Mathematical Systems Biology
Verfasst: 15.04.2018, 10:31
Hi I have following assignment and I have not really a clue on how to solve it, because it is completely different then what we did at class.
The simple fishery model reads , where N is the fish population, K is a carrying capacity, r is the growth rate, and H is the term considering the effect of fishing.
In a refined version, the model is improved to , with parameters H and A being larger than zero.
(a) Why is the refined model more realistic than the original, simple one?
(b) Give a biological interpretation of parameter A; what does it measure?
(c) Show that the refined system can be rewritten in dimensionless form as
(d) Show that the refined system can have one, two, or three fixed points, depending on the numerical values of parameters a and h. Classify the stability of the fixed points.
1(e) Analyze the dynamics of the system near $x=0$, and show that a bifurcation occurs if $h=a$. Which kind of bifurcation is it?
(f) Plot the stability diagram of the system in the pa, hq parameter space. Can hysteresis occur in any of the stability regions?
d and e I have some idea but with the others i am clueless Greetings Max
The simple fishery model reads , where N is the fish population, K is a carrying capacity, r is the growth rate, and H is the term considering the effect of fishing.
In a refined version, the model is improved to , with parameters H and A being larger than zero.
(a) Why is the refined model more realistic than the original, simple one?
(b) Give a biological interpretation of parameter A; what does it measure?
(c) Show that the refined system can be rewritten in dimensionless form as
(d) Show that the refined system can have one, two, or three fixed points, depending on the numerical values of parameters a and h. Classify the stability of the fixed points.
1(e) Analyze the dynamics of the system near $x=0$, and show that a bifurcation occurs if $h=a$. Which kind of bifurcation is it?
(f) Plot the stability diagram of the system in the pa, hq parameter space. Can hysteresis occur in any of the stability regions?
d and e I have some idea but with the others i am clueless Greetings Max