In this paper, we investigate the dynamics of a predator–prey system of an ecological community in which the fear instigated by the predators has an adverse effect on the reproduction rate of prey species, and also on the competition among themselves due to the limited environmental resources. To capture and handle the realistic scenario in a more meaningful way, we have mathematically built up the model system with the assumption that the predators predate on the prey items following Cosner functional response, which increases with increments in the prey and predator populations. The model system has been studied through noteworthy mathematical analysis and an extensive numerical simulation. Our simulation results demonstrate that the predator–prey system stabilizes due to predator’s induced fear suppressing/enhancing the birth/death of prey species. The competition among the predators for the available prey items also has a stabilizing role on the system’s dynamics. In contrast, the increasing growth rate of prey species or predation rate creates instability in the system by changing the stable phase to the limit cycle oscillations. Moreover, the effects of seasonality are also studied by extending the model system to its nonautonomous counterpart. Sufficient conditions are derived so that the seasonally driven system exhibits at least one positive periodic solution. Our numerical results show that the seasonally forced system exhibits periodic solution (globally attractive periodic solution), higher periodic solutions, bursting patterns and the extinction of predator species due to the seasonal variations of some parameters.

在这篇论文中，我们研究了一个生态群落的捕食者-猎物系统的动力学，在这个生态群落中，捕食者引起的恐惧对猎物的繁殖率产生不利影响，并且由于有限的环境影响它们之间的竞争资源。为了以更有意义的方式捕捉和处理现实场景，我们在数学上建立了模型系统，假设捕食者在 Cosner 功能反应之后捕食猎物，随着猎物和捕食者种群的增加而增加。该模型系统已通过值得注意的数学分析和广泛的数值模拟进行了研究。我们的模拟结果表明，捕食者-猎物系统由于捕食者诱发的恐惧抑制/增强猎物物种的出生/死亡而稳定下来。捕食者之间对可用猎物的竞争也对系统的动态具有稳定作用。相反，猎物物种或捕食率的增加通过将稳定阶段改变为极限循环振荡而在系统中造成不稳定。此外，还通过将模型系统扩展到非自主对应系统来研究季节性的影响。导出足够的条件，使得季节性驱动的系统表现出至少一个正周期解。我们的数值结果表明，季节性强制系统表现出周期解（全局有吸引力的周期解），更高的周期解，