A population of fish is modeled by the logistic equation modified to account for harvesting ??/??...
A population of fish is modeled by the logistic equation modified to account for harvesting
??/?? = .25? (1 − (?/4) ) - a
or equivalently
??/?? = − (1/16) ?^2 + (1/4) ? - a
1.) What will happen to the size of the population in the long run? If your answer depends on the initial population size (hint – it should!), be sure to include all possible scenarios.
2.) Use MATLAB to solve this differential equation. (Yes, it is solvable by hand. But trust me, this is better!)
3.) Use MATLAB to graph solution curves to this system with several different initial values. Be sure to show at least one solution curve for each of the scenarios found in #4.
4.) Now choose 2 new values for a; one in which a equals the equilibrium value, and one when a is slightly larger than that. Repeat questions #1 and 2 for each of these values of a.
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A population of fish is modeled by the logistic equation
modified to account for harvesting
??/??...
A population of fish is modeled by the logistic equation modified to account for harvesting: de...
A population of fish is modeled by the logistic equation modified to account for harvesting: de = 25p (1-) -a or equivalently top2 + 3p-a 1. What are the equilibrium solutions? Note: your answer(s) should be expressed in terms of a 2. Determine the range of values of a for which this model has 2 different equilibrium values. When does it have 1 equilibrium? O equilibria? Carefully interpret each of these scenarios in the context of this model. 3. Suppose...
Consider the differential equation . for x20, which models a population of fish with harvesting that...
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Consider the differential equation for , which models a population of fish with harvesting that...
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step by step please
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#2 Consider the following model for the dynamics of a population of size N (measured as number of...
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Suppose that a population of hacteria grows according to the logistic differential equation dP =0.01P-0.0002P2 dt...
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Q1/ Consider the modified logistic population growth equation P = Pla-bP) + ce-P Here, and k...
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A population of fish is modeled by the logistic equation modified to account for harvesting: de = 25p (1-) -a or equivalently top2 + 3p-a 1. What are the equilibrium solutions? Note: your answer(s) should be expressed in terms of a 2. Determine the range of values of a for which this model has 2 different equilibrium values. When does it have 1 equilibrium? O equilibria? Carefully interpret each of these scenarios in the context of this model. 3. Suppose...
Consider the differential equation . for x20, which models a population of fish with harvesting that is governed by the logistic equation and a number of fish H caught and removed every unit if time (harvesting). Here the parameters r, K, and H are all positive. a Assume tht Heate e. 4 rk If H <テ, what levels ofinitial fish population lead to a fish population which does not die out? Assume that H>.What happens to the population of fish...
Exercise 4: Assume that a population is governed by a logistic equation with carrying capacity K intrinsic growth rate r, and initial population size K is subjected to constant effort harvesting: (a) Determine the population size, N(t) (b) Verify that if E< r, the population size will approach the positive steady state, Ni, the carrying capacity K if Erand if E>r, the population will approach the zero steady state, No, astoo. (c) Find the maximum sustainable yield of the population.
What are the solutions to the following diff eq’s?
A fish hatchery employed a mathematician to design a model to predict the population size of fish that the hatchery can expect to find in their pond at any given time. The mathematical model that the mathematician created is: dP dt 25 (a) Draw a one dimensional phase portrait of the autonomous differential equa- tion. What does this differential equation predict for future fish populations for various initial conditions? Describe the...
step by step please
4. Suppose that the logistic equation dt Pla -bP) models a population of fish in a lake after t months during which no fishing occurs. What is the limiting population for this fish population? suppose that, because of fishing, fish are removed from the lake at a rate proportional to the existing fish population. i. Write a differential equation that describes this situation. ii. Show that if the constant of proportionality for the harvest of fish,...
#2 Consider the following model for the dynamics of a population of size N (measured as number of individuals x 10) over time (in months) that is subject to harvesting: The population grows according to a logistic equation in the absence of harvesting and h is a constant per a) Find all equilibria and determine the values of h for which each is stable or unstable. 4aestng andcnstant capita harvest rate. b) Construct the bifurcation plot: plot the equilibria from...
Suppose that a population of hacteria grows according to the logistic differential equation dP =0.01P-0.0002P2 dt where Pis the population measured in thousands and t is time measured in days. Logistic growth differential equations are often quite difficult to solve. Instead, you will analyze its direction field to acquire infom ation about the solutions to this differential equation. a) Calculate the maximum population M that the sumounding environment can austain. (Note this is also calked the "canying capacity"). Hint: Rewrite...
Q1/ Consider the modified logistic population growth equation P = Pla-bP) + ce-P Here, and k are positive constants. The additional term ce represents the immigration. Clearly, the immigration is less when the population is large than when it is small. This decrease may be caused, for example, by the imposition of quotas, or by overcrowding of the region and a resulting deterioration of the favorable conditions that had attracted immigrants. Use Runge Kutta method to find the solution of...
(1 point) The population of Cook island has always been modeled by a logistic equation P' =r(C - P) with growth rate r = 2 and carrying capacity C = 6500 with time t in years. Starting in 2000, 8 citizens of Cook Island have left every year to become a mathematician, never to return. What is the new differential equation modeling the population of the island P? 4500 = 0
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