Finite-time boundary stabilization of fractional reaction-diffusion systems

This paper investigates the boundary finite-time stabilization of fractional reaction-diffusion systems (FRDSs). First, a distributed controller is designed, and sufficient conditions are obtained to ensure the finite-time stability (FTS) of FRDSs under the designed controller. Then, a boundary controller is presented to achieve the FTS. By virtue of Lyapunov functional method and inequality techniques, sufficient conditions are presented to ensure the FTS of FRDSs via the designed boundary controller. The effect of diffusion term of FRDSs on the FTS is also investigated. Both Neumann and mixed boundary conditions are considered. Moreover, the robust finite-time stabilization of uncertain FRDSs is studied when there are uncertainties in the system’s coefficients. Under the designed boundary controller, sufficient conditions are presented to guarantee the robust FTS of uncertain FRDSs. Finally, numerical examples are presented to verify the effectiveness of our theoretical results.

The principal mitochondrial K+ uniport is associated with respiratory complex I

Mitochondria generate ATP via coupling the negative electrochemical potential (proton motive force, Capital Greek (Deltap), consisting of a proton gradient (Capital Greek DeltapH+) and a membrane potential (Capital Greek Psim) across the respiratory chain, to phosphorylation of adenosine diphosphate nucleotide. In turn, DeltapH+ and Capital Greek Psim, are tightly balanced by the modulation of ionic uniporters and exchange-diffusion systems which preserve integrity of mitochondrial membranes and regulate ATP production. Here, we provide direct electrophysiological, pharmacological and genetic evidence that the main mitochondrial electrophoretic pathway for monovalent cations is associated with respiratory complex I, contrary to the long-held dogma that only H+ gradients are built across proteins of the mammalian electron transport chain. Here we propose a theoretical framework to describe how monovalent metal cations contribute to the buildup of H+ gradients and the proton motive force, extending the classical Mitchellian view on chemiosmosis and vectorial metabolism. Keywords: mitochondrial electrogenic transport, chemiosmotic theory, vectorial metabolism, whole-mitochondria electrophysiology.

Bounds on the critical times for the Fisher-KPP equation

The Fisher–Kolmogorov–Petrovsky–Piskunov (Fisher–KPP) equation is one of the prototypical reaction–diffusion equations and is encountered in many areas, primarily in population dynamics. An important consideration for the phenomena modelled by diffusion equations is the length of the diffusive process. In this paper, three definitions of the critical time are given, and bounds are obtained by a careful construction of the upper and lower solutions. The comparison functions satisfy the nonlinear, but linearizable, partial differential equations of Fisher–KPP type. Results of the numerical simulations are displayed. Extensions to some classes of reaction–diffusion systems and an application to a spatially heterogeneous harvesting model are also presented. doi:10.1017/S1446181121000365

Recent advances in the temporal and spatiotemporal dynamics induced by bromate–sulfite-based pH-oscillators

The bromate–sulfite reaction-based pH-oscillators represent one of the most useful subgroup among the chemical oscillators. They provide strong H+-pulses which can generate temporal oscillations in other systems coupled to them and they show wide variety of spatiotemporal dynamics when they are carried out in different gel reactors. Some examples are discussed. When pH-dependent chemical and physical processes are linked to a bromate–sulfite-based oscillator, rhythmic changes can appear in the concentration of some cations and anions, in the distribution of the species in a pH-sensitive stepwise complex formation, in the oxidation number of the central cation in a chelate complex, in the volume or the desorption-adsorption ability of a piece of gel. These reactions are quite suitable for generating spatiotemporal patterns in open reactors. Many reaction–diffusion phenomena, moving and stationary patterns, have been recently observed experimentally using different reactor configurations, which allow exploring the effect of different initial and boundary conditions. Here, we summarize the most relevant aspects of these experimental and numerical studies on bromate–sulfite reaction-based reaction–diffusion systems.