Role of fear in a predator-prey system with ratio-dependent functional response in deterministic and stochastic environment

Roy, Jyotirmoy; Barman, Dipesh; Alam, Shariful

doi:10.1016/j.biosystems.2020.104176

Cited by 55 publications

(21 citation statements)

References 64 publications

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“…A number of papers have discussed at least two species for delayed or non-delayed predator-prey models [18][19][20][21][22][23][24]. It has been shown that the majority of epidemiological models can be represented as a system of differential equations, with time lags frequently included [25,26]. Theoretical studies of plant disease rarely use delay differential equations.…”

Section: Introductionmentioning

confidence: 99%

Artificial intelligence knacks-based stochastic paradigm to study the dynamics of plant virus propagation model with impact of seasonality and delays

et al. 2022

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The presented study deals with the exploitation of the artificial intelligence knacksbased stochastic paradigm for the numerical treatment of the nonlinear delay differential system for dynamics of plant virus propagation with the impact of seasonality and delays (PVP-SD) model by implementing neural networks backpropagation with Bayesian regularization scheme (NNs-BBRS). The PVP-SD model is represented with five classes-based ODEs systems for the interaction between insects and plants. The nonlinear PVP-SD model governs with five populations: S(t) susceptible plants, I(t) infected plants, X(t) susceptible insect vectors, Y (t) infected insect vectors and P(t) predators. Adams numerical procedure is adopted to generate the reference solutions of the nonlinear PVP-SD model based on the variety of cases by varying the plants bite rate due to vectors, vector bite rate due to plants, plant's recovery rate, predator contact rate with healthy insects, predator contact rate with infected insects and death rate caused by insecticides. The approximate solutions of the nonlinear PVP-SD model are determined by executing the designed NNs-BBRS through different target and inputs arbitrary selected samples for the training and testing data. Validation of the consistent precision and convergence of the designed NNs-BBRS is efficaciously substantiated through exhaustive simulations and analyses on mean square error-based merit function, index of regression and error histogram illustrations.

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Section: Introductionmentioning

confidence: 99%

Artificial intelligence knacks-based stochastic paradigm to study the dynamics of plant virus propagation model with impact of seasonality and delays

et al. 2022

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“…In real world, when prey populations perceive some predation risks, they will always show a few anti-predator actions, such as vigilance, foraging actions, and some psychological changes, which cut down the growth speed of the prey species and the survival speed of adults is also impacted accordingly. Recently, many predator-prey population systems containing fear of prey species are studied and some valuable results are reported [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

The Long Time Behavior of Equilibrium Status of a Predator‐Prey System with Delayed Fear in Deterministic and Stochastic Scenarios

Kong

Shao

2022

Journal of Mathematics

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In view of a time lag between the time that the prey perceive predator signals and make some changes or behavior responses, we establish a predator–prey system with direct and indirect predation in this paper. First, we investigate the existence, boundedness, and global asymptotical stability of the positive equilibrium status. Next, by perturbing the mortality rates of prey species and predator species, we stretch the deterministic system to the stochastic scenario and investigate the existence of stochastic process and the global asymptotical stability of the equilibrium status. The analytical findings show that fear affects the value of the equilibrium status, and stochastic disturbance affects its stability, but time delay has no effect if some conditions are satisfied, which are verified by some examples and numerical simulations.

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“…Each one of the previously mentioned functional responses describes a specific manner of the interaction between the prey and the predator. Indeed, the attack performed by the predator on the prey makes a huge perturbation on the evolution of the two species mostly on the prey, where numerous researches discuss this issue [3,8,9,15,20,28,30,37]. This behavior is known as a fear effect, where the main idea is to consider that this fear affects the reproduction of the prey population [37].…”

Section: Introductionmentioning

confidence: 99%

Spatiotemporal behavior in a predator–prey model with herd behavior and cross-diffusion and fear effect

2021

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In this manuscript, we investigate the fear effect on the spatiotemporal behavior of the predator-prey model with prey social behavior and cross-diffusive. Our main interest is to determine the existence of Turing patterns and the fear effect performed by predators on the prey population and the group defense. The fear can lead to a partition of the prey herd which is known as prey escaping. It is obtained that the system has rich dynamics elaborated by the presence of Turing patterns and Turing-Hopf bifurcation. The nature of Turing patterns is successfully discussed by analyzing the amplitude equations with a multiple-timescale technique. After studying the stability of these amplitude equations, it has been identified various Turing patterns driven by the cross-diffusion. Further, the effect of the fear rate or escaping rate on the behavior of the solution is discussed. The theoretical results are checked numerically.

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Role of fear in a predator-prey system with ratio-dependent functional response in deterministic and stochastic environment

Cited by 55 publications

References 64 publications

Artificial intelligence knacks-based stochastic paradigm to study the dynamics of plant virus propagation model with impact of seasonality and delays

Artificial intelligence knacks-based stochastic paradigm to study the dynamics of plant virus propagation model with impact of seasonality and delays

The Long Time Behavior of Equilibrium Status of a Predator‐Prey System with Delayed Fear in Deterministic and Stochastic Scenarios

Spatiotemporal behavior in a predator–prey model with herd behavior and cross-diffusion and fear effect

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