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A variety of oscillations are observed in pancreatic islets.We establish a model, incorporating two oscillatory systems of different time scales: One is the well-known bursting model in pancreatic beta-cells and the other is the…
Pancreatic $\beta$-cells play a central role in maintaining glucose homeostasis through the pulsatile secretion of insulin. This essential function relies not only on intracellular regulatory mechanisms but also on coordinated interactions…
Maintenance of adequate physical and functional pancreatic $\beta$-cell mass is critical for the prevention or delay of diabetes mellitus. It is well established that insulin potently activates mitogenic and anti-apoptotic signaling…
Pancreatic $\beta-$cells regulate insulin secretion through complex oscillations, which are vital for glucose control and diabetes research. In this paper, an existing mathematical model of $\beta-$cell dynamics is analyzed using a…
Pancreatic islets, controlling glucose homeostasis, consist of \alpha, \beta, and \delta\ cells. It has been observed that \alpha\ and \beta\ cells generate out-of-phase synchronization in the release of glucagon and insulin,…
Pancreatic islets are functional units involved in glucose homeostasis. The multicellular system comprises three main cell types; $\beta$ and $\alpha$ cells reciprocally decrease and increase blood glucose by producing insulin and glucagon…
Cells of almost all solid tissues are connected with gap junctions which permit the direct transfer of ions and small molecules, integral to regulating coordinated function in the tissue. The pancreatic islets of Langerhans are responsible…
Metabolic oscillations in single cells underlie the mechanisms behind cell synchronization and cell-cell communication. For example, glycolytic oscillations mediated by biochemical communication between cells may synchronize the pulsatile…
Glucose homeostasis is controlled by the islets of Langerhans which are equipped with alpha-cells increasing the blood glucose level, beta-cells decreasing it, and delta-cells the precise role of which still needs identifying. Although…
Counter-regulatory elements maintain dynamic equilibrium ubiquitously in living systems. The most prominent example, which is critical to mammalian survival, is that of pancreatic {\alpha} and {\beta} cells producing glucagon and insulin…
Fickian diffusion into a core-shell geometry is modeled. The interior core mimics pancreatic Langerhan islets and the exterior shell acts as inert protection. The consumption of oxygen diffusing into the cells is approximated using…
Beta cells in pancreas represent an example of coupled biological oscillators which via communication pathways, are able to synchronize their electrical activity, giving rise to pulsatile insulin release. In this work we numerically analyze…
Pancreatic \b{eta}-cells secrete insulin in response to blood sugar levels to maintain glucose homeostasis. This vital insulin exocytosis is controlled by the cell's bursting behaviours, which are regulated by tight bidirectional coupling…
We investigate localized wave solutions in a network of Hindmarsh-Rose neural model taking into account the long-range diffusive couplings. We show by a specific analytical technique that the model equations in the infrared limit (wave…
In systems that exhibit a bistability between nonlinear traveling waves and the basic state, pairs of fronts connecting these two states can form localized wave pulses whose stability depends on the interaction between the fronts. We…
Mathematical models of glucose, insulin, and pancreatic $\beta$-cell mass dynamics are essential for understanding the physiological basis of type 2 diabetes. This paper investigates the Topp model's discrete-time dynamics to represent…
Major part of a pancreatic islet is composed of beta cells that secrete insulin, a key hormone regulating influx of nutrients into all cells in a vertebrate organism to support nutrition, housekeeping or energy storage. Beta cells…
We consider a model where a population of diffusively coupled limit-cycle oscillators, described by the complex Ginzburg-Landau equation, interacts nonlocally via an inertial field. For sufficiently high intensity of nonlocal inertial…
We address the striking coexistence of localized waves (`pulses') of different lengths which was observed in recent experiments and full numerical simulations of binary-mixture convection. Using a set of extended Ginzburg-Landau equations,…
In a companion paper, we established nonlinear stability with detailed diffusive rates of decay of spectrally stable periodic traveling-wave solutions of reaction diffusion systems under small perturbations consisting of a nonlocalized…