Interaction of two species of squirrels fiercely competing for the same ecological niche onan island is described by Lotka-Volterra-Gause equationsdN1N1(2 – N1 – 2N2) = f(N1, N2),dt(1)dN2N2(3 – N2 – 3N1) = g(N1, N2),dtwhere N1 = N1(t) and N2 = N2(t) are the population densities of the competing species. (c) Sketch the phase portrait of system (1) in the biologically sensible region, i.e. identifyall relevant equilibria in the phase plane and sketch a few typical trajectories clearlyindicating with arrows the direction of the phase trajectories.

So we have to plot a detailed graph of the phase plane of the given system, identifying all the…

Answered: Sketch the phase portrait of system (1)…

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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a) A Multiple Linear Regression Model in the form provided in Equation 1 is required to predict the amount of trips likely to be generated in the Bortianor vicinity in 2040. Y=a+ajX1+æXz+æX3 (Equation 1) where Y= trips/household to work X1= number of cars owned by household X2 = income of household X3 = household size ao, ai, æ and a3 =constants Using the corelation matrix obtained from a base year survey in Table 5, detemine all the possible equations that can be fomulated in the fom of Equation 1 out of which the best predictive model will be selected. Give reasons for your choice of equations. Assume all the independent variables are linearly related to the dependent variable and eachindependent variable is easily projected. Table 5: Comrelation matrix Trips Household size Car Income ownership Trips Car ownership Income Household size 1 0.65 1 0.90 0.89 1 0.97 0.25 0.18 1
Determine the coefficients of a,b,c and d so that the curve will satisfy the stipulated condition
please solve it on paper
not use ai please
9. Find the equation y = ax² + bx + c of the least-square parabola that best fits the given data points (-1,0), (0,3), (1,3), (2,5), and (3,9).
Data on the relationship between plant age and dry matter in the stalk are given in the Table. X (Age) 4 6 8 1 1 14 16 18 2 3 4 Y (Dry matter, %) 4 4 49 4 51 51 8 8 i) Express the relationship between the exhausted age and dry matter level with the regression equation (Ý = aX + b). ii) Using the obtained equation, estimate what the dry matter% of plants with a age of 22 weeks will be. iii) By drawing the skater diagram, find the correlation coefficient and interpret the found values. ii) iii)
A particular solution and a fundamental solution set are given for the nonhomogeneous equation below and its corresponding homogeneous equation. (a) Find a general solution to the nonhomogeneous equation. (b) Find the solution that satisfies the specified initial conditions. 2xy'' – 8y" = - 16; x>0 y(1) = 4, y'(1) = - 5, y'"(1) = - 28; Yp = x?; (1, x, xº}
What is the stability of the 4 equilibrium points? Does point (0,0) even count?
Data on the relationship between plant age and dry matter in the stalk are given in the Table. X (Age) 4 6 8 10 12 14 16 18 Y (Dry matter, %) 24 28 35 48 44 49 51 51 i) Express the relationship between the exhausted age and dry matter level with the regression equation (Ŷ = aX + b). ii) ii) Using the obtained equation, estimate what the dry matter% of plants with a age of 22 weeks will be. iii) iii) By drawing the skater diagram, find the correlation coefficient and interpret the found values.
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Sketch the phase portrait of system (1) in the biologically sensible region, i.e. identify all relevant equilibria in the phase plane and sketch a few typical trajectories clearly indicating with arrows the direction of the phase trajectories.