## You are here

Homenullcline

## Primary tabs

# nullcline

Let

$\displaystyle\dot{x}_{1}$ | $\displaystyle=$ | $\displaystyle f_{1}(x_{1},\ldots,x_{n})$ | ||

$\displaystyle\vdots$ | ||||

$\displaystyle\dot{x}_{n}$ | $\displaystyle=$ | $\displaystyle f_{n}(x_{1},\ldots,x_{n})$ |

be a system of first order ordinary differential equation. The $x_{j}$ *nullcline* is the set of points which satisfy $f_{j}(x_{1},\ldots,x_{n})=0$. Note that at an intersection point of all the nullclines implies that

$\displaystyle 0$ | $\displaystyle=$ | $\displaystyle f_{1}(x_{1},\ldots,x_{n})$ | ||

$\displaystyle\vdots$ | ||||

$\displaystyle 0$ | $\displaystyle=$ | $\displaystyle f_{n}(x_{1},\ldots,x_{n}).$ |

Hence the intersection point of all the nullclines is an equilibrium point of the system.

example:

Type of Math Object:

Definition

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

34C99*no label found*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff