Steady State Question Understanding

In summary, the conversation discusses two questions related to steady state solutions and maximum yield. For question 5, it is determined that u=0 is a stable solution and u= ±√(1-E) are unstable solutions, only defined for E<1. For question 6, it is determined that u=0 will not give maximum yield and the solution for maximum yield is E=2/3.
  • #1
mt91
15
0
1596323380616.png


I've got 2 questions here. I was able to work out question 5 and calculate the steady states. However for question 6 I've got no idea with the wording of the equation and where you would start, so any sort of help would be really helpful, cheers
 
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  • #2
Okay, so for #5 you saw that the "steady state" solutions satisfy u(1- u)(1+u)= Eu. An obvious solution is u=0. If u is not 0, we can divide both sides by u and have $(1- u)(1+ u)= 1- u^2= E$ so $u^2= 1- E$ and the two other steady state solutions are $u= \sqrt{1- E}$ and $u= -\sqrt{1- E}$ which, of course, are only defined for E< 1. u= 0 is obviously a stable solution. The other two are unstable. You haven't said what "u" represents so I have no idea what "biologically relevant" could mean here. (If u is the population of some species then "$u= -\sqrt{1- E}$" is obviously NOT "biologically relevant" since u cannot be negative.)

For #6, if y= Eu(E) then y'= u(E)+ Eu'(E)= 0 at a maximum. Obviously "u(x)= 0" will NOT give "maximum yield". With $u(E)= \sqrt{1- E}= (1- E)^{1/2}$, $u'= -\frac{1}{2}(1- E)^{-1/2}$ and $y'= u(E)+ Eu'(E)= (1- E)^{1/2}-\frac{1}{2}E(1- E)^{-1/2}= 0$ so $(1- E)^{1/2}= \frac{1}{2}E(1- E)^{-1/2}$ and $2(1- E)= E$, $2- 2E= E$, $2= 3E$, and $E= \frac{2}{3}$.
 

Related to Steady State Question Understanding

1. What is Steady State Question Understanding?

Steady State Question Understanding is a method used in natural language processing to analyze and comprehend a question in order to provide an accurate response. It involves breaking down the question into smaller components, understanding the relationships between those components, and using this information to generate a response.

2. How is Steady State Question Understanding different from other question answering methods?

Unlike other question answering methods, Steady State Question Understanding is a continuous process that is able to handle a wide range of questions and language variations. It also takes into account the context and background information to provide a more accurate response.

3. What are the applications of Steady State Question Understanding?

Steady State Question Understanding has various applications in fields such as virtual assistants, chatbots, and information retrieval systems. It can also be used in customer service, education, and research to provide quick and accurate responses to user inquiries.

4. How does Steady State Question Understanding work?

The process of Steady State Question Understanding involves several steps, including parsing the question, identifying the relevant entities and relations, and using knowledge bases and algorithms to generate a response. It also involves continuously updating and refining the response based on the context and user feedback.

5. What are the challenges of implementing Steady State Question Understanding?

One of the main challenges of implementing Steady State Question Understanding is the complexity of natural language. Understanding the nuances and variations in human language can be difficult, and requires a large amount of data and advanced algorithms. Additionally, the continuous learning and updating process can also be challenging to manage and maintain.

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