Predator System Research Articles

Dynamics of an infected prey–generalist predator system with the effects of fear, refuge and harvesting: deterministic and stochastic approach

Dynamics of an infected prey–generalist predator system with the effects of fear, refuge and harvesting: deterministic and stochastic approach

Study of two species prey–predator model in imprecise environment with harvesting scenario

This study proposes and explores a prey–predator model that presents a functional response to group behavior of prey–predator harvesting. We study a non-linear model of prey–predator growths in two species. The proposed model is supported by theoretical and numerical results. Some numerical descriptions are provided to help our analytical and theoretical conclusions. For all possible parameter values occurring in a prey–predator system, we solved it by using both VIM (variational iteration method) and HPM (homotopy perturbation method). We also used MATLAB coding to compare our approximate analytical expressions with numerical simulations. We have found that there is no significant difference when comparing analytical and numerical results.

Influence of fear effect on a Holling type III prey-predator system with the prey refuge

<abstract><p>The aim of the paper is to study the impact of anti-predator behavior caused by dread of predator species in a prey predator system with Holling III type functional response and prey shelters. Firstly, we analyze the dynamic behavior of the system, including the stability of the system and demonstrating the occurrence of Hopf bifurcation around the positive equilibrium point and the existence of limit cycle emerging through Hopf bifurcation. Secondly, through the study of the effect of fear and refuge, we discover that the increase of fear level can improve the stability of the system by eliminating periodic solutions and decrease the populations of predator species at the coexist equilibrium, but not cause the extinction of the predators, and prey refuge also plays very vital role in the persistence of the predators. Finally, the rationality of the results is verified by numerical simulation.</p></abstract>

SUFFICIENT AND NECESSARY CONDITIONS FOR PERSISTENCE AND EXTINCTION OF A STOCHASTIC TWO-PREY ONE-PREDATOR SYSTEM

This paper applies a new approach for stochastic Kolmogorov systems generalized by Hening and Nguyen to describe the dynamics of a stochastic two independent prey one predator system perturbed by white noise. Through calculating Lyapunov exponents, we thoroughly address the stability of the ergodic invariant probability measures. Sufficient and necessary conditions under which the species persist as well as conditions under which some species go extinct are established for this three dimensional models. One of the key points is that the critical cases for Lyapunov exponents being zero are considered. Finally, some numerical simulations illustrate the analytical results.

The effect of fear on the dynamics of two competing prey-one predator system involving intra-specific competition

A three-species food web model consisting of two competing prey – one predator with fear is created mathematically in the current work. Intra-specific competition within the predator's population, as well as a modified Holling type II functional response, are used. The study's goal is to look at the role of fear and intra-specific competition. Following a discussion of the solution's existence and uniqueness, other dynamical features of the solution, such as stability, persistence, and local bifurcation, were studied. Ultimately, the system is studied numerically with Matlab to fully understand global dynamics and the impact of altering parameter values. Different dynamical behaviors are discovered, such as stable point, stable line, and bi-stability.

Growth Parameters of Sentani Gudgeon Fish (Oxyeleotris heterodon) in Sentani Lake, Papua

ABSTRACTThe Sentani Gudgeon Fish (Oxyeleotris heterodon, Weber 1907) from the family Butidae with the general name Sentani Gudgeon is known locally as Gabus Malas and Himen. Sentani Snakehead Fish is one source of animal protein that is very important for the community around Lake Sentani. The population of the Sentani Gudgeon Fish species is at a crucial level. The issue could be affected by environmental pressures, continuous catches, competition with introduced species from outside Papua, intensive predation systems, and imbalances in ecological systems. The condition made a decline in population size until it became extinct. Gudgeon Sentani fish is the main target of catching in the lake. This condition significantly affects stock, size when first captured, population decline, reproductive cycle, and average catch. Until now, data and information on the growth of snakehead fish as the basis for fisheries management in the waters of Lake Sentani are not widely known. Considering the importance of preserving the native species of Lake Sentani, especially the Snakehead Fish, efforts to manage the fisheries in Lake Sentani's waters are urgent. This research was conducted in March - October 2020, located at Lake Sentani. The specimens were obtained from the catch of fishers with various gill nets and chopsticks. Enumerators or field assistants assisted the recording of the number and measurement of the total length of fish caught by fishermen daily. The results of the analysis showed: asymptotic size (L?) 46.20 cm, growth coefficient (K) 0.29, the total mortality rate (Z) 0.80 per year, natural mortality (M) 0.74 per year, the mortality rate due to fishing (F) 0.06 per year and exploitation rate (E) 0.075 per year.

Coexistence states of a Lotka Volterra cooperative system with cross diffusion

In this work we study the steady state cross diffusive Lotka Volterra cooperative system. We have incorporated different type of cross diffusive term at each trophic level. Using bifurcation theory, we derive sufficient conditions which ensures existence of positive solutions of the system. The analysis carried out allows us to give an affirmative answer to the question that whether cooperative species under the influence of cross diffusion can co exist or not. We have also compared the results obtained for the competitive Lotka Volterra system with our results and an ecological explanation is provided to understand the difference. • To study a cooperative Lotka Volterra prey predator system with different type of cross diffusion at each trophic level. • To show using bifurcation theory that these positive solution branches tend to have an extension that is globally defined. • To find out through the analysis carried out whether a cross diffusive cooperative system admits coexistence states. • Comparison of the results with the corresponding predator prey system.

Coexistence in a four-species food web model with general functional responses

The dynamics of an intraguild predation system is analyzed. Two shared resources, a middle predator and a top predator are considered in the model. Parameter conditions for coexistence in the intraguild system are given. The coexistence of species, through the existence of an equilibrium point or a stable limit cycle or an invariant torus is shown. Conditions to have Andronov-Hopf and Hopf-Hopf bifurcation are given. Then, limit sets and complex dynamical behaviors, can exhibit in the system. For a wide family of functional responses, these results are valid. Numerical simulations with varied functional responses are given and different limit sets are shown.

Prey–predator interactions and body size relationships between annual cicadas and spiders in Japan

ABSTRACT Cicada (Hemiptera) emergence is a major resource pulse that produces diverse effects on terrestrial food webs. Most studies have focused on periodical cicadas; however, little is known regarding the prey–predator interactions and size relationships between annual cicadas and predators, with knowledge being exclusively limited to the cicada–bird systems. Here, we focused on the interactions between annual cicadas and spiders in Japan. Based on direct observations and posts on social networking services and blogs on the Internet, we aimed to (1) reveal the major spider taxa as the predators of annual cicadas, (2) identify the major cicada taxa as the prey of spiders, and (3) characterise the prey–predator body size relationships between annual cicadas and spiders. Large orb-web spiders of the family Araneidae were identified as the major predators of annual cicadas. Spiders preyed on diverse cicada species, and prey species composition varied among the predator species. Regarding body size ratio, spiders tended to prey on cicadas larger than themselves (prey–predator body size ratio >1). We suggest that orb-weavers may function as one of the key predators of annual cicadas. Annual and periodical cicadas may be preyed upon by predators that use different foraging modes (web-builders or cursorial hunters). Further examination of these prey–predator interactions will contribute to the understanding of the cicada–predator systems.

Reactivity and recovery in an exploited one prey two predators system at equilibrium

Reactivity and recovery in an exploited one prey two predators system at equilibrium

Influence of the Fear Effect on a Holling Type II Prey–Predator System with a Michaelis–Menten Type Harvesting

In this work, a prey–predator system with Holling type II response function including a Michaelis–Menten type capture and fear effect is put forward to be studied. Firstly, the existence and stability of equilibria of the system are discussed. Then, by considering the harvesting coefficient as bifurcation parameter, the occurrence of Hopf bifurcation at the positive equilibrium point and the existence of limit cycle emerging through Hopf bifurcation are proved. Furthermore, through the analysis of fear effect and capture item, we find that: (i) the fear effect can either stabilize the system by excluding periodic solutions or destroy the stability of the system and produce periodic oscillation behavior; (ii) increasing the level of fear can reduce the final number of predators, but not lead to extinction; (iii) the harvesting coefficient also has significant influence on the persistence of the predator. Finally, numerical simulations are presented to illustrate the results.

Biological control of infection pervasive via pest: a study of prey–predator model incorporating prey refuge under fuzzy impreciseness

ABSTRACT The prey–predator systems exist in almost all ecological systems and the refuge stage is highly concerned with such ecological systems in which the prey goes out of reach of the attacking region of the predator. In this paper, dynamical behaviour of predator and prey species with Holling type III response function is investigated. We add refuge in prey species and also additional predators are introduced into the system. Firstly, the crisp model is formulated with these effects and the boundedness, existence, conditions of local and global stability, local bifurcation and Hopf bifurcation are discussed. The crisp model is transformed into the fuzzy model to incorporate the unpredictable behaviour and using the Root Mean Square (RMS) defuzzification method, the fuzzy model is reduced to the defuzzified model in order to avoid the complexity of the analysis of the solution. Further, numerical simulations are performed with the help of MATLAB, MATCONT package and we examine solution curves and phase portraits in two different cases, in the presence and in the absence of additional predators along with the Hopf bifurcation scenarios. Finally, the sensitivities of the controlling parameters are plotted graphically and presented their significances in controlling the infection of the prey.

Complex spatiotemporal dynamics of a harvested prey–predator model with Crowley–Martin response function

The formation of spatiotemporal patterns is one of the most important part in the prey–predator dynamical system. In this paper, we investigate the local dynamics as well as the Turing structure through diffusion-driven instability by taking more general Crowley–Martin response function in the prey–predator system with the effect of linear harvesting of prey and predator. All the feasible equilibrium points are extracted. Boundedness, persistence, local and global stability, and Hopf bifurcation are established for some suitable parametric conditions. The parametric space for which the Turing spatial structure takes place is found out. Different kinds of patterns are demonstrated depending on the ecological parameters of the local system and diffusion coefficients.

Oscillations and Pattern Formation in a Slow-Fast Prey-Predator System.

We consider the properties of a slow-fast prey-predator system in time and space. We first argue that the simplicity of the prey-predator system is apparent rather than real and there are still many of its hidden properties that have been poorly studied or overlooked altogether. We further focus on the case where, in the slow-fast system, the prey growth is affected by a weak Allee effect. We first consider this system in the non-spatial case and make its comprehensive study using a variety of mathematical techniques. In particular, we show that the interplay between the Allee effect and the existence of multiple timescales may lead to a regime shift where small-amplitude oscillations in the population abundances abruptly change to large-amplitude oscillations. We then consider the spatially explicit slow-fast prey-predator system and reveal the effect of different timescales on the pattern formation. We show that a decrease in the timescale ratio may lead to another regime shift where the spatiotemporal pattern becomes spatially correlated, leading to large-amplitude oscillations in spatially average population densities and potential species extinction.

Studies of different types of bifurcations analyses of an imprecise two species food chain model with fear effect and non-linear harvesting

Study of a food chain model under uncertainty is quite difficult. Because, in an uncertain food chain model, the biological parameters can’t be determined accurately. The aim of this work is to study the stability and local bifurcations (Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation) of an imprecise prey–predator system in an uncertain environment. The proposed imprecise model is formulated by considering two more realistic factors: the effect of a fear factor on the growth rate of prey population and non-linear harvesting of predator population. To study the proposed imprecise system mathematically, the dynamical interactions between the imprecise species are presented by the system of governing interval differential equations. And to study the dynamics of the proposed imprecise system theoretically, it is modelled in a precise way by the linear parametric representation of the interval. Then all the theoretical analyses, including Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens (BT) bifurcation of the interior equilibrium point of the proposed imprecise model are discussed in parametric form. To verify all the theoretical analyses of the proposed imprecise model, numerical simulations with interval-valued hypothetical data of the imprecise parameters are performed graphically. Finally, the work is concluded with some biological consequences.

Bifurcation analysis and chaos control of discrete prey–predator model incorporating novel prey–refuge concept

This article investigates a prey–predator model incorporating a novel refuge proportional to prey and inverse proportion to the predator. We find conditions for the local asymptotic stability of fixed points of the proposed prey–predator model. This article presents Neimark–Sacker bifurcation (NSB) and period-doubling bifurcation (PDB) at particular parameter values for positive equilibrium points of the proposed refuge-based prey–predator system. The system exhibits the chaotic dynamics at increasing values of the bifurcation parameter. The hybrid control methodology will control the chaos of the proposed prey–predator dynamical system and discuss the chaotic situation for different biological parameters through graphical analysis. Numerical simulations support the theoretical outcome and long-term chaotic behavior over a broad range of parameters.

Uniformly historic behaviour in compact dynamical systems

In this paper, we study a dichotomy of higher-order repeated time averages of a compact dynamical system acting on an infinite dimensional Banach space. We also discuss one feature so-called uniformly historic behaviour of a compact dynamical system which causes the non-existence of time averages. In its own turn, this feature will eventually cause the non-existence of higher-order repeated time averages. The best example for a compact dynamical system having uniformly historic behaviour is a discrete-time Kolmogorov system of predator–prey interactions. As an application, we also provide some examples of three-species predator–prey interactions in which uniformly historic behaviour can be observed.

Impact of Fear Effect in a Two Prey-One Predator System with Switching Behaviour in Predation

Impact of Fear Effect in a Two Prey-One Predator System with Switching Behaviour in Predation

Role of Allee effect in prey and hunting cooperation in a generalist predator

Cooperation is a very common phenomenon in the predator population. It can also be considered as one kind of Allee effect. By cooperation, we mean that the consumption rate per predator is dependent on the density of the predator. Despite a few recent studies the study of such systems is rare in the literature. It is well known from previous studies that incorporation of Allee effect in prey population enables the models to address many complex dynamical features. On the other hand, the dynamics of a generalist predator in a prey–predator system is also a very important area of research on populations. In this work, we concentrate on a model where Allee effect is incorporated in the prey growth in the presence of hunting cooperation in a generalist predator to observe how the Allee effect and the hunting cooperation affect the dynamics. Here we mainly study the stability and bifurcation of the system and hence describe the global dynamics to see how the Allee effect in prey and hunting cooperation affect the system dynamics.

Diffusion driven finite time blow-up and pattern formation in a mutualistic preys-sexually reproductive predator system: A comparative study

Species have the general tendency to sustain their own survival chance in the ecology. In this paper, we design different diffusive model systems in which two prey populations make mutualistic relationship in which they are getting benefited from each other with their usual growth rate and sexually reproductive generalist predator preys upon the prey according to their functional responses. In the absence of generalist predator, there is no sign of mutualism between two prey. Sometimes environment may turn favourable for the invasive species, causing the growth of their population to outbreak. Biological control is an adopted strategy to limit harmful populations. To establish a control strategy that decreases the harmful population to healthy levels as opposed to high and risky levels, five different diffusive models have been introduced associated to their functional responses which are either prey dependent (Holling type-III and IV) or predator dependent (Beddington–DeAngelis, Crowley–Martin and and Hassel–Varley). The blow up phenomenon at finite time in spatial cases have been discussed for all the model systems. For each model system, mathematical conditions are established under which species can blow up at finite time. Spatio-temporal dynamics and weakly nonlinear analysis have been thoroughly studied. Stability analysis of these model systems have been investigated and concentrated on discussing the Turing patterns. Theoretical analysis of the patterns formations has been described by using amplitude equations and the results are validated by numerical simulations. Mathematical computations of the structural models have been studied and explored their blow up phenomena under the effects of diffusion with the pattern formation of preys and predator populations in the spatiotemporal domain.The best chance of survival of the species upon diffusion has been discussed elaborately.