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# 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.

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new question: Lorenz system by David Bankom

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new correction: examples and OEIS sequences by fizzie

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new correction: Define Galois correspondence by porton

Oct 7

new correction: Closure properties on languages: DCFL not closed under reversal by babou

new correction: DCFLs are not closed under reversal by petey

Oct 2

new correction: Many corrections by Smarandache

Sep 28

new question: how to contest an entry? by zorba

new question: simple question by parag