The set of steady state solutions to a reaction–diffusion equation modeling an autocatalytic chemical reaction is completely determined, when the reactor has spherical geometry, and the spatial dimension is n= 1 or 2 for any reaction order, or n 3 for subcritical reaction order. Bifurcation approach and analysis of linearized problems are used to establish exact multiplicity and precise global ...

A necessary and sufficient condition is applied to determine the possibility of multiple positive steady states in a complex, active membrane transport model with a cycle, which is performed by pump proteins coupled to a source of metabolic energy. A set of rate constants and two corresponding steady states are computed. Hysteresis phenomena are observed. A signature of multiplicity is derived,...

Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space...

“Ignition/extinction” phenomena and steady-state multiplicity were discovered in an autohumidi$cation polymer electrolyte membrane fuel cell. At steady state, the water produced by the fuel cell reaction is balanced by water removal by the 7owing reactant gas streams. Ignition, corresponding to a high fuel cell current, arises from positive feedback between the water produced by the reaction an...

This paper proposes several statistical tests for finite state Markov games to examine the null hypothesis that the data are generated from a single equilibrium. We formulate tests of (i) the conditional choice and state transition probabilities, (ii) the steady-state distribution, and (iii) the conditional state distribution given an initial state. In a Monte Carlo study we find that the test ...

introduction: the prevalence of hearing loss in neonates is 2-5 out of every 1,000 live births. global health committee, american academy of otolaryngology, and american academy of pediatrics have recommended that hearing loss in infants be identified, and treated when possible, prior to 6 months of age. this study was designed with the aim to screen the hearing of neonates in mashhad, iran. me...

Start-up and dynamic responses to changes in load are reported for a dry feed, autohumidified polymer electrolyte membrane fuel cell PEMFC . The fuel cell current can be ignited by water injection; criteria are derived for the required water injection as functions of fuel cell size, temperature, and reactant feed rates. Steady-state multiplicity is observed where the fuel cell current can be ei...

An Ambrosetti-Prodi type exact multiplicity result is proved for a diffusive logistic equation with harvesting. We show that a modified diffusive logistic mapping has exactly either zero, or one, or two pre-images depending on the harvesting rate. It implies that the original diffusive logistic equation with harvesting has at most two positive steady state solutions.

Fluid-mediated interaction between catalyst particles alone issho wn to yield severul interesting and significant phenomena in a catalytic reactor that have been generally attributed in the past to direct interaction between particles. Thus, collaborative interaction between particles and the fluid may enhance or abate steady-state multiplicity, and reverse stability behavior. From the simple s...