![]() ![]() There is no doubt that harvesting is an influential issue from both an ecological and economic standpoint as well as from a social perspective. However, in reality, fear of predators can affect more than reproduction it can also affect the death rates of prey population 5, 19, 20. The cost of fear on prey reproduction is the main consideration in prey–predator models 4, 18. Different prey–predator systems have been empirically observed to demonstrate such phenomena 16, 17. Due to this, prey species compensate with mortality risk, affecting their growth and mortality rates. Directly, predators kill and consume their prey, but indirectly they instil fear in the prey population, which leads to significant behavioral changes in them (prey) such as vigilance, social behavior, habitat, foraging activity, reproductive cycle, etc. There are increasing numbers of evidences that predators impact their prey both directly (consumptive impacts) and indirectly (non-consumptive impacts). ratio-dependent or Beddington-DeAngelis), increased with increasing predator density. Due to the assumption that predators were foraging collectively, the above functional response, unlike the others (e.g. This type of behavior can be observed in biological species, such as a school of tuna searching and contacting herds of prey before hunting them 12. The schooling behavior of predators and prey populations is explained by a functional response that is predator-dependent, which is outlined by Cosner et al. But, the Holling family does not consider predator interference in the response function, whereas some biologists claim that predator interference must be included in the response function, particularly when predators compete for food or search for food 8, 9, 11. Functional responses from the Holling family are commonly used to describe prey–predator interactions 7. Different types of functional responses were developed in 7, 8, 9, 10. The functional response describes the mechanism by which predators feed on prey in prey–predator interactions, which is a central component of population dynamics. ![]() To understand the dynamics of prey–predator interactions on a global scale, numerous research studies have been conducted 1, 2, 3, 4, 5, 6. Over the last few decades, the scientific community has been studying prey–predator interactions extensively as one of the most exhibited examples of interspecies interactions. In order to shape the evolution of organisms, interspecies interactions are imperative. However, higher values of environmental disturbances lead the species to extinction. Our findings exhibit that during stochastic processes, model species fluctuate around some average values of the deterministic steady-state for lower environmental disturbances. Notably, several simulation runs are conducted to obtain time series solutions, histograms, and stationary distributions. Simulation results of stochastic system includes time series solutions of one simulation run and corresponding phase portraits. Further, we have studied the deterministic model in fluctuating environment. There is bistability between coexistence and predator-free equilibrium points in the system. Harvesting effort has both stabilizing and destabilizing effects. We find that consumption rate of predator, fear and harvesting effort give complex dynamics in the neighbourhood of BT-points. We have investigated the local stability of the equilibrium points and different types of bifurcations, such as transcritical, saddle-node, Hopf and Bogdanov–Takens (BT). ![]() In addition, we consider that the consumption rate of predators, i.e., the functional response, is dependent on schooling behavior of both species. In this work, a prey–predator model with fear dropping prey’s birth as well as death rates and nonlinear harvesting, is investigated. In order to ensure the future of our ecosystems, we need to protect our planet’s biodiversity. The well-being of humans is closely linked to the well-being of species in any ecosystem, but the relationship between humans and nature has changed over time as societies have become more industrialized. ![]()
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