BIOMECHANICS, BIOENGINEERING AND MATHEMATICAL BIOLOGY Seminar

PROGRAM

Predavanja možete pratiti i online putem MITEAM stranice Seminara iz Biomehanike, bioinžinjeringa i matematičke biologije: https://miteam.mi.sanu.ac.rs/asset/pkPCEADMcffpGhjaQ

Plan rada Seminara iz Biomehanike, bioinžinjeringa i matematičke biologije za NOVEMBAR 2025.

Ponedeljak 03.11.2025. u 16:00, Kneza Mihaila 36, sala 301f i Online
Petar Ćirković, Mathematical Institute SANU, Belgrade, Serbia
BIFURCATION ANALYSIS OF AN INTRAGUILD PREDATION THREE-LEVEL FOOD WEB MODEL WITH HARVESTING ON TOP TWO LEVELS
Over the past decades, mathematical modeling of food webs has received increasing attention, as it enables a deeper understanding of the complex interactions within ecological communities. In an omnivory food web, a predator feeds on species from more than one trophic level. Intraguild predation (IGP) is a special kind of omnivoryit’s defined as the killing and eating of species that use similar, often limiting, resources and are thus potential competitors.
Harvesting is an important method for preventing and controlling the excessive growth of populations and plays a key role in maintaining ecological balance. In the literature, different types of harvesting functions have been proposed in mathematical predator-prey models. The most commonly used are constant, proportional, and nonlinear Michaelis–Menten type harvesting functions. To avoid overexploitation and species extinction, hunting and fishing must be practiced in an optimal manner.
In this lecture, the dynamics of an intraguild predation three-level food web model are analyzed by incorporating a nonlinear Michaelis-Menten type harvesting on the intermediate predator and proportional harvesting on the intraguild (IG) predator. The positivity and boundedness of solutions, as well as the existence and stability of the possible equilibria, are investigated. The effect of harvesting is studied through a detailed bifurcation analysis. The existence of saddle-node, transcritical, pitchfork, Hopf, generalized Hopf, Bogdanov-Takens, and Zero-Hopf bifurcations is shown. Optimal harvesting thresholds for predators that prevent their extinction are identified. Parameter regions of extinction and coexistence are determined. The results show that the system can exhibit multistability and sensitivity to initial conditions.