Exercise 5.(Fishery Model) The equation N = rN(1 – ) – H represent aKsimple population model of a fishery with the term -H representing a constant harvestingrate (H > 0).a) Show that the system can be written in dimensionless form asdx= #(1–2) – hdTfor suitably defined dimensionless quantities.b) Plot the vector fields for different values of h (show all qualitative behaviors).c) Show that a bifurcation happens at a critical value he, determine the value, and classifythe bifurcation.d) Discuss the long-time behavior of the population for h < he and h > he, and give abiological interpretation to both cases.e)have explored. Determine what the flaw is and advance a possible solution. (Hint: it isrelated to a missing fixed point)This model has a major flaw compared to other population models we

Answered: Image /qna-images/answer/8dd83eb2-2cd7-4927-ab14-abf0f81ca1bf.jpg

Exercise 5. (Fishery Model) The equation N = rN(1 –) – H represent a simple population model of a fishery with the term –H representing a constant harvesting rate (H > 0). a) Show that the system can be written in dimensionless form as dr = ¤(1–¤) – h dr for suitably defined dimensionless quantities.

Exercise 5. (Fishery Model) The equation N = rN(1 –) – H represent a simple population model of a fishery with the term –H representing a constant harvesting rate (H > 0). a) Show that the system can be written in dimensionless form as dr = ¤(1–¤) – h dr for suitably defined dimensionless quantities.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Use EROS and backward substitution to solve the system Ax= b, where (三) (6) 21 1 and 1. -3 -1 What is the rank of A?
Let bt represent the number of bacteria (measured in millions) at time t (measured in hours).This system can be modeled by the following updating function:bt+1 = 1.5btLet b0 =7.Iterate the discrete time dynamical system for a few steps:b1 = _______b2 = _______b3 = _______Write down a solution to the discrete-time dynamical system.Solution: b(t) = ______ Use your solution to compute the following:b(1) = _______b(2) = _______b(3) = _______Do your answers agree with your iterations? (yes/no) _________
Match b and a system representation to its corresponding difference equation y[n] = -1.46x[n] - 3.53x[n-1] + 3.93x[n-2] - 2.86y[n-1] - 4.1y[n-2] -0.65y[n-3] y[n] = -1.46x[n] - 3.53x[n-1] + 3.93x[n-2] + 2.86y[n-1] + 4.1y[n-2] + 0.65y[n-3] y[n] = 1.46x[n] + 3.53x[n-1] - 3.93x[n-2] + 2.86y[n-1] + 4.1y[n-2] + 0.65y[n-3] y[n] = -1.46x[n] - 3.53x[n-1] - 3.93x[n-2] + 2.86y[n-1] + 4.1y[n-2] + 0.65y[n-3] y[n] = 1.46x[n] + 3.53x[n-1] - 3.93x[n-2] - 2.86y[n-1] - 4.1y[n-2] -0.65y[n-3] 1. 2. 3. 4. 5. b = [-1.46 -3.53 3.93]; a = [1 2.86 4.1 0.65] b = [-1.46 -3.53 -3.93]; a = [1 -2.86 -4.1 -0.65] b = [-1.46 -3.53 3.93]; a = [1 -2.86 -4.1 -0.65] b = [1.46 3.53 -3.93]; a = [1 2.86 4.1 0.65] b = [1.46 3.53 -3.93]; a = [1 -2.86 -4.1 -0.65]
0 = x12 - 2x1 – x2 + 0.5 0 = 4x22 - 4 + x12 [x1, x2]0=[2.5, 1.25] and perform only one Newton’s iteration to find [x1, x2]1 for the following system of nonlinear equations Calculate x1 and x2
The table below shows the projected values (in millions of dollars) of hardback college textbooks sold in the United States for the years 2007 to 2009. Year Value 2007 4412 C = 2008 4471 2009 4556 (a) Create a system of linear equations for the data to fit the curve y = at² + bt + c, where t is the year and t = 7 corresponds to 2007, and y is the value of the textbooks. = 4412 = 4471 = 4556 (b) Use Cramer's Rule to solve your system. a = b =
Question 5 Read the question and type your response in the box provided. Your response will be saved autor Solve this system of equations by graphing. Be sure to identify the solution. y = x + 2 y = 2x-1 A BIU E E X, x' * ©2021 Illuminate Education , Inc.
1. 2. form: form: Solve the system of equations. Put your solutions, if there is one, in parametric X1 -X1 2x1 X1 + -X1 + X2 + 3x2 + - X2 X3 = 0 + 2x3 = T Solve the system of equations. Put your solutions, if there is one, in parametric X3 + Xx3 0 + X2 + 4x3 0 1 = 2 2x2 + 5x3 = 4
Consider the discrete-time dynamical system bt+1 = 2.0bt for a bacterial population. Supposing each bacterium takes up 104 μm3, write the updating function for the total volume of bacteria (in μm3) as afunction of the volume the year before:vt+1 = _____ vt + ___ μm3
2s Transfer function of a linear system is given as H(s) Find the output y(t) due s+6 to the input e-3tu(t).
Ок Denote the owl and wood rat populations at time k by x = Rk where k is in months, Ok is the number of owls, and R is the number of rats (in thousands). Suppose OK and RK satisfy the equations below. Determine the evolution of the dynamical system. (Give a formula for XK.) As time passes, what happens to the sizes of the owl and wood rat populations? The system tends toward what is sometimes called an unstable equilibrium. What might happen to the system if some aspect of the model (such as birth rates or the predation rate) were to change slightly? Ok+1 = (0.2)0k + (0.5)RK Rk+1=(-0.16)0k + (1.1)Rk Give a formula for xk- xk = 4 ( D +C₂1