References in periodicals archive ?
Staying within the nullcline boundary for vehicle envelope control using a sliding surface," Vehicle System Dynamics, 51(2), 199-217, 2013, doi:10.
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].
Point P located on the portrait in region (I) is set as the starting point, which is above the nullcline of u.
Notice that the shape of the consumer nullcline is different than previous nullclines associated with consumer-resource models in that the consumer nullcline can intersect along the R = 0 axis.
A]-R planar equilibrium [Mathematical Expression Omitted] will necessarily lie to the left of the Cs nullcline, and therefore [C.
i] nullclines intersect) must take place where R is increasing (i.
A nullcline is the curve where the derivatives for the differential equations for calcium and ROS are set to zero.
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.
direct) competition among Daphnia changes the vertical grazer nullcline.
As we mentioned earlier, the parameter, b, controls the gaps between the two nullclines on the right side of the uv-plane (see Figure 1(a)).
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.
The material on equilibria and nullclines will be useful for understanding an important body of theoretical ecology.