A deterministic and fractional order mathematical approach: Prey-predator dynamics in higher education systems

Abstract

This study explores the dynamic relationship between academic stress and student populations in higher education using a deterministic and fractional-order prey-predator framework, where stress acts as the predator and students as the prey. Equilibrium conditions are used to study the system's stability, while bifurcation analyses reveals critical transitions, including flip, fold, Hopf, and Neimark-Sacker bifurcations. Global stability analysis provides insight into the long-term behavior of students under academic constraints, and criteria for persistence and the basic reproduction number are established. The fractional-order approach effectively captures memory effects that influence students’ responses. Lyapunov exponents and numerical simulations further elucidate stability thresholds and the emergence of chaotic dynamics. Additionally, bifurcation diagram and basin of attraction analyses illustrate shifts in equilibrium states. The findings suggest that policy interventions targeting highly sensitive factors can significantly influence system dynamics, leadingto measurable changes in academic stress levels and overall stability. The study provides both theoretical and practical insights, demonstrating that undergraduate students tend to experience higher levels of stress than graduate students, primarily due to strict curriculum, more frequent examinations, and limited autonomy in undergraduate education.

J. Bangladesh Acad. Sci. 50(1); 71-98: March 2026