Elements of Numerical Mathematical Economics with Excel

4.6. Tourism fight between two competing regions

As a first economic example, let us model a “fight” between two regions to attract tourists. The system of two differential equations is as follows:

{ y ˙ 1 ( t ) = − y 1 ( t ) + 3 y 2 ( t ) y ˙ 2 ( t ) = 5 y 1 ( t ) − 3 y 2 ( t )

where y ₁(t) and y ₂(t) represent the deviations from the normal tourism advertising budget for the two competing regions, so that if:

{ y ( t ) < 0 ⇒ c o u n t r i e s a r e s p e n d i n g l e s s t h a n t h e n o r m a l b u d g e t y ( t ) = 0 ⇒ c o u n t r i e s a r e