Ground squirrels engage in alarm calls to alert their fellow squirrels that a pr

Question

Ground squirrels engage in alarm calls to alert their fellow squirrels that a predator may be present. Silent squirrels may start calling if they hear a call. Over time, calling squirrels may stop calling if the danger has not materialized. With this information, write equations about the rate of change of the two populations of silent and caling squirrels. If it helps, draw a flow diagram representing the number of silent and calling ground squirrels over time and label flow rates above each arrow in the diagram.

Explanation / Answer

solution

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Let number of calling squirrels at any point of time be x1 and the number of silent squirrels at any time be x2.Total number of squirrels be x = x1 + x2

Since the number of squirrels remains constant implies dx/dt = 0

=> dx/dt = dx1/dt + dx2/dt = 0

=> dx1/dt = - dx2/dt

Lets say rate of change of calling squirrels increases linearly with the number of calling squirrels and the number of squirrels who might stop calling also varies linearly with the number of silent squirrels

=> dx1/dt = k1x1 - k2x2

=> dx2/dt = -(k1x1 - k2x2)

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