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In this work, we propose and investigate a predator-prey model where the prey population is structured by sex and the predators (unstructured) depredate based on sex-bias. We provide conditions for the existence of equilibrium points and perform local stability analysis on them. We derive global stability conditions for the extinction state. We show the possible occurrence of Hopf and saddle-node bifurcations. Multiple Hopf bifurcations are observed as the sex-biased predation rate is varied. This variation also shows the opposite consequences in the densities of the sex-structured prey. Our results show that sex-biased predation can cause both stabilizing and destabilizing effects for certain parameter choices. It can also cause an imbalanced sex-ratio, which has ecological consequences. Furthermore when intraspecific competition among predators is minimized, it can lead to the extinction of prey. We discuss the ecological implications and application of our results to the biocontrol of invasive species susceptible to sex-biased predation. [ABSTRACT FROM AUTHOR]

The Trojan Y Chromosome (TYC) strategy is a biological control method for controlling invasive populations with an XX–XY sex determinism, wherein a modified organism is introduced into an invasive population to skew the sex ratio over time, causing local extinction. However, the classical three compartment TYC model possesses blow-up solutions, for large initial conditions [Takyi EM, Beauregard MA, Griffin T, Bobo L, Parshad RD, On large and small data blow-up solutions in the Trojan Y Chromosome model, Axioms 11(3):120, 2022]. We investigate model improvements via accounting for a modified logistic term, female mating preference, competition between males and supermales and pair formation. Each one of these models is dynamically explored and is shown to possess global in-time non-negative solutions, in any parameter and initial data regime, and the models are also effective in facilitating extinction of the invasive wild type. [ABSTRACT FROM AUTHOR]

Synchronization of food chain models is an intensely investigated area in dynamical systems. Two pioneering models in three species food chain systems exhibiting chaotic dynamics are the Hastings and Powell (HP) model and the Upadhyay and Rai (UR) model. These are known to synchronize, even though the top predators in the two models behave differently. In the current manuscript, we show that although the HP and UR models synchronize for certain initial conditions, they do not synchronize for arbitrarily large initial conditions due to the blow-up dynamics present in the UR model. Thus, the synchronization of these model systems is purely a local (in initial data) phenomenon. Interestingly, we find that a similar result holds for the modified UR model as well, which has global in-time solutions for any positive initial condition. Thus, the lack of synchrony could also be attributed to the difference in the top predator's feeding preferences in the model systems. Our results have large-scale applications to population synchrony in tri-trophic food chains. [ABSTRACT FROM AUTHOR]

Cannibalism, or intraspecific predation, is the act of an organism consuming another organism of the same species. In predator-prey relationships, there is experimental evidence to support the existence of cannibalism among juvenile prey. In this work, we propose a stage-structured predator-prey system where cannibalism occurs only in the juvenile prey population. We show that cannibalism has both a stabilizing and destabilizing effect depending on the choice of parameters. We perform stability analysis of the system and also show that the system experiences a supercritical Hopf, saddle-node, Bogdanov-Takens and cusp bifurcation. We perform numerical experiments to further support our theoretical findings. We discuss the ecological implications of our results.