Dynamics of predator–prey system with fading memory

Sahoo, Banshidhar; Poria, Swarup

doi:10.1016/j.amc.2018.11.013

Cited by 17 publications

(9 citation statements)

References 28 publications

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“…Hence, the biological impacts are more reasons to use the fading effects of the memory that can significantly alter the dynamics. Few more recent studies based on the density of past prey using the prey-predator interactions are presented in the references [3][4][5][6].…”

Section: Introductionmentioning

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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Section: Introductionmentioning

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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“…Among the variety of models, the predator-prey models with different Holling type functional response are refined so as to better reflect the specific characteristics of the different populations or economical needs. A number of interesting works exhibiting quite rich and complicated dynamics have been performed by the theoretical and mathematical biologists in the last few decades considering Holling type functional responses ( [7][8][9][10][11][12][13]). The literatures mentioned above investigate the stabilities and the analyses of codimension-one bifurcation of discrete predator-prey models.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics in a discrete-time predator-prey system

Liu

2022

Preprint

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In this article, the nonlinear dynamics of a discrete-time predator-prey system with simplified Holling type IV functional response are reported. Possible codimension-two bifurcations (1:2, 1:3 and 1:4 strong resonances) are investigated under variation of two parameters for certain critical values. For each bifurcation, normal form coefficients along with its scenario are investigated thoroughly. Besides, the numerical simulations have been done, in addition to supporting the analytical findings, more behaviors are extracted from the model, such as fractal structures, mode-locking structures, etc. Our results generate and improve some known results and show that the discrete model has richer dynamics than the continuous one.

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“…Bulai and Venturino [18] have pointed out that the stable solution was independent of the shape of the herb for competition, its influence was immeasurable. Sahoo and Poria [19] have proposed that the predator-prey system with fading memory has rich dynamic behaviors, such as supercritical and subcritical Hopf bifurcation, these results were still important. Pal et al [20] have raised that an increase in the hunting cooperation induced fear may destabilize the system and produce periodic solution via Hopf bifurcation and limit cycles may be supercritical and subcritical, these results were crucial.…”

Section: Introductionmentioning

confidence: 99%