d

= 100