The population of prey is denoted æ(t) (in millions) and the population of predators is denoted y(t) (in millions). We assume that: • In the absence of predators, the prey population satisfies the logistic growth model with a carrying capacity K (in millions). • In the absence of prey, the predator population decays at a rate proportional to the predator population. • The prey population decays at a rate proportional to the product of prey and predators. • The predator population grows at a rate proportional to the product of prey and predators. These assumptions lead to the following nonlinear system of differential equations: = ax (1 –) - Bæy K = yxY – Sy where a, B, y, and 8 are positive constants. Assume that K > . The [K' is locally asymptotically stable. equilibrium ye = True False

The population of prey is denoted æ(t) (in millions) and the population of predators is denoted y(t) (in millions). We assume that: • In the absence of predators, the prey population satisfies the logistic growth model with a carrying capacity K (in millions). • In the absence of prey, the predator population decays at a rate proportional to the predator population. • The prey population decays at a rate proportional to the product of prey and predators. • The predator population grows at a rate proportional to the product of prey and predators. These assumptions lead to the following nonlinear system of differential equations: = ax (1 –) - Bæy K = yxY – Sy where a, B, y, and 8 are positive constants. Assume that K > . The [K' is locally asymptotically stable. equilibrium ye = True False

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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Question

The population of prey is denoted æ(t) (in millions) and the population
of predators is denoted y(t) (in millions). We assume that:
• In the absence of predators, the prey population satisfies the logistic
growth model with a carrying capacity K (in millions).
• In the absence of prey, the predator population decays at a rate
proportional to the predator population.
• The prey population decays at a rate proportional to the product of
prey and predators.
• The predator population grows at a rate proportional to the product
of prey and predators.
These assumptions lead to the following nonlinear system of differential
equations:
(1 -*)
y/ = yay – Sy
K) - Bry
= ax
where a, B, y, and d are positive constants. Assume that K > . The
equilibrium ye =
is locally asymptotically stable.
True
False

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