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Objectives: Solve a system of ODEs using built-in Matlab functions like ode45(). You must be able to setup the inputs properly by hand or in Matlab. The Lotka-Volterra predator-prey model uses first-order differential equations to estimate the populations of two interacting species, p₁ and p2- dpi dt dp2 dt = a*pi-ß* P1 * P2 Script = 8 * P1 * P2-Y * P2 where a is the prey's growth rate, ß is the prey's death rate, & is the predator's growth rate and y is the predator's death rate. We want to model the population of snow hares (pi) and Canadian lynxes (p2). Assume: ▪ the population at t=0 is 100 hares and 5 lynxes ▪ all rates are constant ▪ no other factors influence population size Your final script should: 1. implement the predator-prey model with a = 0.48, ß= 0.025, y = 0.68 and 8 = 0.02. 2. solve the system of differential equations at all timepoints in tYears = 0:0.25:100 using ode45 and the initial populations provided in po 3. assign the resulting population estimates to a 2-column matrix named ppPop. Prey should be in the first column and predator in the second Make sure you supply a time vector instead of a time span to the solver ensures the solutions are evaluated at the same time points for the grader tool. 1 pe = [100 5]; % population of snow hares, lynxes at t=0 2 tYears = 0:0.25:100; % discrete time interval, in years 4% Add your code below 6 % Model parameters (can be moved to where needed in your script) 7 a = 0.48; % prey's growth rate 8 b = 0.025; % prey's death rate 9 c = 0.68; % predator's death rate 10 d = 0.02; % predator's growth rate 11

Objectives: Solve a system of ODEs using built-in Matlab functions like ode45(). You must be able to setup the inputs properly by hand or in Matlab. The Lotka-Volterra predator-prey model uses first-order differential equations to estimate the populations of two interacting species, p₁ and p2- dpi dt dp2 dt = a*pi-ß* P1 * P2 Script = 8 * P1 * P2-Y * P2 where a is the prey's growth rate, ß is the prey's death rate, & is the predator's growth rate and y is the predator's death rate. We want to model the population of snow hares (pi) and Canadian lynxes (p2). Assume: ▪ the population at t=0 is 100 hares and 5 lynxes ▪ all rates are constant ▪ no other factors influence population size Your final script should: 1. implement the predator-prey model with a = 0.48, ß= 0.025, y = 0.68 and 8 = 0.02. 2. solve the system of differential equations at all timepoints in tYears = 0:0.25:100 using ode45 and the initial populations provided in po 3. assign the resulting population estimates to a 2-column matrix named ppPop. Prey should be in the first column and predator in the second Make sure you supply a time vector instead of a time span to the solver ensures the solutions are evaluated at the same time points for the grader tool. 1 pe = [100 5]; % population of snow hares, lynxes at t=0 2 tYears = 0:0.25:100; % discrete time interval, in years 4% Add your code below 6 % Model parameters (can be moved to where needed in your script) 7 a = 0.48; % prey's growth rate 8 b = 0.025; % prey's death rate 9 c = 0.68; % predator's death rate 10 d = 0.02; % predator's growth rate 11

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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6.1
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Objectives: Solve a system of ODEs using built-in Matlab functions like ode45(). You must be able to setup the inputs properly by hand or in Matlab. The Lotka-Volterra predator-prey model uses first-order differential equations to estimate the populations of two interacting species, p₁ and p2- dpi dt dp2 dt = a*pi-ß* P1 * P2 Script = 8 * P1 * P2-Y * P2 where a is the prey's growth rate, ß is the prey's death rate, & is the predator's growth rate and y is the predator's death rate. We want to model the population of snow hares (pi) and Canadian lynxes (p2). Assume: ▪ the population at t=0 is 100 hares and 5 lynxes ▪ all rates are constant ▪ no other factors influence population size Your final script should: 1. implement the predator-prey model with a = 0.48, ß= 0.025, y = 0.68 and 8 = 0.02. 2. solve the system of differential equations at all timepoints in tYears = 0:0.25:100 using ode45 and the initial populations provided in po 3. assign the resulting population estimates to a 2-column matrix named ppPop. Prey should be in the first column and predator in the second Make sure you supply a time vector instead of a time span to the solver ensures the solutions are evaluated at the same time points for the grader tool. 1 pe = [100 5]; % population of snow hares, lynxes at t=0 2 tYears = 0:0.25:100; % discrete time interval, in years 4% Add your code below 6 % Model parameters (can be moved to where needed in your script) 7 a = 0.48; % prey's growth rate 8 b = 0.025; % prey's death rate 9 c = 0.68; % predator's death rate 10 d = 0.02; % predator's growth rate 11
Transcribed Image Text:Objectives: Solve a system of ODEs using built-in Matlab functions like ode45(). You must be able to setup the inputs properly by hand or in Matlab. The Lotka-Volterra predator-prey model uses first-order differential equations to estimate the populations of two interacting species, p₁ and p2- dpi dt dp2 dt = a*pi-ß* P1 * P2 Script = 8 * P1 * P2-Y * P2 where a is the prey's growth rate, ß is the prey's death rate, & is the predator's growth rate and y is the predator's death rate. We want to model the population of snow hares (pi) and Canadian lynxes (p2). Assume: ▪ the population at t=0 is 100 hares and 5 lynxes ▪ all rates are constant ▪ no other factors influence population size Your final script should: 1. implement the predator-prey model with a = 0.48, ß= 0.025, y = 0.68 and 8 = 0.02. 2. solve the system of differential equations at all timepoints in tYears = 0:0.25:100 using ode45 and the initial populations provided in po 3. assign the resulting population estimates to a 2-column matrix named ppPop. Prey should be in the first column and predator in the second Make sure you supply a time vector instead of a time span to the solver ensures the solutions are evaluated at the same time points for the grader tool. 1 pe = [100 5]; % population of snow hares, lynxes at t=0 2 tYears = 0:0.25:100; % discrete time interval, in years 4% Add your code below 6 % Model parameters (can be moved to where needed in your script) 7 a = 0.48; % prey's growth rate 8 b = 0.025; % prey's death rate 9 c = 0.68; % predator's death rate 10 d = 0.02; % predator's growth rate 11
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