ON A PERIODIC PREY-PREDATOR SYSTEM WITH INFINITE DELAYS

Based on the theory of coincidence degree,the existence of positive periodic solutions is established for a periodic prey predator system with infinite delays (t)=x(t)[α(t)-γ(t)y(t)-γ(t)∫ ∞ 0K 1(t,s)y(t-s) d s- ∫ ∞ 0∫ ∞ 0R 1(t,s,θ)y(t-s)y(t-θ) d θ d s], (t)=y(t)[-β(t)+μ(t)x(t)+μ(t)∫ ∞ 0K 2(t,s)x(t-s) d s+ ∫ ∞ 0∫ ∞ 0R 2(t,s,θ)x(t-θ)x(t-s) d θ d s],where α,γ,β,μ are positive continuous ω periodic functions, K i∈C (R×[0,∞),(0,∞))( i =1,2) are ω periodic with respect to their first arguments,.respectively, R i∈C (R×[0,∞)×[0,∞),(0,∞))( i =1,2) are ω periodic with respect to their first arguments,respectively.

Stability and Bifurcation of a Prey-Predator System with Additional Food and Two Discrete Delays

In this paper,the impact of additional food and two discrete delays on the dynamics of a prey-predator model is investigated.The interaction between prey and predator is considered as Holling Type-II functional response.The additional food is provided to the predator to reduce its dependency on the prey.One delay is the gestation delay in predator while the other delay is the delay in supplying the additional food to predators.The positivity,boundedness and persistence of the solutions of the system are studied to show the system as biologically well-behaved.The existence of steady states,their local and global asymptotic behavior for the non-delayed system are investigated.It is shown that(i)predator’s dependency factor on additional food induces a periodic solution in the system,and(ii)the two delays considered in the system are capable to change the status of the stability behavior of the system.The existence of periodic solutions via Hopf-bifurcation is shown with respect to both the delays.Our analysis shows that both delay parameters play an important role in governing the dynamics of the system.The direction and stability of Hopf-bifurcation are also investigated through the normal form theory and the center manifold theorem.Numerical experiments are also conducted to validate the theoretical results.

Effect of random movement and cooperative hunting in the prey-predator system:A dynamical approach

Self-diffusion prerequisite is obtained as the spreading approach of biological populations.Cooperative hunting is a common behavior in predator populations that promotes predation and the coexistence of the prey-predator system.On the other side,the Allee effect among prey may cause the system to become unstable.In this paper,a difusive prey predator system with cooperative hunting and the weak Allee effect in prey populations is discussed.The linear stability and Hopf-bifurcation analysis had been used to examine the system's stability.From the spatial stability of the system,the conditions for Turing instability have been derived.The multiple-scale analysis has been used to derive the amplitude equations of the system.The stability analysis of these amplitude equations leads to the formation of Turing patterns.Finally,numerical simulations are used to analyze spatial patterns forming in 1-D and 2-D.The studies indicate that the model can generate a complex pattern structure and that self-diffusion has a drastic impacton species distribution.

NONLINEAR SINGULARLY PERTURBED PREDATOR-PREY REACTION DIFFUSION SYSTEMS

A class of nonlinear predator prey reaction diffusion systems for singularly pe rturbed problems are considered.Under suitable conditions, by using theory of di fferential inequalities the existence and asymptotic behavior of solution for in itial boundary value problems are studied.

POSITIVE PERIODIC SOLUTION OF A NEUTRAL PREDATOR-PREY SYSTEM

In this paper, the existence o f a positive periodic solution to the following neutral predator_prey system (t)=rH(t)1-a 1(t)H(t-τ)+a 2(t-τ)K-α(t)H(t)P(t), (t)=-b(t)P(t)+β(t)H(t)P(t) is studied,in which r,a 2,K and τ are positive constants, and a 1(t ),α(t),b(t) and β(t) are positive continuous functions of period ω .

Periodic Solutions of Periodic Delay Predator-Prey System with Nonmonotonic Functional Response

By using the continuation theorem of coincidence degree theory, sufficient conditions are obtained for the existence of positive periodic solutions of a delayed predator prey system with nonmonotonic functional response in a periodic environment.

A CONDITION OF THE EXISTENCE OF STABLE POSITIVE STEADY-STATE SOLUTIONS FOR A ONE PREDATOR TWO PREY SYSTEM

One predator two prey system is a research topic which has both the theoretical and practical values. This paper provides a natural condition of the existence of stable positive steady-state solutions for the one predator two prey system. Under this condition we study the existence of the positive steady-state solutions at vicinity of the triple eigenvalue by implicit function theorem, discuss the positive stable solution problem bifurcated from the semi-trivial solutions containing two positive components with the help of bifurcation and perturbation methods.

Persistence in Non-Autonomous Lotka-Volterra System with Predator-Prey Ratio-Dependence and Density Dependence

The main purpose of this article is considering the persistence non-autonomous Lotka-Volterra system with predator-prey ratio-dependence and density dependence. We get the sufficient conditions of persistence of system, further have the necessary conditions, also the uniform persistence condition, which can be easily checked for the model is obtained.

The Predatory Function of Three Spiders to Two Insect Pests in Rice Within a Multi-species Co-existence System

The prey-seeking behavior of three spiders (X1-Pirata subpiraticus, X2-Clubiona japonicola and X3-Tetragnatha japonica) for brown plant hopper (X4-Nilaparvata lugens) and rice spittle bug (X5-Cal-litettix versicolor) was investigated, as well as how interference between and within species occurred, by using a quadratic regression rotational composite design. Six predation models derived from the analysis of interactions among and within predators and preys were developed. The total predatory capacity of spiders on rice insect pests after coexistence for one day can be expressed as follows: Y3 = 32.795 + 2.25X1 + 1.083X2 + 0.5X3 + 10.167X4 + 3.167X5 - 1.67X12 - 2.42X22 - 3.295X32 - 0.045X42 + 0.455X52 - 3.125X1X2 + 0.375X1X3 -0.625X1X4 - 0.375X1X5 + 0.375X2X3 - 0.875X2X4 + 0.125X2X5 + 0.375X3X4 - 0.375X3X5 + 0.125X4X5. The principal efficiency analysis using this model indicated that increases in insect pest density significantly increased predation by predators; this was much greater than the effect of any single predator. X4 had a greater effect than X5; however, X4 and X5 demonstrated little interspecific interference and even promoted each other and increased predation rates as the densities of the two pests increased. Among the three predators, an increase in the density of X, had the greatest effect on the increase in predation, X3 had the second, X2 the third greatest effect. As predator density increased inter- and intra-species interference occurred, which were largely related to the size, activity, niche breadth, niche overlap and searching efficiency of the predators. X2 produced the greatest interference between different individuals and between any other predator species. X3 had the second greatest, which reduced predation levels at high predator densities. Because of these factors, the highest predation rate was obtained at a prey density of 120 per 4 rice-hills. The optimal proportion of the three predators in the multi-predator prey system was X1: X2: X3 = 5.6:1.3:4.1.

Turing Instability of Diffusive Predator⁃Prey System with Gompertz Growth

This paper mainly focus on the research of a predator⁃prey system with Gompertz growth of prey.When the system does not contain diffusion,the stability conditions of positive equilibrium and the occurring condition of the Hopf bifurcation are obtained.When the diffusion term of the system appears,the stable conditions of positive equilibrium and the Turing instability condition are also obtained.Turing instability is induced by the diffusion term through theoretical analysis.Thus,the region of parameters in which Turing instability occurs is presented.Then the amplitude equations are derived by the multiple scale method.The results will enrich the pattern dynamics in predator⁃prey systems.

A Review of the Mathematical Models for the Impact of Seasonal Weather Variation and Infections on Prey Predator Interactions in Serengeti Ecosystem

Interaction between prey and predator species is a complex and non-linear process. Understanding various phenomena in the dynamics of prey-predator systems is vital to both mathematical ecology and conservation biology. Mathematical models on prey-predator systems have been the hot sport providing important information regarding the interactions of prey and predator species in various ecosystems. In this paper, a review of the available mathematical models on prey-predator systems was done. Our aim was to assess their structure, behaviour, available control strategies, population involved and their ability in predicting the future behaviour of the ecosystems. We observed diversities in the reviewed mathematical models, some model incorporated factors such as drought, harvesting and prey refuge as the factors that affect ecosystems, some ignored the contribution of environmental variations while others considered the variable carrying capacity. Most of the models reviewed have not considered the contribution of diseases and seasonal weather variation in the dynamics of prey predator systems. Some of the reviewed models do not match the real situation in most modelled ecosystems. Thus, to avoid unreliable results, this review reveals the need to incorporate seasonal weather variations and diseases in the dynamics of prey predator systems of Serengeti ecosystem.

No evidence of predator odor avoidance in a North American bird community

Recent advances in our understanding of avian chemical communication have highlighted the importance of olfaction in many aspects of avian life.Prior studies investigating predator avoidance behaviors in response to predator odor cues have produced mixed results across species and contexts.Here we assess if a community of birds in eastern Pennsylvania displays avoidance behaviors towards predator odor cues in a natural foraging setting.We use clay caterpillars to measure foraging activity by birds in the presence of predator(bobcat)urine,non-predator(rabbit)urine,and water controls in two different environmental contexts(field vs.forest).Although we detected a weak trend for birds to forage less at predator urine-treated sites,we found no significant difference in avian foraging between the site types.We did find that foraging rates between environmental contexts changed significantly over the course of the experiment,with forest sites showing decreasing foraging rates and field sites showing increasing foraging rates.Our results reinforce the published literature that avoidance of predator odors by birds may not be ubiquitous across contexts and species.

Marine Predators Algorithm with Deep Learning-Based Leukemia Cancer Classification on Medical Images

In blood or bone marrow,leukemia is a form of cancer.A person with leukemia has an expansion of white blood cells(WBCs).It primarily affects children and rarely affects adults.Treatment depends on the type of leukemia and the extent to which cancer has established throughout the body.Identifying leukemia in the initial stage is vital to providing timely patient care.Medical image-analysis-related approaches grant safer,quicker,and less costly solutions while ignoring the difficulties of these invasive processes.It can be simple to generalize Computer vision(CV)-based and image-processing techniques and eradicate human error.Many researchers have implemented computer-aided diagnosticmethods andmachine learning(ML)for laboratory image analysis,hopefully overcoming the limitations of late leukemia detection and determining its subgroups.This study establishes a Marine Predators Algorithm with Deep Learning Leukemia Cancer Classification(MPADL-LCC)algorithm onMedical Images.The projectedMPADL-LCC system uses a bilateral filtering(BF)technique to pre-process medical images.The MPADL-LCC system uses Faster SqueezeNet withMarine Predators Algorithm(MPA)as a hyperparameter optimizer for feature extraction.Lastly,the denoising autoencoder(DAE)methodology can be executed to accurately detect and classify leukemia cancer.The hyperparameter tuning process using MPA helps enhance leukemia cancer classification performance.Simulation results are compared with other recent approaches concerning various measurements and the MPADL-LCC algorithm exhibits the best results over other recent approaches.

一类食饵具有阶段结构的时滞Predator-Prey系统的周期解(英文)

研究了一类时滞Predator-Prey系统,其中Prey种群是具有两个生命阶段的种群,即幼年阶段和成年阶段。Predator种群只能捕食Prey幼年种群。通过应用Gaines和Mawhin重合度理论的连续函数定理,给出了系统正周期解存在的充分条件。

The Influence of Transgenic cry1Ab/cry1Ac,cry1C and cry2A Rice on Non-Target Planthoppers and Their Main Predators Under Field Conditions

Transgenic Bt rice has been shown to be an effective means of controlling Lepidoptera pests of rice. However, the potential roles of transgenic rice on planthoppers and their predators need to be investigated before its commercialization. Population density, species dominance and population dynamics are important parameters of arthropods populations in field. So the impacts of three transgenic Bt rice strains expressing crylAb/crylAc, crylC and cry2A on population density, species dominance and population dynamics of three species of planthoppers （Nilaparvata lugens, Sogatella furcifera and Laodelphax striatellus） and their three main predators （ Cyrtorhinus lividipennis, Pirata subpiraticus and Theridium octomaculatum） were evaluated at three sites in Hubei Province, China, in the current study. The results showed that among three species of planthoppers, both in transgenic and non-transgenic rice field, the predominant species ofplanthoppers within phytophagous guild was S. furcifera at any site either growing season （46-50%）. Significantly higher population density ofN. lugens was observed in T2A-1 field relative to Minghui 63 field at Wuxue in 2010. The species dominance of predator, P. subpiraticus, in TT51 field was significantly higher than that in T 1 C-19 and T2A-1 fields in 2009 at Xiaogan site. Sampling date significantly influenced six arthropods except for P. subpiraticus in 2010. The interaction between rice strain^sampling date had no significant adverse effects on the population dynamics of three species of planthoppers and their predators, except for several individual species in 2009. The interaction among rice strain^sampling date^sampling site also had no significant effect on six arthropods except for S. furcifera in 2009. The results indicated that transgenic Bt rice expressing crylAb/crylAc, cry2A and crylC had no significant adverse effects on the population dynamics of three planthoppers and their predators in most investigated data and sampling site.

Effects of Transgenic Bt+CpTI Cotton on Field Abundance of Non-Target Pests and Predators in Xinjiang, China

Transgenic insect-resistant cotton is being increasingly planted in Xinjiang cotton-planting regions, where geographical climate conditions and species composition of pests and natural enemies are greatly unique in China. Limited studies have been conducted on the ecological impacts of transgenic insect-resistant cotton, especially for transgenic double genes （Bt＋CpTI） cotton, in this region. In this study, the potential effects of transgenic Bt＋CpTI cotton on the seasonal abundance of non-target pests and predators were assessed from 2009 to 2011 in Korla, Xinjiang. The results showed that species composition and seasonal abundance of 5 groups of pests and 5 groups of predators were not significantly different between transgenic Bt＋CpTI cotton and non-transgenic cotton every year. It suggests that transgenic Bt＋CpTI cotton per se does not affect the population dynamics of non-target pests and predators on this crop in Xinjiang.

Nest predators, nest-site selection and nest success of the Emei Shan Liocichla(Liocichla omeiensis), a vulnerable babbler endemic to southwestern China

Background: The Emei Shan Liocichla(Liocichla omeiensis) is a globally vulnerable babbler, endemic to southwestern China. We investigated its nest predators, nest-site selection and nest success at the Laojunshan National Nature Reserve in Sichuan, China in order to identify the precise nesting-habitat requirements of the species, and to test whether the nest-site-selection cues, preferred by the Emei Shan Liocichla, are positively associated with nest success.Methods: We used infrared cameras to determine nest predators. We compared the microhabitat attributes between nest and random sites, as well as successful and failed nests. We used Binary Logistic Regression to determine the most important variables affecting nest-site selection of the Emei Shan Liocichla. We used the nest survival analysis in Program MARK to estimate daily nest survival rates(DSR). Nest success was calculated using the Mayfield method.Results: In total 56 nests were found. The DSR for all nests that contained at least one egg was 0.9564 ± 0.0091(95 % CI 0.9346–0.9711)(n = 40), while the total nest success was 27.5 %. We identified four categories of predators in 10 nest predation events, i.e. squirrels(n = 5), snakes(n = 3), raptors(n = 1) and wasps(n = 1). We found that:(1) nest predation was the primary reason for nest failure of the Emei Shan Liocichla,(2) tree cover, bamboo cover, liana abundance and distance to forest edge or gap were the most important variables affecting nest-site selection of this species, and(3) the nest-site-selection variables we measured appeared not to be positively associated with nest success.Conclusions: Our findings suggest that the Emei Shan Liocichla tended to select nest sites near forest edges or gaps with good concealment and that nest-site selection by this species was nonrandom but not necessarily adaptive. Reducing forest-edge development and protecting bamboo stands should be effective for conservation of this species.

A QTL associated with leaf trichome traits has a major influence on the abundance of the predatory mite Typhlodromus pyri in a hybrid grapevine population

The abundance of predatory phytoseiid mites,Typhlodromus pyri,important biological control agents of spider mite pests in numerous crops,is positively influenced by the density of leaf trichomes and tuft-form domatia in vein axils.Identification of the genetic regions controlling both trophic levels could facilitate the improvement of predatory mite habitat in breeding programs.The abundance of T.pyri and non-glandular trichomes was measured in a segregating F1 family derived from the cross of the complex Vitis hybrid,‘Horizon’,with Illinois 547-1(V.rupestris B38×V.cinerea B9),finding positive correlation among traits.High density genetic maps were used to localize one major quantitative trait locus(QTL)on chromosome 1 of Illinois 547-1 associated with both predatory mite abundance and leaf trichomes.This QTL explained 23%of the variation in phytoseiid abundance and similar amounts of variance in domatia rating(21%),domatia size(16%),leaf bristle density(37%in veins and 33%in blades),and leaf hair density(20%in veins and 15%in blades).Another nine QTL distributed among chromosomes 1,2,5,8,and 15 were associated solely with trichome density,and explained 7–17%of the phenotypic variation.Combined,our results provide evidence of the genetic architecture of non-glandular trichomes in Vitis,with a major locus influencing trichome densities,domatia size and predatory mite abundance.This information is relevant for breeding grapevines with a more favorable habitat for biological control agents.

一类含扩散与时滞的Prey-Predator模型的周期解

利用上下解方法以及比较原理研究了一类含扩散与时滞的Prey-Predator模型,证明在一定条件下该模型的零平衡态及半平凡周期解的全局稳定性,并获得了这个系统具有一对周期拟解的充分条件.对任意的非负初值函数,这一对周期拟解构成的区间是此系统的一个吸引子.

Generalization of predator recognition:Velvet geckos display anti-predator behaviours in response to chemicals from non-dangerous elapid snakes

Many prey species detect chemical cues from predators and modify their behaviours in ways that reduce their risk ofpredation. Theory predicts that prey should modify their anti-predator responses according to the degree of threat posed by thepredator. That is, prey should show the strongest responses to chemicals of highly dangerous prey, but should ignore or respondweakly to chemicals from non-dangerous predators. However, if anti-predator behaviours are not costly, and predators are rarelyencountered, prey may exhibit generalised antipredator behaviours to dangerous and non-dangerous predators. In Australia, mostelapid snakes eat lizards, and are therefore potentially dangerous to lizard prey. Recently, we found that the nocturnal velvetgecko Oedura lesueurii responds to chemicals from dangerous and non-dangerous elapid snakes, suggesting that it displays generalisedanti-predator behaviours to chemicals from elapid snakes. To explore the generality of this result, we videotaped the behaviourof velvet geckos in the presence of chemical cues from two small elapid snakes that rarely consume geckos: the nocturnalgolden-crowned snake Cacophis squamulosus and the diurnal marsh snake Hemiaspis signata. We also videotaped geckos in trialsinvolving unscented cards (controls) and cologne-scented cards (pungency controls). In trials involving Cacophis and Hemiaspischemicals, 50% and 63% of geckos spent long time periods (> 3 min) freezing whilst pressed flat against the substrate, respectively.Over half the geckos tested exhibited anti-predator behaviours (tail waving, tail vibration, running) in response to Cacophis(67%) or Hemiaspis (63%) chemicals. These behaviours were not observed in control or pungency control trials. Our resultssupport the idea that the velvet gecko displays generalised anti-predator responses to chemical cues from elapid snakes.Generalised responses to predator chemicals may be common in prey species that co-occur with multiple, ecologically similar,dangerous predators [Current Zoology 56 (3): 337-342, 2010].