Hunting cooperation in a prey-predator model with maturation delay

We investigate the dynamics of a prey-predator model with cooperative hunting among specialist predators and maturation delay in predator growth. First, we consider a model without delay and explore the effect of hunting time on the coexistence of predator and their prey. When the hunting time is long enough and the cooperation rate among predators is weak, prey and predator species tend to coexist. Furthermore, we observe the occurrences of a series of bifurcations that depend on the cooperation rate and the hunting time. Second, we introduce a maturation delay for predator growth and analyse its impact on the system's dynamics. We find that as the delay becomes larger, predator species become more likely to go extinct, as the long maturation delay hinders the growth of the predator population. Our numerical exploration reveals that the delay causes shifts in both the bifurcation curves and bifurcation thresholds of the non-delayed system.

Induced Resistance in Fruit and Vegetables: A Host Physiological Response Limiting Postharvest Disease Development

Harvested fruit and vegetables are perishable, subject to desiccation, show increased respiration during ripening, and are colonized by postharvest fungal pathogens. Induced resistance is a strategy to control diseases by eliciting biochemical processes in fruits and vegetables. This is accomplished by modulating the progress of ripening and senescence, which maintains the produce in a state of heightened resistance to decay-causing fungi. Utilization of induced resistance to protect produce has been improved by scientific tools that better characterize physiological changes in plants. Induced resistance slows the decline of innate immunity after harvest and increases the production of defensive responses that directly inhibit plant pathogens. This increase in defense response in fruits and vegetables contributes to higher amounts of phenols and antioxidant compounds, improving both the quality and appearance of the produce. This review summarizes mechanisms and treatments that induce resistance in harvested fruits and vegetables to suppress fungal colonization. Moreover, it highlights the importance of host maturity and stage of ripening as limiting conditions for the improved expression of induced-resistance processes.

Analysis of a negative binomial host-parasitoid model with two maturation delays and impulsive resource input

To study the interaction of parasitoids and their insect hosts in laboratory environment, we propose a mathematical model incorporating impulsive resource inputs, stage-structure, maturation times and negative binomial distribution of parasitoid attacks. According to the adaptability of the insect host to the environment, we obtain conditions under which the system is uniformly permanent in two cases, which guarantee that the host and its parasitoid can coexist. By applying fixed point theory, we show existence of the positive periodic solution where the host and its parasitoid can coexist, and also obtain the conditions that ensure the existence of the parasitoid-extinction periodic solution. Our numerical analysis confirms and extends our theoretical results. The simulations show that when the total amount of resource is fixed, a smaller amount of recourse inputs with a shorter period of impulsive delivery results in smaller oscillation amplitude in the insect host population. However, the development of parasitoid population is not affected by the resource management strategy. It is also demonstrated that larger maturation times, either the host's or the parasitoid's, lead to the decline of the parasitoid population. But larger parasitoid's maturation time does accelerate the host's population growth. These are helpful for us to acquire a deeper knowledge of the host-parasitoid interaction in laboratory environment.

Stage-structured cannibalism with delay in maturation and harvesting of an adult predator

A three-dimensional stage-structured predator-prey model is proposed and analyzed to study the effect of predation and cannibalism of the organisms at the highest trophic level with non-constant harvesting. Time lag in maturation of the predator is introduced in the system and conditions for local asymptotic stability of steady states are derived. The length of the delay preserving the stability is also estimated. Moreover, it is shown that the system undergoes a supercritical Hopf bifurcation when the maturation time lag crosses a certain critical value. Computer simulations have been carried out to illustrate various analytical results.