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Lecture

9.6 Predator-Prey Systems Question #1 (Easy)


Department
Mathematics
Course Code
MAT136H1
Professor
all

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9.6 Differential Equations
Predator & Prey Systems
Question #1 (Easy): Understanding the Predator-Prey System
Strategy
Differential equations can be used to represent the prey and predator population rate of change system.
Given variables x and y, and the differential equations provided with terms that contribute to the
growth and decline in the rate of population growth, the predator and prey system can be analyzed.
Sample Question
For the predator-prey system, determine which variables of x and y represents the prey and predator
population. Is the growth of the prey restricted only by the predators or by other factors as well? Do the
predators feed only on the prey or on other food sources as well? Explain.

    

   
Solution
Notice that when   , 
   meaning it is declining in the absence of variable . The predators
feed on predator, therefore represents the predator population. Then the other variable represents
prey population. The growth of prey population is restricted by  which only involves variable
and , thus it is restricted only by the predators and no other external factors. Likewise, the predator
population increases by the term  which only involves variables and , thus there is no other
food source besides the prey.
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