Predator Model Research Articles

Cloud security game theory scoring from predation models in simulation

Cloud security game theory scoring from predation models in simulation

Multi-species prey–predator dynamics during a multi-strain pandemic

Small and large scale pandemics are a natural phenomenon repeatably appearing throughout history, causing ecological and biological shifts in ecosystems and a wide range of their habitats. These pandemics usually start with a single strain but shortly become multi-strain due to a mutation process of the pathogen causing the epidemic. In this study, we propose a novel eco-epidemiological model that captures multi-species prey–predator dynamics with a multi-strain pandemic. The proposed model extends and combines the Lotka–Volterra prey–predator model and the Susceptible–Infectious–Recovered epidemiological model. We investigate the ecosystem’s sensitivity and stability during such a multi-strain pandemic through extensive simulation relying on both synthetic cases as well as two real-world configurations. Our results are aligned with known ecological and epidemiological findings, thus supporting the adequacy of the proposed model in realistically capturing the complex eco-epidemiological properties of the multi-species multi-strain pandemic dynamics.

Fractional order prey–predator model incorporating immigration on prey: Complexity analysis and its control

In this paper, the Caputo fractional derivative is assumed to be the prey–predator model. In order to create Caputo fractional differential equations for the prey–predator model, a discretization process is first used. The fixed points of the model are categorized topologically. We identify requirements for the fixed points of the suggested prey–predator model’s local asymptotic stability. We demonstrate analytically that, under specific parametric conditions, a fractional order prey–predator model supports both a Neimark–Sacker (NS) bifurcation and a Flip bifurcation. We present evidence for NS and Flip bifurcations using central manifold and bifurcation theory. The parameter values and the initial conditions have been found to have a profound impact on the dynamical behavior of the fractional order prey–predator model. As the bifurcation parameter is increased, the system displays chaotic behavior. Numerical simulations are shown to demonstrate chaotic behaviors like bifurcations, phase portraits, invariant closed cycles, and attractive chaotic sets in addition to validating analytical conclusions. The suggested prey–predator dynamical system’s chaotic behavior will be controlled by the OGY and hybrid control methodology, which will also visualize the chaotic state for various biological parameters.

Co-Existing Point of Equilibrium in Discretization of Fractional-Order Prey and Predator Model

In this work, a discretization process of a fractional-order prey and predator model is discussed. The aim of this work is to describe the population phenomenon which contains prey and predator. In this research, the prey and predator model by Ghosh et al. (2017) is used. The model has an unique form because it contains prey refuge and additional food to predator. In order to give more details on prey and predator population, the model then modified into fractional order and then discretized. The discretization model has three points of equilibrium and one of them named co-existing point of equilibrium. The numerical simulation is used to perform the stability. The numerical simulation is controlled by using mathematical programming language. It resulted that the co-existing point of equilibrium tends to be stable or converge if a small value of (time step) is selected. Otherwise, if a larger value of is selected, then oscillatory is appeared which means the point of equilibrium become unstable or diverge.

Stability analysis of prey–predator model with two prey and one predator using fuzzy impulsive control

Stability analysis of prey–predator model with two prey and one predator using fuzzy impulsive control

Hopf bifurcation in a delayed prey–predator model with prey refuge involving fear effect

This work investigates a prey–predator model featuring a Holling-type II functional response, in which the fear effect of predation on the prey species, as well as prey refuge, are considered. Specifically, the model assumes that the growth rate of the prey population decreases as a result of the fear of predators. Moreover, the detection of the predator by the prey species is subject to a delay known as the fear response delay, which is incorporated into the model. The paper establishes the preliminary conditions for the solution of the delayed model, including positivity, boundedness and permanence. The paper discusses the existence and stability of equilibrium points in the model. In particular, the paper considers the discrete delay as a bifurcation parameter, demonstrating that the system undergoes Hopf bifurcation at a critical value of the delay parameter. The direction and stability of periodic solutions are determined using central manifold and normal form theory. Additionally, the global stability of the model is established at axial and positive equilibrium points. An extensive numerical simulation is presented to validate the analytical findings, including the continuation of the equilibrium branch for positive equilibrium points.

Discrete Bazykin’s Prey–Predator Model with Stability, Control and Bifurcation

In this paper, we have studied stability, bifurcation analysis and hybrid control in a discrete Bazykin’s model. Specifically, we have examined periodic points, local behavior at fixed points and potential bifurcation analysis of the discrete Bazykin’s model. It is proved that no flip bifurcation occurs at trivial fixed point but Bazykin’s model undergoes Neimark–Sacker bifurcation at interior fixed point. Moreover, hybrid control strategy is utilized in order to control the Neimark–Sacker bifurcation. Finally, extensive numerical simulations are provided to verify theoretical results.

Bang–Bang Control of a Prey–Predator Model with a Stable Food Stock and Hysteresis

Bang–Bang Control of a Prey–Predator Model with a Stable Food Stock and Hysteresis

Hand preference predicts behavioral responses to threats in Barbary macaques.

The structure and functioning of the brain are lateralized-the right hemisphere processes unexpected stimuli and controls spontaneous behavior, while the left deals with familiar stimuli and routine responses. Hemispheric dominance, the predisposition of an individual using one hemisphere over the other, may lead to behavioral differences; particularly, an individual may be programed to act in a certain way concerning hemispheric dominance. Hand preference is a robust estimator of hemispheric dominance in primates, as each hemisphere controls the opposing side of the body. Studies have found links between hand preference and the exhibition of behaviors in contexts such as exploring and manipulating objects. However, little is known whether hand preference predicts behavioral variations in other ecologically relevant contexts like predation. We investigated the relationship between hand preference and behavioral responses to two types of predator models in captive Barbary macaques (Macaca sylvanus) (n = 22). Besides, a nonpredator novel object was included as control. We found 91% of the macaques to be lateralized with no group-level bias. A higher rate of tension and focus (behavioral response) behavior was found in predator contexts than in the novel object condition. Unlike their right-hand counterparts, individuals with a strong left-hand preference elicited frequent focus and tension behavior toward the predator models. Additionally, the behavioral response varied with predator type. We also found an interaction effect between hand preference and predator type. Our study suggests that hand preference can reliably predict behavioral variations in the context of potential predation. While these results are consistent with lateralized brain function, indicating lateralization a neural mechanism of behavioral variation, the interaction effect between hand preference and predator type elucidates the importance of context-specificity when investigating laterality noninvasively. Future research on other nonhuman primates using the current framework may provide insights into the evolution of laterality and underlying behavioral predispositions.

A prey–predator model with three interacting species

We consider a class of discrete time prey–predator models with three interacting species defined on the two-dimensional simplex. For some choices of parameters of the operator describing the evolution of the relative frequencies, we show that the trajectories approach a heteroclinic cycle and that the ergodic hypothesis does not hold. Moreover, we prove that any order Cesàro mean of the trajectories diverges. For another class of parameters, we show that all orbits starting from the interior of the simplex converge to the unique fixed point of the operator while for the remaining choices of parameters all orbits converge to one of the vertices of the simplex. Contrary to many authors, we study discrete time models but we include a speed function f in the dynamics which allows us to approximate the continuous-time case arbitrarily well when f is small.

Hopf Bifurcation in a Modified Leslie-Gower Two Preys One Predator Model and Holling Type II Functional Response with Harvesting and Time-Delay

In this paper, a modified Leslie-Gower two preys one predator model and Holling type II functional response with harvesting and time-delay were discussed. Model analysis is carried out by determining fixed points, then analyzing the stability of the fixed points and discussing the existence of the Hopf bifurcation. In some conditions that occur in nature indicate the occurrence of hunting of prey and predator species by humans. Therefore, this model is modified by adding the assumption that prey and predators are being harvested. Another modification given to the model is the use of time delays.The delay time term is for taking into account the case that the members of the predator species need time from birth to predation for being active predators. The first case is a model without time delay, it is obtained that 3 fixed points are unstable and 7 fixed points are stable. One of them is the interior fixed point tested with the Routh-Hurwitz criteria. The second case is a model with a delay time, the critical delay value is obained. Hopf bifurcation occurs when the delay time value is equal to the critical delay value and also fulfills the transversality condition. Observations on the model simulation are carried out by varying the value of the delay time. When the Hopf bifurcation occurs, the graph on the solution plane shows a constant oscillatory movement. If the value of the delay time given is less than the critical value of the delay, the controlled system solution goes to a balanced state. Then when the delay time value is greater than the critical delay value, the system solution continues to fluctuate causing an unstable system condition.

Trade-off and chaotic dynamics of prey–predator system with two discrete delays

In our ecological system, prey species can defend themselves by casting strong and effective defenses against predators, which can slow down the growth rate of prey. Predator has more at stake when pursuing a deadly prey than just the chance of missing the meal. Prey have to "trade off" between reproduction rate and safety and whereas, predator have to "trade off" between food and safety. In this article, we investigate the trade-off dynamics of both predator and prey when the predator attacks a dangerous prey. We propose a two-dimensional prey and predator model considering the logistic growth rate of prey and Holling type-2 functional response to reflect predator's successful attacks. We examine the cost of fear to reflect the trade-off dynamics of prey, and we modify the predator's mortality rate by introducing a new function that reflects the potential loss of predator as a result of an encounter with dangerous prey. We demonstrated that our model displays bi-stability and undergoes transcritical bifurcation, saddle node bifurcation, Hopf bifurcation, and Bogdanov-Taken bifurcations. To explore the intriguing trade-off dynamics of both prey and predator population, we investigate the effects of our critical parameters on both population and observed that either each population vanishes simultaneously or the predator vanishes depending on the value of the handling time of the predator. We determined the handling time threshold upon which dynamics shift, demonstrating the illustration of how predators risk their own health from hazardous prey for food. We have conducted a sensitivity analysis with regard to each parameter. We further enhanced our model by including fear response delay and gestation delay. Our delay differential equation system is chaotic in terms of fear response delay, which is evidenced by the positivity of maximum Lyapunov exponent. We have used numerical analysis to verify our theoretical conclusions, which include the influence of vital parameters on our model through bifurcation analysis. In addition, we used numerical simulations to showcase the bistability between co-existence equilibrium and prey only equilibrium with their basins of attraction. The results that are reported in this article might be useful in interpreting the biological insights gained from studying the interactions between prey and predator.

Optimization of a Prey–Predator Model with Hysteresis and Convection

Optimization of a Prey–Predator Model with Hysteresis and Convection

A fuzzy function granular [formula omitted]-transform and inverse [formula omitted]-transform with application

This study introduces the concept of granular F-transform and investigates its basic properties using the theory of fuzzy numbers and horizontal membership functions. We further present a numerical method based on granular F-transform to solve a fuzzy prey–predator model consisting of two prey and one predator due to its natural variability and investigate the existence of the equilibrium points and their stability.

Influence of Spatial Dispersal among Species in a Prey–Predator Model with Miniature Predator Groups

Dispersal among species is an important factor that can govern the prey–predator model’s dynamics and cause a variety of spatial structures on a geographical scale. These structures form when passive diffusion interacts with the reaction part of the reaction–diffusion system in such a way that even if the reaction lacks symmetry-breaking capabilities, diffusion can destabilize the symmetry and allow the system to have them. In this article, we look at how dispersal affects the prey–predator model with a Hassell–Varley-type functional response when predators do not form tight groups. By considering linear stability, the temporal stability of the model and the conditions for Hopf bifurcation at feasible equilibrium are derived. We explored spatial stability in the presence of diffusion and developed the criterion for diffusion-driven instability. Using amplitude equations, we then investigated the selection of Turing patterns around the Turing bifurcation threshold. The examination of the stability of these amplitude equations led to the discovery of numerous Turing patterns. Finally, numerical simulations were performed to validate the outcomes of the analysis. The outcomes of the theoretical study and numerical simulation were accorded. Our findings demonstrate that spatial patterns are sensitive to dispersal and predator death rates.

Positive solutions to the prey–predator equations with dormancy of predators

AbstractThe time-global unique classical positive solutions to the reaction–diffusion equations for prey–predator models with dormancy of predators are constructed. The feature appears on the nonlinear terms of Holling type $\rm I\!I$ functional response. The crucial step is to establish time-local positive classical solutions by using a new approximation associated with time-evolution operators. Although the system does not equip usual comparison principle for solutions to partial differential equation, a priori bounds are derived by enclosing and renormalising arguments of solutions to the corresponding ordinary differential equations. Furthermore, time-global existence, invariant regions and asymptotic behaviours of solutions follow from such a priori bounds.

Concurrent dilution and amplification effects in an intraguild predation eco-epidemiological model

The dilution and amplification effects are important concepts in the field of zoonotic diseases. While the dilution effect predicts that pathogen prevalence is negatively correlated with increased species diversity, the opposite trend is observed when the amplification effect occurs. Understanding how interspecific interactions such as predation and competition within a community influence disease transmission is highly relevant. We explore the conditions under which the dilution and amplification effects arise, using compartmental models that integrate ecological and epidemiological interactions. We formulate an intraguild predation model where each species is divided into two compartments: susceptible and infected individuals. We obtained that increasing predation increases the disease transmission potential of the predator and the density of infected individuals, but decreases the disease transmission potential of the prey, as well as their density. Also, we found that interspecific competition always helps to decrease the number of infected individuals in the population of the two species. Therefore, dilution and amplification effects can be observed simultaneously but depending on different types of cological interactions.

Study of co-dimension two bifurcation of a prey–predator model with prey refuge and non-linear harvesting on both species

Study of co-dimension two bifurcation of a prey–predator model with prey refuge and non-linear harvesting on both species

Spatio-temporal pattern selection in a prey–predator model with hunting cooperation and Allee effect in prey

In this work, we have studied the temporal as well as spatio-temporal dynamics of a prey–predator model with additive Allee effect in prey growth and hunting cooperation among the specialist predators. Hunting cooperation impacts both the stability and the existence scenario of the coexistence equilibrium of the temporal model. The temporal system is capable of exhibiting a wide range of local bifurcations such as transcritical, saddle–node, Hopf, Bogdanov–Takens bifurcations and a global Homoclinic bifurcation. For the diffusive system, the well-posedness is first proved. Then Turing instability is investigated to understand the relationship between the diffusion and the hunting cooperation behind the stationary pattern formation. By employing weakly nonlinear analysis, the amplitude equation of stationary solution is derived, and using the stability of amplitude equation, the pattern selection of several stationary patterns such as spot, stripe, and their combinations have been discussed under various parameter regimes. Extensive numerical simulations are carried out to verify the analytical results. Main contribution of this work is the identification of all possible stationary patterns depending upon the signs of the coefficients involved in the amplitude equation. In addition, some time-dependent nonhomogeneous irregular solutions are observed for parameter values in the Hopf domain or Turing–Hopf domain. With the help of time-series analysis of the obtained numerical results, we have established that the time and space-varying solution is spatio-temporal chaos.

Dynamics of a delay-induced prey–predator system with interaction between immature prey and predators

In biological pest control systems, several pests (including insects, mites, weeds, etc.) are controlled by biocontrol agents that rely primarily on predation. Following this biocontrol management ecology, we have created a three-tier prey–predator model with prey phase structure and predator gestation delay. Several studies have demonstrated that predators with Holling type-II functional responses sometimes consume immature prey. A study of the well-posedness and local bifurcation (such as saddle-node and transcritical) near the trivial and planer equilibrium points is carried out. Without any time lag, the prey development coefficient has a stabilizing impact, while increasing attack rate accelerates instability. Energy transformation rate and handling time are shown to cause multiple stability switches in the system. Numerical results demonstrate time delay is the key destabilizer that destroys stability. Our model can replicate more realistic events by including time-dependent factors and exploring the dynamic behavior of nonautonomous systems. In the presence of time delay, sufficient conditions of permanence and global attractivity of the nonautonomous system are derived. Finally, MATLAB simulations are performed to validate the analytical findings.