Deterministic and Stochastic Mathematical Population Dynamics Models.

      Аннотация: We consider mathematical population dynamics models in deterministic and stochastic environments. For deterministic environments, we study three models: an intraguild model with the effects of spatial heterogeneous environment and fast migration of individuals; a fishery model with Marine Protected Area where fishing is prohibited and an area where the fish population is harvested; a predator-prey model which has one prey and two predators with Beddington-DeAngelis functional responses. For stochastic environments, we study SIRS epidemic model and predator-prey models under telegraph noise. We try to present the dynamical behavior of these models and show out the existence or vanishing of species in the models.

Ключевые слова: Intraguild predation, fast migration, fish school, marine protected area, three level system, Lotka-Volterra equation, predator-prey system, SIRS model, telegraph noise.