A dynamic interplay between Allee effect and time delay in a mathematical model with weakening memory

Gökçe, Aytül

doi:10.1016/j.amc.2022.127306

Cited by 3 publications

(2 citation statements)

References 30 publications

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“…In this context, fractional derivatives exhibit non-local characteristics, effectively capturing memory effects, while time delays convey information about earlier states [35]. In this study,firstly the classical system given by (2.1)-(2.3) is revisited and stability analysis around the coexistence equilibrium is determined [28]. Then the reformulation of the model allows us to analyse the system with fractional order operators in (2.4)-(2.6).…”

Section: Discussionmentioning

confidence: 99%

A numerical approach for a dynamical system of fractional infectious disease problem

GÜRBÜZ,

HATİPOĞLU,

GÖKÇE

2024

Hacettepe Journal of Mathematics and Statistics

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In this study, a dynamical system to explain a disease model with environmental stress in a general aspect is considered. The model is expressed by the standard differential equations and its Caputo fractional form. We describe a numerical approach based on the numerical technique of Adams-Bashforth-Moulton for the solution of the system of differential equations including the initial conditions. Besides, we indicate briefly the existence, uniqueness, and convergence of the technique. One of the subjects of the study is to contribute with a new design of the present technique to obtain numerical solutions to such problems in the literature which can be investigated for further approximations. Further, we provide the stability analysis around the coexistence equilibrium. Additionally, we illustrate the findings to show the behaviour of the system, time evolution, and the phase plane plots for the specific parameters.

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Section: Discussionmentioning

confidence: 99%

A numerical approach for a dynamical system of fractional infectious disease problem

GÜRBÜZ,

HATİPOĞLU,

GÖKÇE

2024

Hacettepe Journal of Mathematics and Statistics

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“…There are many investigations that have been presented based on the Allee effects and Holling 3 rd type using the functional response [42]. The delayed mathematical model with the Holling 3 rd type using the functional response is provided as [43]:…”

Section: Mathematical Modelmentioning

confidence: 99%

A Stochastic Framework for Solving the Prey-Predator Delay Differential Model of Holling Type-III

Ruttanaprommarin¹,

Sabir²,

Núñez³

et al. 2023

Computers, Materials &Amp; Continua

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The current research aims to implement the numerical results for the Holling third kind of functional response delay differential model utilizing a stochastic framework based on Levenberg-Marquardt backpropagation neural networks (LVMBPNNs). The nonlinear model depends upon three dynamics, prey, predator, and the impact of the recent past. Three different cases based on the delay differential system with the Holling 3 rd type of the functional response have been used to solve through the proposed LVMBPNNs solver. The statistic computing framework is provided by selecting 12%, 11%, and 77% for training, testing, and verification. Thirteen numbers of neurons have been used based on the input, hidden, and output layers structure for solving the delay differential model with the Holling 3 rd type of functional response. The correctness of the proposed stochastic scheme is observed by using the comparison performances of the proposed and reference data-based Adam numerical results. The authentication and precision of the proposed solver are approved by analyzing the state transitions, regression performances, correlation actions, mean square error, and error histograms.

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Supervised neural learning for the predator-prey delay differential system of Holling form-III

Ruttanaprommarin

Sabir

Saïd

et al. 2022

MATH

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<abstract> <p>The purpose of this work is to present the stochastic computing study based on the artificial neural networks (ANNs) along with the scaled conjugate gradient (SCG), ANNs-SCG for solving the predator-prey delay differential system of Holling form-III. The mathematical form of the predator-prey delay differential system of Holling form-III is categorized into prey class, predator category and the recent past effects. Three variations of the predator-prey delay differential system of Holling form-III have been numerical stimulated by using the stochastic ANNs-SCG procedure. The selection of the data to solve the predator-prey delay differential system of Holling form-III is provided as 13%, 12% and 75% for testing, training, and substantiation together with 15 neurons. The correctness and exactness of the stochastic ANNs-SCG method is provided by using the comparison of the obtained and data-based reference solutions. The constancy, authentication, soundness, competence, and precision of the stochastic ANNs-SCG technique is performed through the analysis of the correlation measures, state transitions (STs), regression analysis, correlation, error histograms (EHs) and MSE.</p> </abstract>

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A dynamic interplay between Allee effect and time delay in a mathematical model with weakening memory

Cited by 3 publications

References 30 publications

A numerical approach for a dynamical system of fractional infectious disease problem

A numerical approach for a dynamical system of fractional infectious disease problem

A Stochastic Framework for Solving the Prey-Predator Delay Differential Model of Holling Type-III

Supervised neural learning for the predator-prey delay differential system of Holling form-III

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