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(a) Let N be the Numic population and P the Prenumic population in the great basin. As- suming 1-dimensional model for t
Posted: Mon May 23, 2022 11:23 am
by answerhappygod
- A Let N Be The Numic Population And P The Prenumic Population In The Great Basin As Suming 1 Dimensional Model For T 1 (60.85 KiB) Viewed 30 times
(a) Let N be the Numic population and P the Prenumic population in the great basin. As- suming 1-dimensional model for the space variable I, use the competing species equations given in the article to write the reaction-diffusion equations for and Use the specific numbers for the parameters that are given in the article. (6) Find and solve the competing species equation DN N(ri-aN - BP) dt DP P(r2-9N - 8P) dt corresponding the the parameters from above. Sketch the general solution. (e) Suppose N = U(z - cit), V = U', P = W(- 034), Z = W'. Find the 4 x 4 system of ODE's for U, V, W, Z corresponding to the reaction-diffusion equation. (d) Find all critical points for the equations in c). (e) Find a critical point of the form (a,0,0,0). Find conditions for which the eigenvalues are real. If the eigenvalues are real, how many are negative? Find a critical point of the form (0,0,0,0). Find conditions for which the eigenvalues are real. If the eigenvalues are real, how many are negative? (8) Assume the two critical points above are connected by a solution that goes from the point with the largest member of positive eigenvalues to the point with the largest number of negative eigenvalues, and that a c = c Sketch U(z -ct) and W(z-ct) for t = 0,1,2. Page 3 I (1) Compute the minimum wave speed for which the critical points have only real eigenvalues. At the minimum wave speed, how many years would it take for the Numie population to overtake the great basin? Since this is a 1-dimensional model, estimate the time it takes to traverse the length of one side of the square region used to approximate the great basin in the paper. How does this compare with what we have said about the time period of the Numic spread? G) The actual way that a circular traveling wave moves outward from a point in 2-dimensions is -- where is the 1-dimensional wavelength and R is the radius of the wave front. Solve for t(R) vesing R-200 kom att 0 How long does it take for R to get to 1000 kun? Explain why this matches the conclusion of the paper