Bifurcations in planar, quadratic mass-action networks with few reactions and low molecularity.

In this paper we study bifurcations in mass-action networks with two chemical species and reactant complexes of molecularity no more than two. We refer to these as planar, quadratic networks as they give rise to (at most) quadratic differential equations on the nonnegative quadrant of the plane. Our aim is to study bifurcations in networks in this class with the fewest possible reactions, and the lowest possible product molecularity.

Melatonin improves cognitive dysfunction and decreases gliosis in the streptozotocin-induced rat model of sporadic Alzheimer's disease.

Introduction: Alzheimer's disease (AD) and other forms of dementia have a devastating effect on the community and healthcare system, as neurodegenerative diseases are causing disability and dependency in older population. Pharmacological treatment options are limited to symptomatic alleviation of cholinergic deficit and accelerated clearance of β-amyloid aggregates, but accessible disease-modifying interventions are needed especially in the early phase of AD. Melatonin was previously demonstrated to improve cognitive function in clinical setting and experimental studies also.

Evaluation of the Aquatic Toxicity of Several Triazole Fungicides.

Fungicides play an important role in crop protection, but they have also been shown to adversely affect non-target organisms, including those living in the aquatic environment. The aim of the present study is to combine experimental and computational approaches to evaluate the effects of flutriafol, metconazole, myclobutanil, tebuconazole, tetraconazole and triticonazole on aquatic model organisms and to obtain information on the effects of these fungicides on , a freshwater plant, at the molecular level. The EC (the half-maximum effective concentration) values for the growth inhibition of in the presence of the investigated fungicides show that metconazole (EC = 0.

Oscillations in three-reaction quadratic mass-action systems.

It is known that rank-two bimolecular mass-action systems do not admit limit cycles. With a view to understanding which small mass-action systems admit oscillation, in this paper we study rank-two networks with bimolecular source complexes but allow target complexes with higher molecularities. As our goal is to find oscillatory networks of minimal size, we focus on networks with three reactions, the minimum number that is required for oscillation.

Oscillations in Planar Deficiency-One Mass-Action Systems.

Whereas the positive equilibrium of a planar mass-action system with deficiency zero is always globally stable, for deficiency-one networks there are many different scenarios, mainly involving oscillatory behaviour. We present several examples, with centers or multiple limit cycles.