Pattern formation of a diffusive predator‐prey model with herd behavior and nonlocal prey competition

Djilali, Salih

doi:10.1002/mma.6036

Cited by 50 publications

(13 citation statements)

References 33 publications

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“…This demonstrates the broad class of interaction functionality that we can consider in this study. For further details, e see [7,10,11,13]. Based on the above-mentioned mathematical and biological backgrounds, the paper is structured as follows:…”

Section: Introductionmentioning

confidence: 99%

Dynamical behavior of two predators–one prey model with generalized functional response and time-fractional derivative

Djilali

Ghanbari

2021

Adv Differ Equ

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The behavior of any complex dynamic system is a natural result of the interaction between the components of that system. Important examples of these systems are biological models that describe the characteristics of complex interactions between certain organisms in a biological environment. The study of these systems requires the use of precise and advanced computational methods in mathematics. In this paper, we discuss a prey–predator interaction model that includes two competitive predators and one prey with a generalized interaction functional. The primary presumption in the model construction is the competition between two predators on the only prey, which gives a strong implication of the real-world situation. We successfully establish the existence and stability of the equilibria. Further, we investigate the impact of the memory measured by fractional time derivative on the temporal behavior. We test the obtained mathematical results numerically by a proper numerical scheme built using the Caputo fractional-derivative operator and the trapezoidal product-integration rule.

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Section: Introductionmentioning

confidence: 99%

Dynamical behavior of two predators–one prey model with generalized functional response and time-fractional derivative

Djilali

Ghanbari

2021

Adv Differ Equ

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“…It can be predicted that in the future, a definition covering all definitions of fractional operators available in the literature may be introduced. To learn more about the content of this study, we refer the readers to [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43].…”

Section: Introductionmentioning

confidence: 99%

Fractional methicillin-resistant Staphylococcus aureus infection model under Caputo operator

Acay

Khan

Yusuf

2021

J. Appl. Math. Comput.

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This study provides a detailed exposition of in-hospital community-acquired methicillinresistant S. aureus (CA-MRSA) which is a new strain of MRSA, and hospital-acquired methicillin-resistant S. aureus (HA-MRSA) employing Caputo fractional operator. These two strains of MRSA, referred to as staph, have been a serious problem in hospitals and it is known that they give rise to more deaths per year than AIDS. Hence, the transmission dynamics determining whether the CA-MRSA overtakes HA-MRSA is analyzed by means of a non-local fractional derivative. We show the existence and uniqueness of the solutions of the fractional staph infection model through fixed-point theorems. Moreover, stability analysis and iterative solutions are furnished by the recursive procedure. We make use of the parameter values obtained from the Beth Israel Deaconess Medical Center. Analysis of the model under investigation shows that the disease-free equilibrium existing for all parameters is globally asymptotically stable when both R H 0 and R C 0 are less than one. We also carry out the sensitivity analysis to identify the most sensitive parameters for controlling the spread of the infection. Additionally, the solution for the above-mentioned model is obtained by the Laplace-Adomian decomposition method and various simulations are performed by using convenient fractional-order α.

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“…As it is mentioned before, the contact between the prey and the predators is exclusively on the boundary of the prey pack, and it is proportional to

\sqrt{u}

. The presence of herd behavior is the subject of investigation of many recent research activities we mention a few, 7,9–25 which shows the big importance of such as modelization for anticipating the behavior of some animals in nature. For more reading about mathematical modeling of natural phenomenon, we cite the previous papers 26–38 …”

Section: Introductionmentioning

confidence: 99%

Pattern formations of a delayed diffusive predator–prey model with predator harvesting and prey social behavior

Djilali

Bentout

2021

Math Methods in App Sciences

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In this research, we are interested in analyzing the behavior of a diffusive predator–prey model in the presence of predator rivalry and prey social behavior. The predator rivalry affects hugely the behavior of predator and the prey, so we are interested in analyzing the complex dynamics generated by the presence of predator harvesting and its influence on the behavior of the solution. For the mathematical purpose, we will concentrate on analyzing the system in the absence of diffusion where the existence of Hopf bifurcation is investigated; also, we proved that the presence of the time lags generates interesting patterns, which it can lead to instability even Hopf bifurcation. The stability of the homogeneous and nonhomogeneous periodic solution generated by the presence of Hopf bifurcation is established using the normal form. The mathematical obtained results are checked numerically using graphical representations.

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Pattern formation of a diffusive predator‐prey model with herd behavior and nonlocal prey competition

Cited by 50 publications

References 33 publications

Dynamical behavior of two predators–one prey model with generalized functional response and time-fractional derivative

Dynamical behavior of two predators–one prey model with generalized functional response and time-fractional derivative

Fractional methicillin-resistant Staphylococcus aureus infection model under Caputo operator

Pattern formations of a delayed diffusive predator–prey model with predator harvesting and prey social behavior

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