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Date: 21-5-2018
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Date: 20-12-2018
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Date: 11-6-2018
536
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1. A prey population increases at a rate (proportional to the number of prey) but is simultaneously destroyed by predators at a rate (proportional to the product of the numbers of prey and predators).
2. A predator population decreases at a rate (proportional to the number of predators), but increases at a rate (again proportional to the product of the numbers of prey and predators).
This gives the coupled differential equations
(1) |
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(2) |
solutions of which are plotted above, where prey are shown in red, and predators in blue. In this sort of model, the prey curve always lead the predator curve.
Critical points occur when , so
(3) |
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(4) |
The sole stationary point is therefore located at .
REFERENCES:
Boyce, W. E. and DiPrima, R. C. Elementary Differential Equations and Boundary Value Problems, 5th ed. New York: Wiley, p. 494, 1992.
Zwillinger, D. Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, p. 135, 1997.
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كيف تساهم الأطعمة فائقة المعالجة في تفاقم مرض يصيب الأمعاء؟
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مشروع ضخم لإنتاج الهيدروجين الأخضر يواجه تأخيرًا جديدًا
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المجمع العلمي يختتم دورته القرآنية في فن الصوت والنغم بالطريقة المصرية
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