nullcline


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nullcline

A curve drawn in the phase portrait along which one of the state variables does not change in time; nullclines are used frequently in 2-D systems.
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Once the spiking cycle line reaches the H nullcline at 30 mV, it will reset to the starting point, causing a periodic spiking behavior.
With respect to the latter, the nullcline [G.sub.1] (given by (33)) changes to [G'.sub.1], where [G'.sub.1] = -[G.sub.1], while [G.sub.2] (34) remains the same.
C., "Staying within the nullcline boundary for vehicle envelope control using a sliding surface," Vehicle System Dynamics, 51(2), 199-217, 2013, doi:10.1080/00423114.2012.720377.
And piecewise linear (PWL) nullcline is introduced inspired by this to build a series of PWL models that can describe the dynamical behavior of many common cell types, such as rich spiking and bursting dynamics [8, 9].
The phase plane {n, p} is separated by the vertical nullcline L denoted as rK - rn - apK = 0 and the horizontal nullcline M denoted as -2[mu] + 3[alpha]an - [alpha]C = 0 into different regions, both the signs of dn/df and dp/df do not change in every part.
If [delta] is great enough to damp intrinsic oscillations in the constituent CR pairs, the representing point will slide along the nullcline [[??].sub.1] = 0 (slow manifold of the system (47a)-(47b)), steadily tending to point (48) Figure 6(a)).
The simple models employed in the original paradox of enrichment papers (Rosenzweig 1971, Gilpin 1972) have a strictly vertical predator nullcline, and thus predict that the algae should not increase with enrichment.
The voltage (dashed) and slow variable (dotted) nullclines show a fixed point that leads to large amplitude, stable, limit cycle oscillations.
Therefore, asymptotic dynamics for large values of [r.sub.1], [r.sub.2] is related to the dynamics of (5) for large r, as it determines the direction of the vector-field in the region between the nullclines. Three generic types of the model dynamics when at least one steady state exists are presented in Figure 2.
However, parameter manipulation can shift nullclines and reproduce the mentioned experimental data.
From (1) nullclines for the prey are found from setting [alpha]x - [beta]yx = 0 and their geometric representations are defined by y = [alpha]/[beta] and x = 0.