Trouble creating differential equation from a flow line

In summary, the conversation is about creating a differential equation from a flow line to model the population of deer. The flow line has two nodes, a sink and a source, and the desired equation includes the equilibrium points y=2 and y=1. Various attempts have been made to rearrange the equation, but the suggested equation of \frac{dy}{dt}=y(1-y)(2-y) may be a close match.
  • #1
highc1157
4
0
Hi,

I am having trouble creating a differential equation from my flow line that models population of deer. The flow line has two nodes, a sink (attractor), and a source (repeller). I need to come up with a D.E from the flow line.

my "skeleton equation looks like this"

dp/dt = p(1-(p/4))((p/6)-1)(1-(y/8))

but this doesn't work, I've rearranged so many ways and doesn't match the flow line
 
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  • #2
How about:

[tex]\frac{dy}{dt}=y(1-y)(2-y)[/tex]

y=2 is a source and y=1 is a sink. May not match exactly what you want but it does include the type of equilibrium points you want.
 

1. How do I create a differential equation from a flow line?

To create a differential equation from a flow line, you first need to understand the concept of a flow line. A flow line is a curve that shows the direction of a flow of a physical quantity, such as a fluid or a vector field. To create a differential equation, you need to use the mathematical relationships between the physical quantities involved in the flow, such as velocity, acceleration, and position. These relationships can be represented by differential equations.

2. What is the importance of creating a differential equation from a flow line?

Creating a differential equation from a flow line is important because it allows us to mathematically model and predict the behavior of a flow. This is particularly useful in many scientific and engineering fields, such as fluid dynamics, electromagnetism, and thermodynamics.

3. What are the steps to creating a differential equation from a flow line?

The steps to creating a differential equation from a flow line can vary depending on the specific flow and physical quantities involved. However, in general, the steps involve identifying the variables and their relationships, writing the equations that describe these relationships, and then simplifying and manipulating the equations to obtain the final differential equation.

4. Can a single flow line have multiple differential equations?

Yes, a single flow line can have multiple differential equations. This is because different physical quantities involved in the flow may have different relationships and therefore require different equations to describe them. Additionally, different types of flows may require multiple equations to fully describe their behavior.

5. Are there any tools or software available to help create differential equations from flow lines?

Yes, there are various tools and software available that can assist in creating differential equations from flow lines. Many mathematical and scientific software packages, such as MATLAB, Mathematica, and Wolfram Alpha, have built-in functions for solving and manipulating differential equations. Additionally, there are online calculators and equation solvers specifically designed for this purpose.

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