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dR/dt = [gR/(R+R_m)] - dR, t>0,

where g,R_m and d are all positive parameters and R(0) =R_0

(a) Describe the biological meaning of each term in the equation.

(b) Determine the steady-states of the system and discuss any constraints on the model parameters for the model to admit biologically meaningful solutions.

(c) Determine the steady-state stability and discuss any variation in this with respect to the model parameter values.

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a) gR represents the exponential growth of population

dR represents the exponential decay of population

g is the growth rate

d is the decay rate

what does R and R_m represent?

how can I define this term gR/(R+R_m)?

what is (R+R_m)? does it affect the gR for the grow?

b)

In single steady -state system, dR/dt =0

[gR/(R+R_m)] - dR =0

gR -dR(R+R_m) =0

R[g -d(R+R_m)] =0

either R=0

OR g -d(R+R_m)= 0

g- dR_m =0 (R=0)

R_m = g/d

R* = g/d (R_m = R*)

SO we have : (R*1, R*2) =(0, g/d)

is my R*1, R*2 correct. I am concern about R*2 because not sure about if I am allow to do _m = R*.

I am not sure constraint on the model parameters to admit biologically meaning solutions?

c)

to determine steady-state stability

let f(R) = [gR/(R+R_m)] - dR

df/dR = g ln(R+R_m) -d .

My differentiation may be wrong and don't know the term R_m while differentiating with respect to R.

I really don't know after that. and I know my answer is still incomplete.

please help me.