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dR dt dF dt 2(1-7) ¹ R-RF -16F +4RF

dR dt dF dt 2(1-7) ¹ R-RF -16F +4RF

Advanced Engineering Mathematics
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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Question

Generate a slope field in that shows the solution curve in the RF-plane (rabbit/fox) for the system of predator-prey equations with initial conditions R(0)=8 and F(0)=1

This image contains a system of differential equations, likely modeling a biological or ecological process. The equations are: 1. \(\frac{dR}{dt} = 2 \left(1 - \frac{R}{3}\right)R - RF\) 2. \(\frac{dF}{dt} = -16F + 4RF\) These equations describe how two variables, \(R\) and \(F\), change over time (\(t\)). - The first equation models the rate of change of \(R\). It includes a term \(2 \left(1 - \frac{R}{3}\right)R\), which is likely a logistic growth term affected by the presence of \(F\). This suggests that \(R\) might represent a population with natural growth and some interaction with \(F\). - The second equation models the rate of change of \(F\). The term \(-16F\) suggests \(F\) might have a high rate of decay or death, while \(4RF\) indicates interaction with \(R\), possibly a consumptive relationship. This system can be used to study interactions such as predator-prey dynamics, competition, or symbiosis. Analyzing these equations can provide insights into the stability and behavior of the modeled system over time.
Transcribed Image Text:This image contains a system of differential equations, likely modeling a biological or ecological process. The equations are: 1. \(\frac{dR}{dt} = 2 \left(1 - \frac{R}{3}\right)R - RF\) 2. \(\frac{dF}{dt} = -16F + 4RF\) These equations describe how two variables, \(R\) and \(F\), change over time (\(t\)). - The first equation models the rate of change of \(R\). It includes a term \(2 \left(1 - \frac{R}{3}\right)R\), which is likely a logistic growth term affected by the presence of \(F\). This suggests that \(R\) might represent a population with natural growth and some interaction with \(F\). - The second equation models the rate of change of \(F\). The term \(-16F\) suggests \(F\) might have a high rate of decay or death, while \(4RF\) indicates interaction with \(R\), possibly a consumptive relationship. This system can be used to study interactions such as predator-prey dynamics, competition, or symbiosis. Analyzing these equations can provide insights into the stability and behavior of the modeled system over time.
Expert Solution
Step 1

Given system of equation:

dRdt = 21-R3R-RFdFdt = -16F+4RF

To find:

The solution of the given system. 

Draw the slope field.

 

steps

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Follow-up Question

That is not what I needed. I needed a FIGURE, a SLOPE FIELD given the initial conditions. Possibly generated with geogebra application

dR dt dF dt 2(1-B) ¹ R-RF -16F +4RF
Transcribed Image Text:dR dt dF dt 2(1-B) ¹ R-RF -16F +4RF
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