Localized Modulated Wave Solutions in Interaction Between Pancreatic $$-\beta$$ Cell and Electromagnetic Fields

The objective of this paper is to examine the interaction between biological systems and environmental electric or magnetic fields. The hypothesis that the pancreatic \(\beta\) -cell plays a pivotal role in glucose homeostasis by secreting insulin, the sole hormone capable of reducing the concentration of glucose in the blood, is examined herein. The research focuses on elucidating the characteristics of the system when an external excitation is applied. In this study, we demonstrate that insulin dynamics can be driven by the complex Ginzburg-Landau equation through a multi-scale expansion in the semi-discrete approximation. The localized solutions of the complex Ginzburg-Landau equation are reported. Subsequently, the following solutions were proposed for studying the dynamic properties of insulin. In the wake of these analyses, the results reveal that there are two specific frequency ranges for the natural frequency of the \(\beta\) -cell system. In summary, insulin propagates in pancreatic \(\beta\) -cells using both temporal and spatial dimensions in the form of localized modulated waves.