Lesson plan
Nullcline
In mathematical analysis, nullclines, sometimes called zero-growth isoclines, are encountered in a system of ordinary differential equations : x_1'=f_1(x_1, \ldots, x_n) : x_2'=f_2(x_1, \ldots, x_n) :: \vdots : x_n'=f_n(x_1, \ldots, x_n) where x' here represents a derivative of x with respect to another parameter, such as time t . The j 'th nullcline is the geometric shape for which 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. Nullclines are useful for visualization in phase plane plot analysis. Nullclines split the plot into regions of potentially similar dynamics .
Article summary
In mathematical analysis, nullclines, sometimes called zero-growth isoclines, are encountered in a system of ordinary differential equations : x_1'=f_1(x_1, \ldots, x_n) : x_2'=f_2(x_1, \ldots, x_n) :: \vdots : x_n'=f_n(x_1, \ldots, x_n) where x' here represents a derivative of x with respect to another parameter, such as time t . The j 'th nullcline is the geometric shape for which 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. Nullclines are useful for visualization in phase plane plot analysis. Nullclines split the plot into regions of potentially similar dynamics .
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