We show that the networks with only positive feedback loops have no stable oscillation but stable equilibria whose stability is independent of the time delays.
Two cases with different values of the parameter M are presented in Additional file 2. It demonstrates that at most two positive values of z ¯ are possible and hence the system may have at most two positive equilibria, whose x, y ‒ coordinates are expressed via z ¯ by the equations (M9).
This work is focused on a system of boundary value problems whose solutions represent the equilibria of a bridge suspended by continuously distributed cables and supported by M intermediate piers.
Together, these studies illustrate an underlying mechanism of allosteric AMPK modulation by AMP and glycogen, whose binding changes the equilibria between alternate AID (AMP) and carbohydrate-binding module (glycogen) interactions.
The starting point is two groups of individuals with initially equal qualifications who play in a sequential game whose rules hinder the calculation of equilibria.
The results on relative equilibria are useful for studies on the motion of many natural satellites, whose motion are close to the relative equilibria.
For the calculation of complex chemical equilibria of multicomponent mixtures containing species whose Gibbs free energies of formation depend very regularly on the structure of the molecules involved, statistical methods of continuous thermodynamics can successfully be put into use.
These problems are models whose formulation includes optimization, variational inequalities, (vector) optimization problems, fixed point problems, saddle point problems, Nash equilibria and complementarity problems as particular cases (see [1, 5, 9]).
Although it is expected that Cif proteins function as monomers in vivo, each of the Cifs produced in this study displays the properties of monomer-dimer equilibria in solution, with the exception of CifBp which purifies as a single species (whose apparent molecular weight suggests a dimeric form).
Since the primary goal of this paper is to derive the existence of equilibria in a novel way without referring to Brouwer's fixed point theorem and not to construct algorithm for computation of equilibria, the algorithm presented below should be treated as a by-product which is important, as we believe, but whose properties should be examined in the future.
