Math Lab 2.2

# Math Lab 2.2 - Victor Liou Dr. McNamara March 10, 2008 Math...

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Victor Liou Dr. McNamara March 10, 2008 Math Lab 2.2 After analysis of all the pairs in the given systems, we can see that the coefficients in front of each term or pair of terms have an effect on the rate of growth. Each coefficient has a specific importance in relating the current size of two populations and the effect each has on the growth of another. We see that in group A of each system the coefficients -5, -3,-4, and -4 in front of the ‘x’ term saythat as the population of x increases, dx/dt will decrease more rapidly unless the population of y increases as well. For the population to have no rate of change, y=5/2, 3/2, 4/3, and 5/3, respectively. The coefficient -4, -5, -3, and -3 in front of ‘y’ term in the dy/dt equationssays that as the population of y increases, the rate of growth of y will decrease. For dy/dt=0, x=4/3, 5/3, 3/2 and 3/2 respectively. The coefficient pairs 2-3 and 3-2 in front of the ‘xy’ terms show that as population and interactions between x and y increase, so will the rate of change of growth. However, population growth relies most greatly on the size of the other population since an increase of the second population can only cause positive growth in the first population. This part of the system is cooperative since the ‘xy’ is positive which shows that interactions between populations will increase growth rate of

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## This note was uploaded on 04/29/2008 for the course MATH 310 taught by Professor Mcnamara during the Spring '08 term at Saint Louis.

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Math Lab 2.2 - Victor Liou Dr. McNamara March 10, 2008 Math...

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