en>Hyacinth: ==External links== *"[http://www.indiana.edu/~knotinfo/descriptions/crosscap_number.html Crosscap Number]", ''KnotInfo''.

2013-05-26T12:11:01Z

==External links== *"[http://www.indiana.edu/~knotinfo/descriptions/crosscap_number.html Crosscap Number]", ''KnotInfo''.

← Older revision		Revision as of 14:11, 26 May 2013
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	~~The title~~ of ~~the writer is Luther~~. ~~Managing people~~ is ~~what I do in my day occupation~~. ~~For many years she'~~s ~~been residing~~ in ~~Kansas~~. The ~~thing I adore most bottle tops gathering and now I have time to take on new things~~.<br><br>~~Also visit my blog post; extended car warranty (~~[http://~~Checkmates~~.co.za/~~index~~.~~php?do=~~/~~profile-1592~~/~~info~~/ ~~click through the up coming page~~])		In [[mathematical analysis]], '''nullclines''', sometimes called zero-growth [[isocline]]s, are encountered in a system of [[ordinary differential equation]]s
			:<math>x_1'=f_1(x_1, \ldots, x_n)</math>
			:<math>x_2'=f_2(x_1, \ldots, x_n)</math>
			::<math>\vdots</math>
			:<math>x_n'=f_n(x_1, \ldots, x_n)</math>

			where <math>x'</math> here represents a [[derivative]] of <math>x</math> with respect to another parameter, such as time <math>t</math>. The <math>j</math>'th nullcline is the geometric shape for which <math>x_j'=0</math>. The [[Fixed_point_(mathematics)\|fixed point]]s of the system are located where all of the nullclines intersect.
			In a two-dimensional [[linear system]], the nullclines can be represented by two lines on a two-dimensional plot; in a general two-dimensional system they are arbitrary curves.

			== History ==

			The definition, though with the name ’directivity curve’, was used in a 1967 article by Endre Simonyi<sup>1</sup>. This article also defined 'directivity vector' as
			<math>\mathbf{w} = \mathrm{sign}(P)\mathbf{i} + \mathrm{sign}(Q)\mathbf{j}</math>,
			where P and Q are the dx/dt and dy/dt differential equations, and i and j are the x and y direction unit vectors.

			Simonyi developed a new stability test method from these new definitions, and with it he studied differential equations. This method, beyond the usual stability examinations, provided semiquantative results.

			==References==
			{{reflist}}

			1.E. Simonyi: The Dynamics of the Polymerization Processes, Periodica Polytechnica Electrical Engineering – Elektrotechnik, Polytechnical University Budapest, 1967

			2. E. Simonyi – M. Kaszás: Method for the Dynamic Analysis of Nonlinear Systems, Periodica Polytechnica Chemical Engineering – Chemisches Ingenieurwesen, Polytechnical University Budapest, 1969

			==External links==
			* {{planetmath reference\|id= 5972\|title=Nullcline}}
			* [http://ocw.mit.edu/NR/rdonlyres/D369E47F-064F-48E0-83CD-3B83725B5555/0/r02sol.pdf Notes] from [[MIT OpenCourseWare]]
			* [http://www.sosmath.com/diffeq/system/qualitative/qualitative.html SOS Mathematics: Qualitative Analysis]

			[[Category:Differential equations]]


			{{mathanalysis-stub}}

			[[de:Isokline]]
			[[nl:nullcline]]

en>Sun Creator: Typo fixing and General, typos fixed: , → , using AWB

2012-07-02T15:05:22Z

Typo fixing and General, typos fixed: , → , using AWB

New page

The title of the writer is Luther. Managing people is what I do in my day occupation. For many years she's been residing in Kansas. The thing I adore most bottle tops gathering and now I have time to take on new things.<br><br>Also visit my blog post; extended car warranty ([http://Checkmates.co.za/index.php?do=/profile-1592/info/ click through the up coming page])

Crosscap number - Revision history

en>Hyacinth: ==External links== *"[http://www.indiana.edu/~knotinfo/descriptions/crosscap_number.html Crosscap Number]", ''KnotInfo''.

en>Sun Creator: Typo fixing and General, typos fixed: , → , using AWB