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Solution 1:
Exponential growth model with rates and death rates a>0 and b>0
i) For the fixed point of the equation
Code:
def function(x,a, b):
return [x*(a-b)]
print("dx/dt=",function(3,3,1))
print("dx/dt=",function(5,9,8))
print("dx/dt=",function(7,2,5))
print("dx/dt=",function(3,3,3))
ii) In the first part we have calculated the fixed-point x=0, and a=b, now we will check the stability
Now, taking the derivative of the function
Now, substituting X=0
Now, taking the second derivative
Here a>0 and b>0 but so it is unstable fixed points. And it is diverging.
Code:
def function(x,a, b):
return [x*(a-b)]
print("dx/dt=",function(3,3,1))
print("dx/dt=",function(5,9,8))
print("dx/dt=",function(7,2,5))
print("dx/dt=",function(3,3,3))
def calc_fixed_point(a,b):
for x in range(a,b):
if (x*(a-b) == 0):
function.append((x,a,b))
print('The system has a fixed point in %s,%s' % (x))
return function(x,a,b)
print(calc_fixed_point(2,4))
Solution 2:
The population growth model,
i) For the calculation of...