Find and classify the steady states

Assignment Help Mathematics

Reference no: EM13193993

Suppose that a population model is the logistic model with harvesting term h, a constant, i.e.

dN/dt=N/ρ(1-kN)-h,

where ρ,k and h are positive constants such that ρk≤1/(4h).

(i) Find and classify the steady states N_1 and N_2, where N_1
(ii) If the initial population is N_0 describe the future of the population for the three cases: (a) 0N_2.
(iii) Show that there is a critical harvesting rate h_c so that if h>h_c then the population dies out regardless of the initial population. Express h_c in terms of ρ and k.
(iv) Obtain the solution of the equation dN/dt=N/ρ(1-kN)-h with ρ=1 and k=1/10 for the harvesting rates h=1.6 and h=5.

Reference no: EM13193993

Questions Cloud

State what is the chemical formula of the precipitate : What is the chemical formula of the precipitate that forms when a a aueous solution of sodium chloride is mixed with an aqueous solution

Describe the data collection methods used in the research : Describe the data collection methods used in the research project. • What did the researchers conclude as a result of their research?

Find out the ph during the titration : Calculate the pH during the titration of 100.0 mL of 0.200 M HCl with 0.400 M NaOH. First what is the initial pH (before any NaOH is added)? - What is the pH after 38.4 mL of NaOH are added?

State the standard molar enthalpy and entropy : The standard molar enthalpy and entropy of the denaturation of a certain protein are 512 kj/mol and 1.60 kj/K mol.comment on the signs and magnitude of these quantities , and calculates the temperature at which the process favors the denatured sta..

Find and classify the steady states : Suppose that a population model is the logistic model with harvesting term h, a constant, i.e.

Explain the game''s nash equilibrium : The entrant and incumbent both only care about their own monetary payoff, what is/are the game's Nash equilibrium.

Find out the volume of the naoh solution : Calculate the volume of the NaOH solution prepared in (2) required to react with all of the t-butyl chloride in 1.0mL of the 0.050M solution prepared in (1)?

Find how many mililiters of the 46% solution you will need : A chemist need 180 milliliters of a 40% solution but has only 28% and 46% solutions available. Find how many mililiters of the 46% solution you will need to get the desired solution.

Explain how do dilute the solution to a ratio : the xylene that received has a density of 0.86 g/ml. Its volume is 2.0 ml, and its concentration is 0.069 g/ml. First of all, need to dilute the solution to a 1:100 ratio (ex: 69000 µg/ml to 690 µg/ml). How do dilute the solution to a 1: 100 ratio..

User Account

All Pages