Let (f u,v =0) and (g u,v =0), we show the existence of non-negative equilibria in Figure 1. Figure 1 The blue curves are the prey-nullclines and the red lines are the predator-isoclines.
The two saddle periodic orbits mentioned above correspond to the two saddle equilibria in Figure 4. Fig. 4 A robust heteroclinic cycle for four all-to-all coupled phase oscillator system analogous to the cycle found in Figure 3 for the Hodgkin-Huxley type system.
Figure 12 CDF of Jaccard similarity Index between equilibria. Figure 12 also shows the distribution of Jaccard similarity for the subset of the network that includes only transit providers (the "provider network").
The Gibbs free energy equation is Since the net free energy change around the cycle is zero, one can write the following relationships for the equilibria in Figure 1: or, in combined form, where diff p Ka oct is (p Ka oct − p Ka) for acids and (p Ka − p Ka oct) for bases.
Assuming that the second-order conditions are met, Glazer and McGuire confine their analysis to symmetric and stable equilibria (see Figure 1), whereby stability requires the slope of the reaction functions in the equilibrium to be smaller than one.
However, there are a considerable number of fixed points that do not follow the tendency: for example, some of the fixed points at low and high GC content clusters satisfy the condition (6.3), many of which are thought to be "repulsive" fixed points leading to the adjacent potential equilibria. Figure 10 shows distribution of fixed points of g GC t)) in all chromosomes.
We assume that protein-protein association is maintained under all conditions and that all specific protein-DNA interactions are accounted for in the equilibria shown in Figure 4. Intermolecular DNA associations have also been observed in some in-vitro experiments [36], [66] because of high DNA concentrations that were used.
The equilibria follow from Figure 3 by neglecting the inhibitor (I = 0).
For anthocyanins the effect of pH on color is due to the complex acid/base equilibria depicted in Figure 16.
However, a stable dampened oscillated pathogen load at equilibria (refer to Figure 12(b)) was observed if medium effect of anti-inflammatory cytokine (dissociation rate equal to a base-10 logarithm 5) was incorporated.
