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The dynamical interactions of prey, middle-predator, and toppredator under the impact of prey odour are depicted in a schematic diagram.
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The odour emitted by prey is typically regarded as a crucial factor in an ecosystem. The objective of this study is to examine the stability and local bifurcations, specifically transcritical and Hopf bifurcation, of a food chain model that takes into account the influence of odour. The proposed model has been developed by incorporating a three-spe...
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Citations
... Although the impact of species' odour is widely recognised in ecological literature, there is a limited amount of research that explores its effect in mathematical models of predator-prey systems. Bhattacharjee et al. [8] discussed a three species food chain model incorporating the effect of prey odour. Xu et al. [5] studied the effect of predator odour on prey species in a predator-prey system. ...
... The occurrence of different bifurcations is explored in Section (7). The analytical findings are validated using numerical simulations in Section (8). Conclusions are drawn in Section (9). ...
... Through this investigation, valuable insights into the ecological dynamics of refuge and odour effect in a prey harvested food chain can be gained. Inspired by the research undertaken by Bhattacharjee et al. [8], we put forward the following model: ...
In this study, an odour-mediated system is developed and studied. In an odor-mediated systems, the sense of smell or odour of species plays a critical role in the interactions between predators and prey. It is widely recognised in scientific literature that these systems are very common and essential across natural ecosystems. These systems are crucial for various behaviors, including foraging, mating, and avoiding predators. In this paper, it is assumed that the presence of prey odour aids the predator in its hunting efforts. It is assumed that both prey and intermediate predators seek refuge against their respective predators upon detecting the odour of their predators. In other words, the odour of predators assists prey species in evaluating the danger and seeking refuge for hiding. This model incorporates the prey species' harvesting as well. We also explore the impact of fading memory on the system by incorporating fractional derivatives into the model. The conditions for both the existence and local stability of the non-negative equilibria are derived. The current model system undergoes both Hopf and transcritical bifurcation when the parameter values are appropriately chosen. The dynamic behaviour of the system is showcased and thoroughly analysed using a range of diagrams, highlighting the the impact of prey refuge and predator odour parameters. This paper extensively examines the long-term impacts of harvesting within the system. The presence of prey odour plays a significant role in promoting a long-term cohabitation dynamic within this specific system. It has been observed that when individuals within the system have a strong memory, it positively affects the stability of the system. Numerical simulations are conducted in order to demonstrate and validate the usefulness of the model being considered, therefore supporting the analytical conclusions.
