In Example 1 we used Lotka-Volterra equations to model populations of rabbits and wolves. Let'smodify those equations as follows:dR= 0.1R(1 – 0.0001R) – 0.003RWdtdW-0.01W + 0.00004RWdtFind all of the equilibrium solutions.Enter your answer as a list of ordered pairs (R, W), where Ris the number of rabbits and W thenumber of wolves. For example, if you found three equilibrium solutions, one with 100 rabbits and 10wolves, one with 200 rabbits and 20 wolves, and one with 300 rabbits and 30 wolves, you wouldenter (100, 10), (200, 20), (300, 30). Do not round fractional answers to the nearest integer.Answer =|

Answered: Image /qna-images/answer/d7805b04-4d01-40e8-8cda-80a4667fa7b1.jpg

Answered: In Example 1 we used Lotka-Volterra…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The average reading score on certain tests is given by y = 0.153x +255.33, where x is the number of years past 1970. In what year would the average reading = score be 258.849 if this model is accurate? The average reading score would be 258.849 in D 58 (Type a whole number.) CIJ #tv N N A ال / Next
Two tanks T1 and T2, respectively contain 200 and 100 liters of water and unspecified amounts of fertilizer. Now, set up a model describing the amount of fertilizer contained in each tank y1(t) and y2(t) at time t. please do not provide solution in image format thank you!
From 2000 through 2009, the population of State A grew more slowly than that of State B. Models that represent the populations of the two states are given by P = 37.5t + 6075 State A P = 168.2t + 5138 State B where P is the population (in thousands) and t represents the year, with t = 0 corresponding to 2000. Use the models to estimate when the population of State B first exceeded the population of State A. (Round your answer to the nearest year.)
2. Linearize the following equation about the equilibrium point (xo, Yo, Zo, uo) * = a X 1+ y² + c y = yu z = xy + u Where z is the output, u is the input and a and care constant.
The same disease is spreading through two populations, say Pi and P2, with the same size. You may assume that the spread of the disease is well described by the SIR model. dSa - BaSaIa dt dla - dt dRa YaIa dt with Sa(0) + I.(0) + R.(0) = N where N denotes the fixed population size. The subscript a identifies the population P or P2. For example, if a = 1, the variables are related to P1. Assume that S1 (0) = S2 (0) and I1(0) = I½(0) and that no interventions such as quarantine or vaccination have been implemented. If the difference in the spread of the disease is due only to the poor over-all health of a population, which population has the best over-all health of the two populations? - Susceptible Population 1 - Susceptible Population 2 700 600 500 400 300 200 100 10 15 20 t P1. P2. Susceptible
A mass weighing 16 pounds is attached to a spring, stretching it 2 feet. A damping mechanism provides a resistance numerically equal to b times the instantaneous velocity. The mass is pulled down 1 foot below equilibrium and released from rest. a. Find the equations of motion for b = 3, b = 4, b = 5. b. Determine if each system is underdamped, critically damped, or overdamped.
5. Okay, time for some mathematics. We're going to focus on the interactions between the hares and their main predators, the lynx. The tool we need is differential equations (last seen when we talked about the S-I-R disease model). We will let H(t) be the density of hares at time t, and L(t) the density of lynx at time t. Our first assumption is that, if there are no lynx around, the hares grow exponentially. Hares lead to more hares and faster growth. This gives us the differential equation (trust me): HP = aH dt where a is a positive constant. Second we assume that, if there are no hares around, the lynx starve and thus their numbers decay exponentially. This gives us: TP = -bL dt
Ок Denote the owl and wood rat populations at time k by x = Rk where k is in months, Ok is the number of owls, and R is the number of rats (in thousands). Suppose OK and RK satisfy the equations below. Determine the evolution of the dynamical system. (Give a formula for XK.) As time passes, what happens to the sizes of the owl and wood rat populations? The system tends toward what is sometimes called an unstable equilibrium. What might happen to the system if some aspect of the model (such as birth rates or the predation rate) were to change slightly? Ok+1 = (0.2)0k + (0.5)RK Rk+1=(-0.16)0k + (1.1)Rk Give a formula for xk- xk = 4 ( D +C₂1

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