On the Hopf bifurcation in control systems with a bounded nonlinearity asymptotically homogeneous at infinity

The paper studies existence, uniqueness, and stability of large-amplitude periodic cycles arising in Hopf bifurcation at infinity of autonomous control systems with bounded nonlinear feedback. We consider systems with functional nonlinearities of Landesman-Lazer type and a class of systems with hysteresis nonlinearities. The method is based on the technique of parameter functionalization and methods of monotone concave and convex operators. (C) 2001 Academic Press.

Differential inclusions and robust control theory

Uncontrolled systems (x) over dot is an element of Ax, where A is a non-empty compact set of matrices, and controlled systems (x) over dot is an element of Ax + Bu are considered. Higher-order systems 0 is an element of Px - Du, where and are sets of differential polynomials, are also studied. It is shown that, under natural conditions commonly occurring in robust control theory, with some mild additional restrictions, asymptotic stability of differential inclusions is guaranteed. The main results are variants of small-gain theorems and the principal technique used is the Krasnosel'skii-Pokrovskii principle of absence of bounded solutions.

Brain monoaminergic neurons and ventilatory control in vertebrates

Monoamines (noradrenaline (NA), adrenaline (AD), dopamine (DA) and serotonin (5-HT) are key neurotransmitters that are implicated in multiple physiological and pathological brain mechanisms, including control of respiration. The monoaminergic system is known to be widely distributed in the animal kingdom, which indicates a considerable degree of phylogenetic conservation of this system amongst vertebrates. Substantial progress has been made in uncovering the participation of the brain monoamines in the breathing regulation of mammals, since they are involved in the maturation of the respiratory network as well as in the modulation of its intrinsic and synaptic properties. On the other hand, for the non-mammalian vertebrates, most of the knowledge of central monoaminergic modulation in respiratory control, which is actually very little, has emerged from studies using anuran amphibians. This article reviews the available data on the role of brain monoaminergic systems in the control of ventilation in terrestrial vertebrates. Emphasis is given to the comparative aspects of the brain noradrenergic, adrenergic, dopaminergic and serotonergic neuronal groups in breathing regulation, after first briefly considering the distribution of monoaminergic neurons in the vertebrate brain. (C) 2008 Elsevier B.V. All rights reserved.