Is Nullcline Only Defined in Two Dimensions?

  • Thread starter Pythagorean
  • Start date
  • Tags
    Definition
In summary, the conversation revolves around the definition and terminology of nullclines in n-dimensional systems. It is mentioned that the Wikipedia page states that nullclines are n-dimensional, but the discussion claims they are only 2D. The question is then posed about the general term for zero solutions in n-dimensional systems and the specific terms for 1D and 3D zero solutions. It is suggested that the first external link on the Wikipedia page may provide more information, but the source is not accessible and a text source is preferred. The conversation also touches on the possibility of nullclines belonging to a more fundamental math subject.
  • #1
Pythagorean
Gold Member
4,409
320
1) is nullcline defined properly here:
http://en.wikipedia.org/wiki/Nullcline

in the discussion section, it is claimed the nullcline is n-dimensional, not just 2d


if the wiki page is right:
2) what is the general term for the zero solutions of an n-dimensional system?

3) what are 1D and 3D zero solutions called? nullpoint, nullplane

thank you,
Pyth
 
Physics news on Phys.org
  • #3
adriank said:
They're still called nullclines. See the first external link on the Wikipedia page.

I could never get that page to load, or even google's cache. I would prefer a text source anyway so that I can edit the wiki page and properly cite it. I couldn't find it in Strogatz "Nonlinear Dynamics and Chaos". He says a thing or two about nullclines, but doesn't give a definition. The wikipedia page seems to actually rip a line off of Strogatz (who uses a 2D system coincidentally).

But perhaps I'm looking in the wrong textbook. Is their a more fundamental math subject that nullclines belong too?
 

FAQ: Is Nullcline Only Defined in Two Dimensions?

What is the definition of a nullcline?

A nullcline is a curve on a graph that represents the points where a variable does not change over time, known as an equilibrium point. It is created by setting one or more variables in a system of differential equations to zero and graphing the resulting equation.

How is a nullcline different from an equilibrium point?

A nullcline is a curve on a graph that represents all the possible equilibrium points for a specific variable, while an equilibrium point is a specific point on the nullcline where the variable does not change over time. In other words, the nullcline is the set of all possible equilibrium points for a variable.

What information can be gained from a nullcline?

A nullcline can provide information about the behavior and stability of a system. The intersection of nullclines for different variables indicates potential equilibrium points, and the slope of the nullcline at those points can indicate the stability of the system.

How are nullclines used in mathematical models?

Nullclines are essential in creating and analyzing mathematical models, particularly in systems of differential equations. They help identify equilibrium points, determine the behavior of a system, and analyze the stability of the system. In some cases, nullclines can also be used to simplify complex systems of equations.

Are nullclines unique to a specific type of system?

No, nullclines can be used in a wide range of systems, including biological, chemical, and physical systems. They are a useful tool for understanding the behavior and stability of any system that can be represented by a set of differential equations.

Similar threads

B 4th spatial dimension thought experiment
Replies
8
Views
572
B Defining handedness, right-left, or clockwise-counterclockwise
Replies
3
Views
2K
Laplace's equation in two dimensions.
Replies
8
Views
4K
I Kaluza-Klein Theory and 5D Einstein Equations
Replies
5
Views
3K
I On the approximate solution obtained through Euler's method
Replies
1
Views
2K
B Is it possible to represent 1D space within 2D space using only one coordinate?
Replies
12
Views
2K
I Exploring 4D Wave Propagation in 3D Solids
Replies
5
Views
4K
I Trying To Conceptualize Two Dimensions Of Time
Replies
2
Views
3K
How would your body change if you were in a 4D space?
Replies
0
Views
2K
I In which sense(s) do square integrable functions go to zero at infinity?
Replies
2
Views
974

Hot Threads

Recent Insights

Back
Top