The population of prey is denoted a (t) (in millions) and the population of predators is...

Transcribed Image Text:

The population of prey is denoted a (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 -*) K) - Bay y = yay – by where a, B, y, and o are positive constants. Assume that K > . The K' is locally asymptotically stable. equilibrium ye = True False The population of prey is denoted a (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 -*) K) - Bay y = yay – by where a, B, y, and o are positive constants. Assume that K > . The K' is locally asymptotically stable. equilibrium ye = True False