1550078481-Ordinary_Differential_Equations__Roberts_

Applications of Systems of Equations 463 Without using any computer software, decide how the results of exercise 2 will be affe ...

464 Ordinary Differential Equations (i) a= 2, b = c = d = e = f = g = h = 1 (ii) a= 2, b = .5, c = d = e = f = g = h = 1 In each ...

Applications of Systems of Equations 465 Leslie-Gower Prey-Predator Model In 1960 , P. H. Leslie and J. C. Gower studied the fol ...

466 Ordinary Differential Equations b. Determine the stability characteristics of the critical point. c. Use computer software t ...

Applications of Systems of Equations 467 As b efore, x is the prey population, y is the predator population, and a, b, c, d, e a ...

468 Ordinary Differential Equations If the growth assumption is changed from the Malthusian law to the logistic law, then the co ...

Applications of Systems of Equations a. Find the critical points of the competitive hunters model (4) dx 2 - = 4x - .5xy - .2x ...

470 Ordinary Differential Equations For a. H = 0, b. H = 4, and c. H = 8 (i) Find the critical points of system (6) in the first ...

Applications of Systems of Equations 471 the number of susceptibles and the number of infectives. Thus, it is assumed that (2) d ...

472 Ordinary Differential Equations S > r / (3), we have dI / dt > 0 and the number of infectives increases. When (JS - r ...

Applications of Systems of Equations 473 on the interval 0 :::; t :::; 10 days for the initial conditions (i) So = 500, Io = 5, ...

474 Ordinary Differential Equations on the rectangle 0 ~ S ~ 500 and 0 ~ I ~ 200. This phase-plane graph is shown in Figure 10.1 ...

Applications of Systems of Equations 475 150 100 50 S(t) oL-.~~~~~~~~....=:::::::::;:::::;==::;~=;==;---l 150 I 100 50 0 2 4 6 8 ...

476 Ordinary Differential Equations EXERCISES 10.6 Consider the epidemic model (7) dS = -.OlSI dt dI - = .OlSI -3I dt dR = 3I ...

Applications of Systems of Equations 477 Use computer software to solve the following epidemic with inoculation model dS dt = -. ...

478 Ordinary Differential Equations Display a graph with S, I, and R. Does an epidemic occur in case (ii)? In each case, what is ...

Applications of Systems of Equations 479 males and 159,271 were females. It is estimated that by the end of 2002, that a total o ...

480 Ordinary Differential Equations b. Use computer software to so lve system (8) on the interval [O, 1] for S 1 = 100 , S2 = 50 ...

Applications of Systems of Equations 481 where c ;:::: 0 is a constant of proportionality, k = mg/£, g is the constant of accele ...

482 Ordinary Differential Equations (Verify this fact.) Since this solution is periodic with period 2n, the origin is a neutrall ...