A Mathematical Modeling Approach to Analyse the Effect of Additional Food in a Predator-Prey Interactions with a White Gaussian Noise in Prey’s Growth Rate

Gökçe, Aytül

doi:10.1007/s40819-021-01234-9

Cited by 3 publications

(2 citation statements)

References 39 publications

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“…Firstly, we are currently in the process of investigating stochastic dynamics of the model, where incorporating white Gaussian noise in the system may lead substantial impact on the dynamics of both species and their stability. 38 Secondly, for mathematical convenience, a particular attention has been paid on the impact of local and constant delay in the predator maturation. Thus, another numerical and theoretical investigation is required to explore the role of more realistic model with non-local delays.…”

Section: Summary Of the Resultsmentioning

confidence: 99%

“…This research may raise many questions in need of further examination. Firstly, we are currently in the process of investigating stochastic dynamics of the model, where incorporating white Gaussian noise in the system may lead substantial impact on the dynamics of both species and their stability 38 . Secondly, for mathematical convenience, a particular attention has been paid on the impact of local and constant delay in the predator maturation.…”

Section: Summary Of the Resultsmentioning

confidence: 99%

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A mathematical model of population dynamics revisited with fear factor, maturation delay, and spatial coefficients

Gökçe

2022

Math Methods in App Sciences

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This study concentrates on the dynamics of a prey-predator model incorporating the fear effect in the birth and death rate of prey, whose physiological changes may give rise to undirect predation. In the presence and absence of time delay, single parameter numerical continuation with respect to two parameters, that are (i) fear level in the death rate of prey and (ii) conversion efficiency by which new predators are introduced through prey consumption in the system, is performed. Basic results on extinction and delay-driven Hopf bifurcation criteria are investigated. Then, the model is extended to involve the spatial dynamics with and without time delay. Theoretical results for orientation and stability of Hopf bifurcation in spatial system are provided by applying the normal form recipe and also the center manifold theory. Classical reaction-diffusion-type models, incorporating self-diffusion, can induce regular (periodic) and irregular (chaotic) oscillations in space. However, space periodic oscillations are not common in prey-predator interactions. Here, it is shown that the dynamics of only diffusion involved model is periodically arranged in space and time. However, introducing a very small value of time delay in predator maturation, spatial dynamics with chaos is initiated as a result of the joint effect of time delay and diffusion. This reassures that time delay has a crucial role in population dynamics incorporated with the role of indirect predation and gives some useful intuition into underlying species interactions. Theoretical results of the model in this paper are supported with numerical experiments.

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Section: Summary Of the Resultsmentioning

confidence: 99%

Section: Summary Of the Resultsmentioning

confidence: 99%

A mathematical model of population dynamics revisited with fear factor, maturation delay, and spatial coefficients

Gökçe

2022

Math Methods in App Sciences

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Stability and bifurcation analysis of delayed tri‐trophic food chain model in poisoned environment with fear effect and additional food

Sivasamy

Banjerdpongchai

Park

2023

Math Methods in App Sciences

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One of the most important goals of theoretical ecologists is to find a strategy for controlling the chaos in ecological models to maintain healthy ecosystems. We investigate the influence of fear and the supply of additional food to predators in a delayed tri‐trophic food chain model, where interference among the species is determined by Holling type‐II functional response. The proposed model incorporates the fact that the growth rates of prey and middle predators are decreased due to the fear of middle and special predators, respectively. The additional food is supplied to both predators by either nature or external agencies. Furthermore, the poisoned prey in the predator's environment is taken into account. In the proposed model, we use two time delays: one for the growth term of the middle predator and another for the gestation delay of the special predator. We determine the conditions for the existence of ecologically feasible equilibrium points and their local and global stability. In addition, we establish the conditions for the existence of Hopf bifurcation around interior equilibrium to seek periodic behavior in nondelayed and delayed models. Numerical investigations are performed to justify the proposed theoretical findings through phase portraits, time series of solutions, and bifurcation diagrams. We observe that the chaotic dynamics of a tri‐trophic food chain model can be controlled by the proper choice of the fear effect and by supplying additional food parameters. As a result, our findings provide more ecological insights into the dynamics of the delayed tri‐trophic food chain model with the fear effect and additional food supply.

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A Mathematical Modelling Approach for a Past-Dependent Prey-Predator System

Gökçe

2022

Journal of Mathematical Sciences and Modelling

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A memory dependent prey-predator model incorporating Allee effect in prey is analysed. For a small and high values of memory rate, the dynamical changes in the prey and predator densities are demonstrated. The equilibria of the proposed model and the local stability analysis corresponding to each equilibrium are presented. The variables of prey and predator species with respect to memory rate are investigated and the existence of the Hopf bifurcation is shown. The analytical part of this paper is supported with detailed numerical simulations.

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A Mathematical Modeling Approach to Analyse the Effect of Additional Food in a Predator-Prey Interactions with a White Gaussian Noise in Prey’s Growth Rate

Cited by 3 publications

References 39 publications

A mathematical model of population dynamics revisited with fear factor, maturation delay, and spatial coefficients

A mathematical model of population dynamics revisited with fear factor, maturation delay, and spatial coefficients

Stability and bifurcation analysis of delayed tri‐trophic food chain model in poisoned environment with fear effect and additional food

A Mathematical Modelling Approach for a Past-Dependent Prey-Predator System

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