Uniformly Strong Persistence for a Delayed Predator-Prey Model

An asymptotically periodic predator-prey model with time delay is investigated. Some sufficient conditions for the uniformly strong persistence of the system are obtained. Our result is an important complementarity to the earlier results

The effects of fear and delay on a predator-prey model with Crowley-Martin functional response and stage structure for predator

Taking into account the delayed fear induced by predators on the birth rate of prey, the counter-predation sensitiveness of prey, and the direct consumption by predators with stage structure and interference impacts, we proposed a prey-predator model with fear, Crowley-Martin functional response, stage structure and time delays. By use of the functional differential equation theory and Sotomayor's bifurcation theorem, we established some criteria of the local asymptotical stability and bifurcations of the system equilibrium points. Numerically, we validated the theoretical findings and explored the effects of fear, counter-predation sensitivity, direct predation rate and the transversion rate of the immature predator. We found that the functional response as well as the stage structure of predators affected the system stability. The fear and anti-predation sensitivity have positive and negative impacts to the system stability. Low fear level and high anti-predation sensitivity are beneficial to the system stability and the survival of prey. Meanwhile, low anti-predation sensitivity can make the system jump from one equilibrium point to another or make it oscillate between stability and instability frequently, leading to such phenomena as the bubble, or bistability. The fear and mature delays can make the system change from unstable to stable and cause chaos if they are too large. Finally, some ecological suggestions were given to overcome the negative effect induced by fear on the system stability

An Impulsive Three-Species Model with Square Root Functional Response and Mutual Interference of Predator

An impulsive two-prey and one-predator model with square root functional responses, mutual interference, and integrated pest management is constructed. By using techniques of impulsive perturbations, comparison theorem, and Floquet theory, the existence and global asymptotic stability of prey-eradication periodic solution are investigated. We use some methods and sufficient conditions to prove the permanence of the system which involve multiple Lyapunov functions and differential comparison theorem. Numerical simulations are given to portray the complex behaviors of this system. Finally, we analyze the biological meanings of these results and give some suggestions for feasible control strategies

Analysis of a Holling-type IV stochastic prey-predator system with anti-predatory behavior and Lévy noise

In this paper, we investigate a stochastic prey-predator model with Holling-type IV functional responses, anti-predatory behavior (referring to prey resistance to predator), gestation time delay of prey and Lévy noise. We investigate the existence and uniqueness of global positive solutions through Itô's formulation and Lyapunov's method. We also provide sufficient conditions for the persistence and extinction of prey-predator populations. Additionally, we examine the stability of the system distribution and validate our analytical findings through detailed numerical simulations. Our paper concludes with the implications of our results

The Dynamics of an Impulsive Predator-Prey System with Stage Structure and Holling Type III Functional Response

Based on the biological resource management of natural resources, a stage-structured predator-prey model with Holling type III functional response, birth pulse, and impulsive harvesting at different moments is proposed in this paper. By applying comparison theorem and some analysis techniques, the global attractivity of predator-extinction periodic solution and the permanence of this system are studied. At last, examples and numerical simulations are given to verify the validity of the main results

Analysis of an Impulsive One-Predator and Two-Prey System with Stage-Structure and Generalized Functional Response

An impulsive one-predator and two-prey system with stage-structure and generalized functional response is proposed and analyzed. By reasonable assumption and theoretical analysis, we obtain conditions for the existence and global attractivity of the predator-extinction periodic solution. Sufficient conditions for the permanence of this system are established via impulsive differential comparison theorem. Furthermore, abundant results of numerical simulations are given by choosing two different and concrete functional responses, which indicate that impulsive effects, stage-structure, and functional responses are vital to the dynamical properties of this system. Finally, the biological meanings of the main results and some control strategies are given

Volcanically-induced floral changes across the Triassic-Jurassic (T-J) transition

The End-Triassic Mass Extinction (ETME) saw the catastrophic loss of ca. 50% of marine genera temporally associated with emplacement of the Central Atlantic Magmatic Province (CAMP). However, the effects of the ETME on land is a controversial topic. Evaluation of the disparate cause(s) and effects of the extinction requires additional, detailed terrestrial records of these events. Here, we present a multidisciplinary record of volcanism and environmental change from an expanded Triassic-Jurassic (T-J) transition preserved in lacustrine sediments from the Jiyuan Basin, North China. High-resolution chemostratigraphy, palynological, kerogen, and sedimentological data reveal that terrestrial conditions responded to and were defined by large-scale volcanism. The record of sedimentary mercury reveals two discrete CAMP eruptive phases during the T-J transition. Each of these can be correlated with large, negative C isotope excursions (CIE-I of -4.7 ‰; CIE-II of -2.9 ‰), significantly reduced plant diversity (with ca. 45% and 44% generic losses respectively), enhanced wildfire (marked by increased fusinite or charcoal content), and major climatic shifts towards drier and hotter conditions (indicated by the occurrence of calcareous nodules, increased Classopollis pollen content, and PCA analysis). Our results show that CAMP eruptions may have followed a bimodal eruptive model and demonstrate the powerful ability of large-scale volcanism to alter the global C cycle and profoundly affect the climate, in turn leading to enhanced wildfires and a collapse in land plant diversity during the T-J transition

Dynamics of an Impulsive Stochastic Predator–Prey System with the Beddington–DeAngelis Functional Response

Taking impulsive effects into account, an impulsive stochastic predator–prey system with the Beddington–DeAngelis functional response is proposed in this paper. First, the impulsive system is transformed into an equivalent system without pulses. Then, by constructing suitable functionals and applying the extreme-value theory of quadratic functions, sufficient conditions on the existence of periodic Markovian processes are provided. The uniform continuity and global attractivity of solutions are also investigated. Additionally, we investigate the extinction and permanence in the mean of all species with the help of comparison methods and inequality techniques. Sufficient conditions on the existence and ergodicity of the stationary distribution of solutions for the autonomous and non-impulsive case are given. Finally, numerical simulations are performed to illustrate the main results