![]() Guo, Higher codimension bifurcation analysis of predator-prey systems with nonmonotonic functional responses. Perko, Differential Equations and Dynamical Systems, vol. Chakraborty, Dynamics of a delay-induced prey-predator system with interaction between immature prey and predators. Pal, Effect of seasonally forced noisy environment on aquatic prey-predator model with water level fluctuations. Ghosh, A study of a prey-generalist predator system considering hunting cooperation and fear effects under interval uncertainty. Kokko, Mate finding, a llee effects and selection for sex-biased dispersal. Pal, Chaos in a nonautonomous model for the interactions of prey and predator with effect of water level fluctuation. González-Olivares, Optimal harvesting in a predator-prey model with Allee effect and sigmoid functional response. Sen, Spatiotemporal dynamics of a prey-predator model with Allee effect in prey and hunting cooperation in a holling type iii functional response. Yu Morozov, Emergence of holling type iii zooplankton functional response: bringing together field evidence and mathematical modelling. Kooi, Modelling holling type ii functional response in deterministic and stochastic food chain models with mass conservation. Ghosh, An autonomous and nonautonomous predator–prey model with fear, refuge, and nonlinear harvesting: Backward, bogdanov-takens, transcritical bifurcations, and optimal control. Ghosh, Studies of dynamical behaviours of an imprecise predator-prey model with holling type ii functional response under interval uncertainty. Mondal, Study of stability and bifurcation of three species food chain model with non-monotone functional response. Liu et al., Dynamics of a predator-prey system with a mate-finding Allee effect. Zhao, Spatiotemporal dynamics of a diffusive predator-prey system with allee effect and threshold hunting. Samanta, Chaos and bistabilities in a food-chain model with allee effect and additional food. Banerjee, Rich bifurcation structure of prey-predator model induced by the allee effect in the growth of generalist predator. Cheung, Weak persistence of a stochastic delayed competition system with telephone noise and allee effect. Courchamp, Multiple Allee effects and population management. Sun, Mathematical modeling of population dynamics with Allee effect. Banerjee, Allee effect in prey versus hunting cooperation on predator-enhancement of stable coexistence. Yakubu, Weak allee effects and species coexistence. ![]() ![]() Banerjee, Analytical detection of stationary and dynamic patterns in a prey-predator model with reproductive allee effect in prey growth. Wei, Predator-prey system with strong Allee effect in prey. Gomulkiewicz, Metapopulation Allee effects, habitat destruction, and extinction in metacommunities. ![]() ![]() Numerically, we notice that the system experiences fascinating dynamics followed by transcritical, saddle node and Hopf bifurcation and finally depicts the bistability scenario for various strengths of consumption rates. Depending on the value of the Allee threshold, the population either achieves a stable steady state or oscillates. The system exhibits a bistability as well as monostable nature as the Allee parameter progressively increases and three limit cycles arise for lesser and higher intensity of the Allee threshold in which an unstable limit cycle separates two stable limit cycles, as their basin. In the context of variations in the carrying capacity, Allee threshold and rate of consumption, numerically we investigate the system’s stability scenario and bifurcation layout in the presence of numerous coexistence equilibria. According to our analysis, the system follows a transcritical bifurcation about the conversion rate and the saddle node, yet also Hopf bifurcation concerning the Allee factor. Initially, we find the system’s equilibrium and its local stability. In the present paper, we examine the effects of the Allee threshold on prey–predator interaction frameworks developed by utilising the Holling type-III response. ![]()
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