We use Dulac criterion to prove the nonexistence of periodic orbits for a class of general predator-prey system with strong Allee effect in the prey population growth. This completes the global bifurcation analysis of typical predator-prey systems with strong Allee effect for all possible parameters.

Predator-prey relationships are a central component of community dynamics. Classic approaches have tried to understand and predict these relationships in terms of consumptive interactions between predator and prey species, but characterizing the interaction this way is insufficient to predict the complexity and context dependency inherent in predator-prey relationships. Recent approaches have b...

The trophic transfer of total mercury (THg) and its bioaccumulation from prey species to the predator fish Trichiurus lepturus was analysed in coastal waters of southeastern Brazil to evaluate the trace element dynamic in this predator-prey system. The isotopic (δ13C and δ15N) relation between this predator and its prey allowed inferences on prey assimilation and predator feeding habits. The TH...

In this paper, a delayed predator–prey system with stage structure is investigated. Sufficient conditions for the system to have multiple periodic solutions are obtained when the delay is sufficiently large by applying Bendixson’s criterion. Further, some numerical examples are given. Keywords—Predator-prey system, Stage structure, Hopf bifurcation, Periodic solutions.

Predator-prey interactions are important drivers in structuring ecological communities. However, despite widespread acknowledgement that individual behaviours and predator species regulate ecological processes, studies have yet to incorporate individual behavioural variations in a multipredator system. We quantified a prevalent predator avoidance behaviour to examine the simultaneous roles of p...

We use Dulac criterion to prove the nonexistence of periodic orbits for a class of general predator-prey system with strong Allee effect in the prey population growth. This completes the global bifurcation analysis of typical predator-prey systems with strong Allee effect for all possible parameters.

Cannibalism is ubiquitous in natural communities and has the potential to alter the functional relationship of predator–prey interactions. Although cannibalistic species are frequently subject to predation, the consequences of cannibalism in the prey for predator–prey interactions are poorly understood. Using a dragonfly larvae system, I provide the first experimental evidence that cannibalism ...

We consider the permanence of a periodic predator-prey system, where the prey disperse in a two-patch environment. We assume the Volterra within-patch dynamics and provide a sufficient and necessary condition to guarantee the predator and prey species to be permanent by using the techniques of inequality analysis. Our work improves previous relevant results.

The arms race of adaptation and counter adaptation in predator-prey interactions is a fascinating evolutionary dynamic with many consequences, including local adaptation and the promotion or maintenance of diversity. Although such antagonistic coevolution is suspected to be widespread in nature, experimental documentation of the process remains scant, and we have little understanding of the imp...

Keywords--Prey-predator system, Time delay, Stability, Hopf bifurcation, Periodic solutions. 1. I N T R O D U C T I O N After the seminal models of Volterra and Lotka in the mid-1920s, predator-prey systems with delay have been studied extensively in recent years. There have been many results on stability, oscillation, persistence, and existence of positive periodic solutions, see for example, ...