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91. Sustainable Harvesting Suppose that a fish population evolves according to a logistic equation and that fish are har- vested at a rate proportional to the population size. If N(t) denotes the population size at time t, then dN N = rN dt hN | K Assume that r = 2 and K = 1000. (a) Find possible equilibria and use the graphical approach to discuss their stability, when h = 0.1. (b) Show that if h

91. Sustainable Harvesting Suppose that a fish population evolves according to a logistic equation and that fish are har- vested at a rate proportional to the population size. If N(t) denotes the population size at time t, then dN N = rN dt hN | K Assume that r = 2 and K = 1000. (a) Find possible equilibria and use the graphical approach to discuss their stability, when h = 0.1. (b) Show that if h

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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91. Sustainable Harvesting Suppose that a fish population evolves according to a logistic equation and that fish are har- vested at a rate proportional to the population size. If N(t) denotes the population size at time t, then dN = IN (1-)- - hN dt K Assume that r = 2 and K = 1000. %3D (a) Find possible equilibria and use the graphical approach to discuss their stability, when h = 0.1. (b) Show that if h <r = 2, then there is a nontrivial equilibrium. Find the equilibrium. (c) Use (i) the eigenvalue approach and (ii) the graphical ap- proach to analyze the stability of the equilibrium you found in (b).
Transcribed Image Text:91. Sustainable Harvesting Suppose that a fish population evolves according to a logistic equation and that fish are har- vested at a rate proportional to the population size. If N(t) denotes the population size at time t, then dN = IN (1-)- - hN dt K Assume that r = 2 and K = 1000. %3D (a) Find possible equilibria and use the graphical approach to discuss their stability, when h = 0.1. (b) Show that if h <r = 2, then there is a nontrivial equilibrium. Find the equilibrium. (c) Use (i) the eigenvalue approach and (ii) the graphical ap- proach to analyze the stability of the equilibrium you found in (b).
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