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0.4 Bifurcations The model dealing with constant harvesting provides an example of bifurcation. A bifur- cation is essentially a dramatic change in the qualitative structure of the phase line, such as the appearance or disappearance of equilibrium solutions (critical values). A bifurcation. diagram for a family of DES is a graph that shows the location and stability of the critical values for each parameter, in our case the parameter is h, the harvesting rate. Consider our example where r = 1 and K = 1600. The critical values satisfy dP P dt dp = rp (1-R) - h = 0, K =rP and these you already solved using the quadratic formula in Part 3.2.a above. (a) Plot the graph of P vs h from (3) for 0 ≤h ≤ 1600. Plot both P+ and P_ for each value of h. Use the values you already found in Part 3.2.a above. (b) What is the bifurcation point and what does it tell you about the limits on h if the goal is a sustainable fishery?

0.4 Bifurcations The model dealing with constant harvesting provides an example of bifurcation. A bifur- cation is essentially a dramatic change in the qualitative structure of the phase line, such as the appearance or disappearance of equilibrium solutions (critical values). A bifurcation. diagram for a family of DES is a graph that shows the location and stability of the critical values for each parameter, in our case the parameter is h, the harvesting rate. Consider our example where r = 1 and K = 1600. The critical values satisfy dP P dt dp = rp (1-R) - h = 0, K =rP and these you already solved using the quadratic formula in Part 3.2.a above. (a) Plot the graph of P vs h from (3) for 0 ≤h ≤ 1600. Plot both P+ and P_ for each value of h. Use the values you already found in Part 3.2.a above. (b) What is the bifurcation point and what does it tell you about the limits on h if the goal is a sustainable fishery?

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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0.4 Bifurcations The model dealing with constant harvesting provides an example of bifurcation. A bifur- cation is essentially a dramatic change in the qualitative structure of the phase line, such as the appearance or disappearance of equilibrium solutions (critical values). A bifurcation. diagram for a family of DES is a graph that shows the location and stability of the critical values for each parameter, in our case the parameter is h, the harvesting rate. Consider our example where r = 1 and K = 1600. The critical values satisfy dP P dt dp = rp (1-R) - h = 0, K =rP and these you already solved using the quadratic formula in Part 3.2.a above. (a) Plot the graph of P vs h from (3) for 0 ≤h ≤ 1600. Plot both P+ and P_ for each value of h. Use the values you already found in Part 3.2.a above. (b) What is the bifurcation point and what does it tell you about the limits on h if the goal is a sustainable fishery?
Transcribed Image Text:0.4 Bifurcations The model dealing with constant harvesting provides an example of bifurcation. A bifur- cation is essentially a dramatic change in the qualitative structure of the phase line, such as the appearance or disappearance of equilibrium solutions (critical values). A bifurcation. diagram for a family of DES is a graph that shows the location and stability of the critical values for each parameter, in our case the parameter is h, the harvesting rate. Consider our example where r = 1 and K = 1600. The critical values satisfy dP P dt dp = rp (1-R) - h = 0, K =rP and these you already solved using the quadratic formula in Part 3.2.a above. (a) Plot the graph of P vs h from (3) for 0 ≤h ≤ 1600. Plot both P+ and P_ for each value of h. Use the values you already found in Part 3.2.a above. (b) What is the bifurcation point and what does it tell you about the limits on h if the goal is a sustainable fishery?
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