where here represents a derivative of with respect to another parameter, such as time . The 'th nullcline is the geometric shape for which . The equilibrium points 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.
The definition, though with the name ’directivity curve’, was used in a 1967 article by Endre Simonyi.[1] This article also defined 'directivity vector' as , 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 semi-quantitative results.
Referencesedit
^E. Simonyi: The Dynamics of the Polymerization Processes, Periodica Polytechnica Electrical Engineering – Elektrotechnik, Polytechnical University Budapest, 1967
Notesedit
E. Simonyi – M. Kaszás: Method for the Dynamic Analysis of Nonlinear Systems, Periodica Polytechnica Chemical Engineering – Chemisches Ingenieurwesen, Polytechnical University Budapest, 1969
nullcline, mathematical, analysis, nullclines, sometimes, called, zero, growth, isoclines, encountered, system, ordinary, differential, equations, displaystyle, ldots, displaystyle, ldots, displaystyle, vdots, displaystyle, ldots, where, displaystyle, here, re. In mathematical analysis nullclines sometimes called zero growth isoclines are encountered in a system of ordinary differential equations x1 f1 x1 xn displaystyle x 1 f 1 x 1 ldots x n x2 f2 x1 xn displaystyle x 2 f 2 x 1 ldots x n displaystyle vdots dd xn fn x1 xn displaystyle x n f n x 1 ldots x n where x displaystyle x here represents a derivative of x displaystyle x with respect to another parameter such as time t displaystyle t The j displaystyle j th nullcline is the geometric shape for which xj 0 displaystyle x j 0 The equilibrium points 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 Contents 1 History 2 References 3 Notes 4 External linksHistory editThe definition though with the name directivity curve was used in a 1967 article by Endre Simonyi 1 This article also defined directivity vector as w sign P i sign Q j displaystyle mathbf w mathrm sign P mathbf i mathrm sign Q mathbf j nbsp 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 semi quantitative results References edit E Simonyi The Dynamics of the Polymerization Processes Periodica Polytechnica Electrical Engineering Elektrotechnik Polytechnical University Budapest 1967Notes editE Simonyi M Kaszas Method for the Dynamic Analysis of Nonlinear Systems Periodica Polytechnica Chemical Engineering Chemisches Ingenieurwesen Polytechnical University Budapest 1969External links edit Nullcline PlanetMath SOS Mathematics Qualitative Analysis Retrieved from https en wikipedia org w index php title Nullcline amp oldid 1124164238, wikipedia, wiki, book, books, library,
