07 - Solve, NSolve, Solving System of Equations.pdf

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University of California - Irvine
Douglas Tobias

Total Score 28/29 HOMEWORK #7 SABRINA LUGO SECTION B #1: The Lotka-Volterra equations are a model to describe the dynamics of the populations of a predator and its prey: x’(t)=ax(t)-bx(t)y(t) y’(t)=-cy(t)+dx(t)y(t) x(t) = the population of the prey at time t y(t)= the popuation of the predator at time t a= the birth rate of the prey b= the rate at which the predators eat teh prey c= the death rate of the predator d= the rate at which the population of the predators increases by eatting the prey a) use NDSolve to generate numerical solutions to this system of differential equations for x(t) and y(t) with initial conditions x(0)=10, y(0)=4, a=1.5, b=1.0, c=3.0, and d=1.0, over the time inter- val 0 btb30. << PlotLegends` General::obspkg : PlotLegends` is now obsolete. The legacy version being loaded may conflict with current Mathematica functionality. See the Compatibility Guide for updating information. LotkaVolterra = 8 x'@tD ã a * [email protected] - b * [email protected] * [email protected], y'@tD ã -c * [email protected] + d * [email protected] * [email protected], [email protected] ã 10, [email protected] ã 4 [email protected], [email protected] Ø [email protected], 30.<[email protected]<< b) Plot the two solutions generated in part (a) on the same plot over the time interval 0btb30. Use PlotRangeØAll if necessary to display the entire curves. Include a legend on your plot. Printed by Wolfram Mathematica Student Edition 2 sclugo_HW7.nb [email protected]_D := [email protected] ê. [email protected]@1DD; [email protected]_D := [email protected] ê. [email protected]@1DD; [email protected]@tD, [email protected]
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