Solve this problem using MATLAB
28.24 Isle Royale National Park is a 210-square-mile archipelago composed of a single large island and many small islands in Lake Superior. Moose arrived around 1900 and by 1930, their population approached 3000, ravaging vegetation. In 1949, wolves crossed an ice bridge from Ontario. Since the late 1950s, the numbers of the moose and wolves have been tracked. (Dash indicates no data.) Year Moose Wolves Year Moose Wolves 1960 700 1961 1962 1963 1964 1965 1966 881 1967 1968 1000 1969 1150 1970 966 1971 1972 836 1973 802 1974815 1975778 1976 641 977507 1978 543 1979 675 1980 577 1981 570 1982 590 1983 811 23 20 25 28 24 23 24 30 41 43 40 42 50 30 17 674 20 23 (a) Integrate the Lotka-Volterra equations from 1960 through 2020. Determine the coefficient values that yield an optimal fit. Compare your simulation with these data using a time-series approach, and comment on the results. (b) Plot the simulation of (a), but use a phase-plane approach (c) After 1993, suppose that the wildlife managers trap one wolf per year and transport it off the island. Predict how the populations of both the wolves and moose would evolve to the year 2020 Present your results as both time-series and phase-plane plots. For this case, as well as for (d), use the following coefficients: a 0.3, b 0.0111,c 0.2106, d 0.0002632. (d) Suppose that in 1993, some poachers snuck onto the island and killed 50% of the moose. Predict how the populations of both the wolves and moose would evolve to the year 2020. Present your results as both time-series and phase-plane plots. 28.24 Isle Royale National Park is a 210-square-mile archipelago composed of a single large island and many small islands in Lake Superior. Moose arrived around 1900 and by 1930, their population approached 3000, ravaging vegetation. In 1949, wolves crossed an ice bridge from Ontario. Since the late 1950s, the numbers of the moose and wolves have been tracked. (Dash indicates no data.) Year Moose Wolves Year Moose Wolves 1960 700 1961 1962 1963 1964 1965 1966 881 1967 1968 1000 1969 1150 1970 966 1971 1972 836 1973 802 1974815 1975778 1976 641 977507 1978 543 1979 675 1980 577 1981 570 1982 590 1983 811 23 20 25 28 24 23 24 30 41 43 40 42 50 30 17 674 20 23 (a) Integrate the Lotka-Volterra equations from 1960 through 2020. Determine the coefficient values that yield an optimal fit. Compare your simulation with these data using a time-series approach, and comment on the results. (b) Plot the simulation of (a), but use a phase-plane approach (c) After 1993, suppose that the wildlife managers trap one wolf per year and transport it off the island. Predict how the populations of both the wolves and moose would evolve to the year 2020 Present your results as both time-series and phase-plane plots. For this case, as well as for (d), use the following coefficients: a 0.3, b 0.0111,c 0.2106, d 0.0002632. (d) Suppose that in 1993, some poachers snuck onto the island and killed 50% of the moose. Predict how the populations of both the wolves and moose would evolve to the year 2020. Present your results as both time-series and phase-plane plots
