# Section 1- Variables and Parameters

## What is the system we are examining?

This system models a predator-prey situation in which the prey species is subdivided into adult and children populations. The purpose of this system is to investigate the effect of child care on a predator-prey situation. It is assumed that the adults are able to protect the children from the predators and therefore only the adult portion of the species is preyed upon. We will proceed to investigate what happens to such a system over a long period of time.

### System:

• c' = ba - gc - dc
• a' = gc - da- uay
• y' = - ny + uay

### Variables:

• a = number of adults (prey)
• c = number of children (prey)
• y = number of predators
• x = a + c = number of prey

Parameters:
• b = birth rate of prey (related to: a)
• g = growing up rate of prey (related to: c)
• d = death rate of prey (related to: a and c)
• u = predation rate (related to: a and y)
• n = net death rate of predators (related to: y)

b,g,d,n,u > 0 in all cases

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