Dynamic behavior analysis of a feedback control predator-prey model with exponential fear effect and Hassell-Varley functional response

The effect of the fear factor on the dynamics of an eco-epidemiological system with standard incidence rate

“…( Wang et al., 2016 ; Wang & Zou, 2017 ). The term accounts for the cost of anti-predator behaviors may take different forms, such as ( Wang et al., 2016 ; Zhang et al., 2023 ), e − kY ( Das & Samanta, 2018 ; Li & Tian, 2023 ), ( Sarkara & Khajanchi, 2020 ). Generally, the fear effect can stabilize or destabilize the considered predator-prey systems, and may cause a significant reduction in the biomass of the population, which are demonstrated in ( Hossain et al., 2020 ; Pal, 2020 ; Sarkara & Khajanchi, 2020 ; Zhang et al., 2019 ).…”

“…They found that the fear effect can reduce the size of species including predator and prey, and may trigger a phenomenon where diseases in the predator population tend to become extinct. But in most of these works, the growth of prey population is unrestricted, which often goes against reality ( Haque & Venturino, 2007 ; Li & Tian, 2023 ). Hence, it is more meaningful to study the dynamics of eco-epidemiological systems with fear effect under the assumption that the prey grow logistically.…”

Complex dynamics of two prey–predator harvesting models with prey refuge and interval‐valued imprecise parameters

“…In the modeling process, these short-term disturbances are often regarded as pulses. Thus, impulsive differential equations (IDEs) provide a natural and effective description in modelling such processes, such as integrated pest management [41][42][43], prey-predator system [44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59], competitive system [60][61][62]. In prey-predator system, the human interventions can be divided into prey-dependent [37,41-43, 47, 48, 51-57], predator-dependent [36,37] and ratio-dependent [63] and prey-predator hybrid-dependent [38,39,64,65].…”