Let p ≥ 2 be a prime. The study of p-adic dynamical systems arises in the study of Diophantine geometry in the constructions of canonical heights. These constructions are utilized for counting rational points on algebraic vertices over a number field. P-adicdynamical systems have been suggested to model a wide range of practical problems, including memory recovery, in recent years. Other applications of p-adic dynamical systems arise in biology, physiology, computer science, combinatorics, automata theory and formal languages, etc. In this talk, we are interested in exploring the long-term behavior of the p-adic discrete dynamical system for the Sigmoid Beverton-Holt model, which arises in mathematical biology. Specifically, we want to look at how the system evolves over time. The Sigmoid Beverton-Holt model is a discrete population model that has a wide variety of different applications in the real world.
For instance, it is applied to estimate insurance premiums, forecast future changes in natural populations, and determine optimum fishing rates in order to handle the issue of diminishing stock sizes in the fishing sector. The fixed points, maximal Siegel disks, attractors, and periodic trajectories for the above-mentioned p-adicdynamical systems are examined in the projective line P1(Qp) of the field of p-adic numbers Qp. Moreover, the corresponding Juliaand Fatou sets are also examined. We will also discuss some open questions on this topic.