The peroxidase-oxidase (PO) reaction is an important example of how oscillating reactions arise in living organisms. The reaction is important mathematically because exhibits many characteristics of chaos. Of these characteristics, sensitive dependence on initial conditions illustrates how predicting the future state of the PO reaction is next to impossible. For this reason, chaotic behavior in...

Oscillatory secretion of insulin has been observed in many different experimental preparations. Here we examine a mathematical model for in vitro insulin secretion from pancreatic beta cells in a flow-through reactor. The analysis shows that oscillations result because of an important interplay between flow rate of the reactor and insulin diffusion. In particular, if the ratio of flow rate to v...

Understanding how biochemical networks lead to large-scale nonequilibrium self-organization and pattern formation in life is a major challenge, with important implications for the design of programmable synthetic systems. Here, we assembled cell-free genetic oscillators in a spatially distributed system of on-chip DNA compartments as artificial cells, and measured reaction-diffusion dynamics at...

Isostables and isostable reduction, analogous to isochrons and phase reduction for oscillatory systems, are useful in the study of nonlinear equations which asymptotically approach a stationary solution. In this work, we present a general method for isostable reduction of partial differential equations, with the potential power to reduce the dimensionality of a nonlinear system from infinity to...

Neuronal synchronization reflected by oscillatory brain activity has been strongly implicated in the mechanisms supporting selective gating. We here aimed at identifying the anatomical pathways in humans supporting the top-down control of neuronal synchronization. We first collected diffusion imaging data using magnetic resonance imaging to identify the medial branch of the superior longitudina...

We investigate the combined influence of chemical reaction and radiation absorption on mixed convective flow in a vertical channel with oscillatory wall temperature and concentration .The non-linear coupled partial differential equations governing the flow heat and mass transfer are solved by a perturbation technique. The effect of various forces acting on the fluid system is analyzed by graphi...

An attempt has been made to measure the theoretically predicted manifestation of a geometric phase in the differential cross section for the H + HD → HD(v' = 2, j' = 5) + H reaction at a center-of-mass collision energy of 1.44 eV (33.2 kcal∕mol). Minute oscillatory differences between calculated differential cross sections that take into account and ignore the effect of geometric phase have pro...

Pattern formation is studied numerically in a three-variable reaction-diffusion model with onset of the oscillatory instability at a finite wavelength. Traveling and standing waves, asymmetric standing-traveling wave patterns, and target patterns are found. With increasing overcriticality or system length, basins of attraction of more symmetric patterns shrink, while less symmetric patterns bec...

We focus on the qualitative analysis of a reaction-diffusion with spatial heterogeneity near a bifurcation. The system is a generalization of the well known FitzHugh-Nagumo system in which the excitability parameter is space dependent. This heterogeneity allows to exhibit concomitant stationary and oscillatory phenomena. We prove the existence of an Hopf bifurcation and determine an equation of...