Part 3 ii) Identify the long-term behavior of the population system, i.e., compute the lim+00 x(t).Note how this limit is related to one of the eigenvectors related to the system matrix A.iii) Suppose that the initial conditions a, b are non-negative and a + b > 0. We want thepopulation of vehicles to be distributed according to the ratio 1: 2 as t → xo. What shouldthe values of kAB, kBA be in order to achieve this? Problem 4. Suppose that you have two spatial locations A and B. You have a populationof self-driving vehicles, that switch from location A to B, with probability KABAT,and fromlocation B to A with probability kBAAt. This can be represented by a "reversible chemicalreaction", with "reaction rates" kAB and and kBAA KAB, BkBAВThe population of self-driving vehicles in each location A and B is given by XA(t) andXB(t), respectively. For At arbitrarily small, given that kABand kba are non-negative con-stant values, the evolution of the population of vehicles in site A and B are given by,*a(t)-KABTA(t) + KBATB(t)(1)KABTA(t) – KBATB(t)(2)TA(0) := a xB(0) = b(3)i) Find the solution to the IVP.

Name: Part 3 ii) Identify the long-term behavior of the population system, i
Uploaded: 2024-03-20T07:06:41.000Z
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Description: Part 3 ii) Identify the long-term behavior of the population system, i.e., compute the lim+00 x(t).Note how this limit is related to one of the eigenvectors related to the system matrix A.iii) Suppose that the initial conditions a, b are non-negative