Consider Example 3, Competitive Hunter Model—Spotted Owls and Hawks. Experiment with dif...

Consider Example 3, Competitive Hunter Model—Spotted Owls and Hawks. Experiment with different values for the coefficients using the starting values given. Then try different starting values. What is the long-term behavior? Do your experimental results indicate that the model is sensitive

a. to the coefficients?

b. to the starting values?

REFERENCE:

EXAMPLE 3 Competitive Hunter Model—Spotted Owls and Hawks

Suppose a species of spotted owls competes for survival in a habitat that also supports hawks. Suppose also that in the absence of the other species, each individual species exhibits unconstrained growth in which the change in the population during an interval of time (such as 1 day) is proportional to the population size at the beginning of the interval. If O_n represents the size of the spotted owl population at the end of day n and H_n represents the competing hawk population, then

Here, k1 and k2 are the constant positive growth rates. The effect of the presence of the second species is to diminish the growth rate of the other species, and vice versa. Although there are many ways to model the mutually detrimental interaction of the two species, we will assume that this decrease is approximately proportional to the number of possible interactions between the two species. Therefore, one sub model is to assume that the decrease is proportional to the product of O_n and H_n. These considerations are modeled by the equations