LOTKA-VOLTERRA DYNAMICS UNDER IMPULSIVE EFFECTS AT VARIABLE TIMES

Résumé

This work investigates a Lotka-Volterra model subject to impulsive effects occurring at variable times. The motivation stems from the need to represent abrupt environmental changes, such as biological control interventions or resource management actions, which naturally introduce discontinuities in ecological systems. By modeling these disturbances through impulsive differential equations (IDEs), we explore the impact of state-dependent impulses on population dynamics. Particular emphasis is given to the analysis of periodic and non-periodic behaviors resulting from different impulsive strategies. The development of this work is supported by numerical simulations that illustrate the effectiveness of impulsive interventions and the conditions under which periodic solutions emerge.

Keywords: Impulsive differential equations, Lotka-Volterra model, periodic solutions.