Bubbling and hydra effect in a population system with Allee effect

• Published in: Ecological complexity Vol. 47; p. 100939
• Main Authors: Garain, Koushik, Mandal, Partha Sarathi
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.09.2021
• Subjects: Allee effect; Bistability; Bubbling effect; extinction; Hydra effect; mortality; Prey-predator system; Tristability; Bubbling effect; Prey-predator system; Tristability; Hydra effect; Bistability
• ISSN: 1476-945X
• DOI: 10.1016/j.ecocom.2021.100939

•A prey-predator system with a component Allee effect in predator population and Holling type-II functional response by including density dependent death rate in predator is investigated.•We investigated our model both analytically and numerically, and highlighted the effect of density independent mortality and Allee effect.•We observed that tristability is possible for our model that includes two stable co-existence fixed points.•The most important phenomena which we observed is hydra effect, i.e., increasing mortality of a species can increase its population size.•We discussed the phenomenon bubbling effect, which indicates increasing and decreasing of amplitudes of limit cycles.•Both bubbling effect and hydra effect in a continuous time preypredator model with component Allee effect and density dependent death rate in predator has yet not been investigated by any one. We present a continuous time predator-prey model and predator’s growth subjected to component Allee effect. The model also includes density dependent mortality of predator. We investigate our model both analytically and numerically, and highlighted the effect of density independent mortality and Allee effect. In our system, we find that a fixed point representing the extinction of predator is always a stable point. When coexistence equilibria exists our system is bistable. We have observed that tristability is possible for our model that includes two stable co-existence fixed point. The most important phenomena which we have observed are hydra effect and cascading effect. Due to component Allee effect in predator the system shows multiple hydra effect. We discuss the phenomenon of bubbling, which indicates increasing and decreasing of amplitudes of cycles. We have presented one-parametric as well as two-parametric bifurcation diagram and also all possible bifurcations that the system could go through.