Impact of predator incited fear and prey refuge in a fractional order prey predator model

Barman, Dipesh; Roy, Jyotirmoy; Alrabaiah, Hussam; Panja, Prabir; Mondal, Sankar Prasad; Alam, Shariful

doi:10.1016/j.chaos.2020.110420

Cited by 52 publications

(13 citation statements)

References 66 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…According to Lemma 3.1 in Barman et al [33], we get x( t+ ) = 0 which contradicts with Equation ( 17) where x( t+ ) < 0. This means that x(t) ≥ 0 for all t ∈ [0, ∞].…”

Section: Theorem 4 If the Initial Condition In Rmentioning

confidence: 79%

Bifurcation analysis of a predator–prey model involving age structure, intraspecific competition, Michaelis–Menten type harvesting, and memory effect

Panigoro

Rahmi

Resmawan

2023

Front. Appl. Math. Stat.

View full text Add to dashboard Cite

The complexity of the dynamical behaviors of interaction between prey and its predator is studied. The prey and predator relationship involves the age structure and intraspecific competition on predators and the nonlinear harvesting of prey following the Michaelis–Menten type term. Some biological validities are shown for the constructed model such as the existence and uniqueness as well as the non-negativity and boundedness of solutions. Three equilibrium points, namely the origin, axial, and interior points, are found including their global dynamics by employing the Lyapunov function along with the generalized Lassale invariant principle. The changes in dynamical behaviors driven by the harvesting and the memory effect are exhibited, including transcritical, saddle-node, backward, and Hopf bifurcations. The appearance of these interesting phenomena is strengthened by giving numerical simulations consisting of bifurcation diagrams, phase portraits, and their time series.

show abstract

“…According to Lemma 3.1 in Barman et al [33], we get x( t+ ) = 0 which contradicts with Equation ( 17) where x( t+ ) < 0. This means that x(t) ≥ 0 for all t ∈ [0, ∞].…”

Section: Theorem 4 If the Initial Condition In Rmentioning

confidence: 79%

Bifurcation analysis of a predator–prey model involving age structure, intraspecific competition, Michaelis–Menten type harvesting, and memory effect

Panigoro

Rahmi

Resmawan

2023

Front. Appl. Math. Stat.

View full text Add to dashboard Cite

show abstract

“…Researchers have demonstrated the utility of this derivative in modeling biological phenomena in a number of articles, taking into account a variety of factors such as the freedom to arrange the derivative, dealing with species memory acquired during their cycle life, genetic traits, and so on. See [21,22,23,24,25,26,27,28,29,30,31,32] for further information. First, we'll go over some definitions and results related to the Caputo fractional derivative [33,34].…”

Section: Contributions Of Various Industrial Combustion and Avalanches Dmentioning

confidence: 99%

“…In a number of papers, researchers have proved the utility of this derivative in modeling biological processes, taking into consideration elements such as the freedom to arrange the derivative, dealing with species memory acquired during their cycle life, hereditary features, and so on. See [21,22,23,24,25,26,27,28,29,30,31] for further information.…”

Section: Introductionmentioning

confidence: 99%

The Exponential Decay Functions for Prey and Predator Species in a Fractional-Order Ecosystem Model with Considering Global Warming Phenomena

Agarwal

Thirthar

Alaoui

2022

Preprint

View full text Add to dashboard Cite

This study examines the memory eﬀect on predator-prey interactions in the face of global warming, employing a fear function with a Holling type II function to characterize the consumer prey and predator species. The eﬀect of global warming on both prey and predators was studied using the exponential decay function. The system’s equilibria are determined, and the system’s stability is established around the equilibrium points. A series of numerical simulations are done to evaluate the theoretical component of the work and show the impacts of global warming, anxiety, and fractional order on our model’s behavior.

show abstract

“…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

View full text Add to dashboard Cite

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.

show abstract

Impact of predator incited fear and prey refuge in a fractional order prey predator model

Cited by 52 publications

References 66 publications

Bifurcation analysis of a predator–prey model involving age structure, intraspecific competition, Michaelis–Menten type harvesting, and memory effect

Bifurcation analysis of a predator–prey model involving age structure, intraspecific competition, Michaelis–Menten type harvesting, and memory effect

The Exponential Decay Functions for Prey and Predator Species in a Fractional-Order Ecosystem Model with Considering Global Warming Phenomena

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

Contact Info

Product

Resources

About