Sign Of Equilibrium Research Articles

Remarks on excitability, stability and sign of equilibria in cooperative systems

The strict positivity of equilibria is known to be equivalent to asymptotic stability in excitable positive linear systems. In contrast with intuition, this property does not hold for nonlinear cooperative systems. However, weaker results are pointed out and proved to be effective in the analysis of several nonlinear cooperative systems.

Excitability, stability, and sign of equilibria in positive linear systems

The relationship between sign and stability of equilibria in positive linear systems is investigated in this paper. In particular it is proved that the well-known result “stability and irreducibility imply strict positivity” can be better specified by introducing the notion of excitability. In fact stability, excitability and strict positivity of the equilibria are three perfectly balanced properties since any one of them is implied by the two others.

The direct synthesis of ammonia

It was shown in a recent paper on “ The Decomposition of Ammonia by Heat,”* that ammonia is decomposed almost (if not quite) completely when heated in a porcelain vessel at about 800° to 1100°, and that there is no sign of equilibrium between the ammonia and its decomposition products at any of the temperatures employed, 677° to 1111°. In order to discover if there is any such state of equilibrium, it was thought better to attempt to reach that state by synthesising ammonia instead of decomposing it, as the testing for and estimation of the ammonia could then be carried out with much greater accuracy.