Dynamics and bifurcations of a discrete‐time Lotka–Volterra model using nonstandard finite difference discretization method

Eskandari, Zohreh; Avazzadeh, Z.; Ghaziani, Reza Khoshsiar; Li, Bo

doi:10.1002/mma.8859

Cited by 60 publications

(20 citation statements)

References 32 publications

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“…Useful information about the past and present of the disease has been reported, which is advantageous in establishing control strategies for its eradication from society. In this regard, valuable work can be found in [11,12,13,14,15,16]. The formation of a mathematical formula consists of conditions regarding the parameters involved in the problem under consideration.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a fractional-order COVID-19 model under the nonsingular kernel of Caputo-Fabrizio operator

Ahmad

Qiu

Rahman

2022

mmnsa

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For the sake of human health, it is crucial to investigate infectious diseases including HIV/AIDS, hepatitis, and others. Worldwide, the recently discovered new coronavirus (COVID-19) poses a serious threat. The experimental vaccination and different COVID-19 strains found around the world make the virus' spread unavoidable. In the current research, fractional order is used to study the dynamics of a nonlinear modified COVID-19 SEIR model in the framework of the Caputo-Fabrizio fractional operator with order b. Fixed point theory has been used to investigate the qualitative analysis of the solution respectively. The well-known Laplace transform method is used to determine the approximate solution of the proposed model. Using the COVID-19 data that is currently available, numerical simulations are run to validate the necessary scheme and examine the dynamic behavior of the various compartments of the model. In order to stop the pandemic from spreading, our findings highlight the significance of taking preventative steps and changing one's lifestyle.

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Section: Introductionmentioning

confidence: 99%

Dynamics of a fractional-order COVID-19 model under the nonsingular kernel of Caputo-Fabrizio operator

Ahmad

Qiu

Rahman

2022

mmnsa

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“…We establish existence conditions for solutions to the inclusion problem (19) for which the right-hand side is non-convex by applying an invariant point theorem for Lmaps. For some related recent applications of crisp mathematical techniques, we refer to [29][30][31][32] and some citations in there. We now recall some needed concepts of fractional calculus and set-valued analysis as follows.…”

Section: An Application To Fractional Differential Inclusion For An E...mentioning

confidence: 99%

On Fractional Differential Inclusion for an Epidemic Model via L-Fuzzy Fixed Point Results

Noorwali¹,

Shagari²

2023

Computer Modeling in Engineering &Amp; Sciences

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The real world is filled with uncertainty, vagueness, and imprecision. The concepts we meet in everyday life are vague rather than precise. In real-world situations, if a model requires that conclusions drawn from it have some bearings on reality, then two major problems immediately arise, viz. real situations are not usually crisp and deterministic; complete descriptions of real systems often require more comprehensive data than human beings could recognize simultaneously, process and understand. Conventional mathematical tools which require all inferences to be exact, are not always efficient to handle imprecisions in a wide variety of practical situations. Following the latter development, a lot of attention has been paid to examining novel L-fuzzy analogues of conventional functional equations and their various applications. In this paper, new coincidence point results for single-valued mappings and an L-fuzzy set-valued map in metric spaces are proposed. Regarding novelty and generality, the obtained invariant point notions are compared with some well-known related concepts via non-trivial examples. It is observed that our principal results subsume and refine some important ones in the corresponding domains. As an application, one of our results is utilized to discuss more general existence conditions for realizing the solutions of a non-integer order inclusion model for COVID-19.

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“…Caputo and Fabrizio further modified the Caputo operator by introducing a non-singular kernel, and in 2016, Atangana and Baleanu proposed a new definition based on Caputo’s concept using a non-local and non-singular kernel [ 21 , 22 ]. Since then, researchers have conducted considerable research on these operators, exploring various mathematical properties and applications in various fields [ 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 ].…”

Section: Introductionmentioning

confidence: 99%

Piecewise Business Bubble System under Classical and Nonsingular Kernel of Mittag–Leffler Law

Zhang

2023

Entropy

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This study aims to investigate the dynamics of three agents in the emerging business bubble model based on the Mittag–Leffler law pertaining to the piecewise classical derivative and non-singular kernel. By generalizing the business bubble dynamics in terms of fractional operators and the piecewise concept, this study presents a new perspective to the field. The entire set of intervals is partitioned into two piecewise intervals to analyse the classical order and conformable order derivatives of an Atangana–Baleanu operator. The subinterval analysis is critical for removing discontinuities in each sub-partition. The existence and uniqueness of the solution based on a piecewise global derivative are tested for the considered model. The approximate root of the system is determined using the piecewise numerically iterative technique of the Newton polynomial. Under the classical order and non-singular law, the approximate root scheme is applied to the piecewise derivative. The curve representation for the piece-wise globalised system is tested by applying the data for the classical and different conformable orders. This establishes the entire density of each compartment and shows a continuous spectrum instead of discrete dynamics. The concept of this study can also be applied to investigate crossover behaviours or abrupt changes in the dynamics of the values of each market.

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Dynamics and bifurcations of a discrete‐time Lotka–Volterra model using nonstandard finite difference discretization method

Cited by 60 publications

References 32 publications

Dynamics of a fractional-order COVID-19 model under the nonsingular kernel of Caputo-Fabrizio operator

Dynamics of a fractional-order COVID-19 model under the nonsingular kernel of Caputo-Fabrizio operator

On Fractional Differential Inclusion for an Epidemic Model via L-Fuzzy Fixed Point Results

Piecewise Business Bubble System under Classical and Nonsingular Kernel of Mittag–Leffler Law

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