稀疏效应捕食—被捕食系统的持久性和周期轨道

考虑一类稀疏效应非自治 Volterra捕食—被捕食系统 .证明了该系统在某些条件下是持久的 ,而且 ,若该系统是周期系统 ,在某些条件下 ,它们存在唯一的严格正周期轨道 ,且是全局渐近稳定的 .

Spatiotemporal distribution of protozooplankton and copepod nauplii in relation to the occurrence of giant jellyfish in the Yellow Sea

The occurrence of the giant jellyfish, Nemopilema nomurai, has been a frequent phenomenon in the Yellow Sea. However, the relationship between the giant jellyfish and protozoa, in particular ciliates, remains largely unknown. We investigated the distribution of nanoflagellates, ciliates, Noctiluca scintillans, and copepod nauplii along the transect 33~N in the Yellow Sea in June and August, 2012, during an occurrence of the giant jellyfish, and in October of that year when the jellyfish was absent. The organisms studied were mainly concentrated in the surface waters in summer, while in autumn they were evenly distributed in the water column. Nanoflagellate, ciliate, and copepod nauplii biomasses increased from early June to August along with jellyfish growth, the first two decreased in October, while N. scintillans biomass peaked in early June to 3 571 pg C/L and decreased in August and October. In summer, ciliate biomass greatly exceeded that of copepod nauplii （4.61-15.04 ~tg C/L vs. 0.34-0.89 pg C/L）. Ciliate production was even more important than biomass, ranging from 6.59 to 34.19 ~tg C/（L.d） in summer. Our data suggest a tight and positive association among the nano-, micro-, and meso-zooplankton in the study area. Statistical analysis revealed that the abundance and total production of ciliate as well as loricate ciliate biomass were positively correlated with giant jellyfish biomass, indicating a possible predator-prey relationship between ciliates and giant jellyfish. This is in contrast to a previous study, which reported a significant reduction in ciliate standing crops due to the mass occurrence ofN. nomurai in summer. Our study indicates that, with its high biomass and, in particular, high production ciliates might support the mass occurrence of giant jellyfish.

EFFECT OF KAIROMONE ON PREDATOR-PREY DYNAMICS -- A DELAY MODEL

In most of the predator-prey systems, prey individuals make transitions between vulnerable and invulnerable states or locations. This transition is regulated by various inducible defense mechanisms. Diel vertical migration （DVM） in zooplankton is the most effective and instantaneous defense observed in zooplankton population. Zooplankton shows downward vertical migration in the daytime in the presence of predators （or predator kairomones） to avoid predation （i.e. refuge use）, and it enters into the surface water again at night to graze phytoplankton. The dynamics of the planktonic ecosystem under DVM of zooplankton along with fish kairomone and the multiple delays due to migration for vulnerable and invulnerable prey and reproduction in the predator population is of considerable interest both in theoretical and experimental ecologists. By developing mathematical model, we analyze such a system. The conditions for which the system enters into Hopf-bifurcation are obtained. Moreover, the conditions for which the bifurcating branches are supercritical are also derived. Our results indicate that DVM along with the effect of kairomone and multiple delays with a certain range are responsible to enhance the stability of the system around the positive interior equilibrium point.

Discriminative predation： Simultaneous and sequential encounter experiments

There are many situations in which the ability of animals to distinguish between two similar looking objects can have significant selective consequences. For example, the objects that require discrimination may be edible versus defended prey, predators versus non-predators, or mates of varying quality. Working from the premise that there are situations in which discrimi- nation may be more or less successful, we hypothesized that individuals find it more difficult to distinguish between stimuli when they encounter them sequentially rather than simultaneously. Our study has wide biological and psychological implications from the perspective of signal perception, signal evolution, and discrimination, and could apply to any system where individuals are making relative judgments or choices between two or more stimuli or signals. While this is a general principle that might seem intuitive, it has not been experimentally tested in this context, and is often not considered in the design of models or experiments, or in the interpretation of a wide range of studies. Our study is different from previous studies in psychology in that a） the level of similarity of stimuli are gradually varied to obtain selection gradients, and b） we discuss the implications of our study for specific areas in ecology, such as the level of perfection of mimicry in predator-prey systems. Our experiments provide evidence that it is indeed more difficult to distinguish between stimuli - and to learn to distinguish between stimuli - when they are encountered sequentially rather than simultaneously, even if the intervening time interval is short .

Optimal harvesting of a prey-predator model with variable carrying capacity

This work deals with a prey-predator model in an environment where the carrying capacities are assumed to be variable with time and one species feeds upon the other. Independent harvesting efforts are applied in either species and asymmetrical intraguild predation occurs. A common resource is consumed by two competing species and at the same time predator also consumes the prey. At first we discuss the model under constant carrying capacity and make the conclusion that no limit cycle exists in this case. Then we discuss the model without intraspecific competition. Our main concern is to cover the above mentioned two cases together, i.e. the model with variable carrying capacity and intraspecific competition. We determine the steady states and examine the dynamical behavior. We also analyze the local and global stability of the interior equilibrium by Routh-Hurwitz criterion and a suitable Lyapunov function respectively. A Hopf bifur- cation occurs with respect to a parameter which is the ratio of predator＇s and prey＇s intrinsic growth rate. The possibility of bionomic equilibrium has been considered. The optimal harvest policy is formulated and solved with Pontryagin＇s maximum principle. Some numerical simulations are given to explain most of the analytical results.

Bifurcation and spatiotemporal patterns of a density-dependent predator-prey model with Crowley-Martin functional response

In this paper, we consider a diffusive density-dependent predator-prey model with Crowley-Martin functional responses subject to Neumann boundary condition. We ana- lyze the stability of the positive equilibrium and the existence of spatially homogeneous and inhomogeneous periodic solutions through the distribution of the eigenvalues. The direction and stability of Hopf bifurcation are determined by the normal form theory and the center manifold theory. Finally, numerical simulations are given to verify our theoretical analysis.

GLOBAL ASYMPTOTIC STABILITY FOR A TWO-SPECIES DISCRETE RATIO-DEPENDENT PREDATOR-PREY SYSTEM

The dynamical behaviors of a two-species discrete ratio-dependent predator-prey sys- tem are considered. Some sufficient conditions for the local stability of the equilibria is obtained by using the linearization method. Further, we also obtain a new sufficient condition to ensure that the positive equilibrium is globally asymptotically stable by using an iteration scheme and the comparison principle of difference equations, which generalizes what paper [G. Chen, Z. Teng and Z. Hu, Analysis of stability for a discrete ratio-dependent predator-prey system, Indian J. Pure Appl. Math. 42（1） （2011） 1-26] has done. The method given in this paper is new and very resultful comparing with papers [H. F. Huo and W. T. Li, Existence and global stability of periodic solutions of a discrete predator--prey system with delays, Appl. Math. Comput. 153 （2004） 337-351; X. Liao, S. Zhou and Y. Chen, On permanence and global stability in a general Gilpin- Ayala competition predator prey discrete system, Appl. Math. Comput. 190 （2007） 500-509] and it can also be applied to study the global asymptotic stability for general multiple species discrete population systems. At the end of this paper, we present an open question.

NONCONSTANT PREY HARVESTING IN RATIO-DEPENDENT PREDATOR-PREY SYSTEM INCORPORATING A CONSTANT PREY REFUGE

This paper deals with the problem of nonconstant harvesting of prey in a ratio-dependent predator-prey system incorporating a constant prey refuge. Here we use the reasonable catch-rate function instead of usual catch-per-unit-effort hypothesis. The existence, as well as the stability of possible equilibria, is carried out. Bionomic equilibrium of the system is determined and optimal harvest policy is studied with the help of Pontryagin＇s maximum principle. The key results developed in this paper are illustrated using numer- ical simulations. Our results indicate that dynamic behavior of the system very much depends on the prey refuge parameter and increasing amount of refuge could increase prey density and may lead to the extinction of predator population density.

Stochastic rules for predator and prey hunting and escape behavior in a lattice-based model

Understanding of ecosystem resilience and stability requires comprehending predator- prey dynamics because ecosystems consist of dynamically interacting subsystems that include predator-prey relationships. This relationship is closely related to the hunting- escaping strategies employed by the predator and prey. Therefore, understanding the effects of hunting and escaping strategies on ecosystems will lead to a better under- standing of these systems. As an approach for describing the predator-prey interaction, lattice-based models have been adopted because this approach has strong advantages for simulating various dynamical processes of individual-individual interaction. In the models, each lattice cell is either considered as an attractive/repulsive cell, or an indi- vidual cell, or else it is empty. The attractive （or repulsive cell） can be interpreted as the prey （or predator） of the individual. These states allow us to incorporate the ecological processes of local antagonistic interactions, namely the spread of disturbances （by the predator） and regrowth or recovery （by the prey）. These processes are directly related to the strategic behavior of individuals, such as hunting and escaping. In this study, we suggest a simple and effective mapping formula as a stochastic rule to describe the hunt- ing and escaping behavior. This formula could be widely used not only in the behavior but also in competitive and cooperative relationships.

Effects of historically familiar and novel predator odors on the physiology of an introduced prey

Predator odors can elicit fear responses in prey and predator odor recognition is generally associated with physiological responses. Prey species are often more likely to respond to the odor of familiar ra- ther than alien predators. However, predator na＇ivety in an introduced prey species has rarely been investigated. We examined the physiological response, as shown by changes in ventilatory vari- ables, of an introduced terrestrial herbivore, the European rabbit Oryctolagus cuniculus, in Australia, to the odor of potential predators and to control odors （distilled water and horse）, to explore if res- ponses were limited to historical （cat and fox） predators, or extended to historically novel predators （snake and quoll）. All odors except distilled water elicited a response, with rabbits showing long- term higher respiratory frequencies and lower tidal volumes after introduction of the odors, indi- cating an increase in alertness. However, the intensity of the rabbits＇ reaction could not be directly linked to any pattern of response with respect to the history of predator-prey relationships. Rabbits exhibited significantly stronger reactions in response to both cat and quoll odors than they did to dis- tilled water, but responses to horse, fox, and snake odor were similar to that of water. Our results show that the introduced rabbit can respond to both historical and novel predators in Australia, and suggest that shared evolutionary history is not necessarily a prerequisite to predator odor recognition.

Traveling wave solutions for a diffusive predator-prey model with predator saturation and competition

The purpose of this paper is to study the traveling wave solutions of a diffusive predator- prey model with predator saturation and competition functional response. The system admits three equilibria： a zero equilibrium E0, a boundary equilibrium E1 and a posi- tive equilibrium E. under some conditions. We establish the existence of two types of traveling wave solutions which connect E0 and E. and E1 and E., respectively. Our main arguments are based on a simplified shooting method, a sandwich method and constructions of appropriate Lyapunov functions. Our particular interest is to investi- gate the oscillation of both types of traveling wave solutions when they approach the positive equilibrium.

Harvest control for a delayed stage-structured diffusive predator-prey model

In this paper, we have considered a delayed stage-structured diffusive prey-predator model, in which predator is assumed to undergo exploitation. By using the theory of partial functional differential equations, the local stability of an interior equilibrium is established and the existence of Hopf bifurcations at the interior equilibrium is also discussed. By applying the normal form and the center manifold theory, an explicit algorithm to determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is derived. Finally, the complex dynamics are obtained and numerical simulations substantiate the analytical results.

Parameter uncertainty in biomathematical model described by one-prey two-predator system with mutualism

In this paper, a three-species system consisting of two predators which are in mutual- ism with each other and preying on the same single prey is considered. Also, the prey and first predator are harvested under optimal conditions. The values of the biological parameters depend on the collection of data from the experts as well as on the nature of the environment in which prey predator system are considered. So the biological para- meters are not precise in reality. This paper presents a different approach to study the prey-predator model with imprecise biological parameters. All the possible equilibrium points are identified and the local as well as global stability criteria under imprecise- ness are discussed. The possibility of existence of bionomic equilibrium is discussed. The optimal harvesting policy is studied using Pontryagin＇s maximum principle. Numerical examples are provided to support the proposed approach.

THE EFFECTS OF HARVESTING AND TIME DELAY ON PREDATOR-PREY SYSTEMS WITH BEDDINGTON-DEANGELIS FUNCTIONAL RESPONSE

The combined effects of harvesting and time delay on predator-prey systems with Beddington-DeAngelis functional response are studied. The region of stability in model with harvesting of the predator, local stability of equilibria and the existence of Hopf bifurcation are obtained by analyzing the associated characteristic equation due to the two-parameter geometric criteria developed by Ma, Feng and Lu [Discrete Contin. Dyn. Syst. Set B 9 （2008） 397-413]. The global stability of the positive equilibrium is inves- tigated by the comparison theorem. Furthermore, local stability of steady states and the existence of Hopf bifurcation for prey harvesting are also considered. Numerical simulations are given to illustrate our theoretical findings.