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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 image: plot W(t) = P(waiting time <= t) by robert_dodier

new question: Prove a formula is part of the Gentzen System by LadyAnne

Mar 30

new question: A problem about Euler's totient function by mbhatia

new problem: Problem: Show that phi(a^n-1), (where phi is the Euler totient function), is divisible by n for any natural number n and any natural number a >1. by mbhatia

new problem: MSC browser just displays "No articles found. Up to ." by jaimeglz

Mar 26

new correction: Misspelled name by DavidSteinsaltz

Mar 21

new correction: underline-typo by Filipe

Mar 19

new correction: cocycle pro cocyle by pahio

Mar 7

new image: plot W(t) = P(waiting time <= t) (2nd attempt) by robert_dodier

new image: expected waiting time by robert_dodier

new image: plot W(t) = P(waiting time <= t) by robert_dodier