Dynamical behavior of a stochastic Nicholson’s blowflies model with distributed delay and degenerate diffusion

Mu, Xiaojie; Jiang, Daqing; Hayat, Tasawar; Alsaedi, Ahmed; Ahmad, Bashir

doi:10.1007/s11071-020-05944-5

Cited by 10 publications

(5 citation statements)

References 17 publications

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“…By constructing appropriate Lyapunov functions and several useful inequalities, several criteria for the permanence, extinction, periodic solutions, and global attractiveness of the system were obtained. From this study, we found that the main results and system (6) can be seen as supplements and extensions of the previously results and systems [1][2][3][4][5][6][7][8][9][10][11][12].…”

Section: Discussionsupporting

confidence: 70%

“…On the other hand, stochastic population dynamical systems [9,10,15,17] refer to mathematical models that describe the changes in population size over time, taking into account the random fluctuations and uncertainties in environmental factors and demographic processes. These models are typically used in ecology, biology, and conservation biology to study the dynamics of populations and predict their future behaviors.…”

Section: Discussionmentioning

confidence: 99%

“…Therefore, we need to introduce variable delay into nonautonomous models. There has been some studies [9][10][11][12][13][14][15] related to the study of Nicholson's blowflies models with continuous time delays.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics in a Competitive Nicholson’s Blowflies Model with Continuous Time Delays

Muhammadhaji

2023

Symmetry

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In this study, we examine a competitive Nicholson blowflies model with time-varying coefficients and continuous time delays. In the case of coincidence degree theory, constructing appropriate Lyapunov functionals and using several inequalities, several conditions on the extinction, periodic solution, permanence, and global attractiveness of the system are derived. Finally, three examples with numerical simulations are presented to validate the practicability and feasibility of the obtained theoretical results.

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Section: Discussionsupporting

confidence: 70%

Section: Discussionmentioning

confidence: 99%

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Dynamics in a Competitive Nicholson’s Blowflies Model with Continuous Time Delays

Muhammadhaji

2023

Symmetry

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“…• The existing theories of the probability density function are only suitable for two-dimensional population models and three-dimensional epidemic models [81,6,80,50]. We generalize the relevant theories to arbitrary dimensional stochastic models and derive an approximate expression of local density function of the stationary distribution of system (4).…”

Section: Introductionmentioning

confidence: 99%

Stationary distribution, extinction, density function and periodicity of an n-species competition system with infinite distributed delays and nonlinear perturbations

Zhou

Dai

2023

DCDS-B

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<p style='text-indent:20px;'>In this paper, we examine an n-species Lotka-Volterra competition system with general infinite distributed delays and nonlinear perturbations. The stochastic boundedness and extinction are first studied. Then we propose a new <inline-formula><tex-math id="M1">\begin{document}$ p $\end{document}</tex-math></inline-formula>-stochastic threshold method to establish sufficient conditions for the existence of stationary distribution <inline-formula><tex-math id="M2">\begin{document}$ \ell(\cdot) $\end{document}</tex-math></inline-formula>. By solving the corresponding Fokker–Planck equation, we derive the approximate expression of the distribution <inline-formula><tex-math id="M3">\begin{document}$ \ell(\cdot) $\end{document}</tex-math></inline-formula> around its quasi-positive equilibrium. For the stochastic system with periodic coefficients, we use the <inline-formula><tex-math id="M4">\begin{document}$ p $\end{document}</tex-math></inline-formula>-stochastic threshold method again to obtain the existence of positive periodic solution. Besides, the related competition exclusion and moment estimate of species are shown. Finally, some numerical simulations are provided to substantiate our analytical results.</p>

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“…where B(t) is the standard Brownian motion defined on the complete probability space (Ω, F, P) with a filtration {F} t≥0 satisfying the usual conditions (i.e., it is right continuous and increasing, and F 0 contains all P-null sets), σ 2 represents the intensity of the Brownian motion. However, after studying E. Allen [21] and other scholars' [22,23] researches, we know that the average value of modified transmission rate over an arbitrary time interval [0, T ] satisfies 1…”

Section: Introductionmentioning

confidence: 99%

Dynamical analysis and numerical simulation of a stochastic influenza transmission model with human mobility and Ornstein-Uhlenbeck process

Zhang,

Su,

Jiang

2023

Preprint

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With the inevitable environmental perturbations and complex population movements, the analysis of troublesome influenza is harder to proceed. Studies about the epidemic mathematical models can not only forecast the development trend of influenza, but also have a beneficial influence on the protection of health and the economy. Motivated by this, a stochastic influenza model incorporating human mobility and the Ornstein-Uhlenbeck process is established in this paper. Based on the existence of the unique global positive solution, we obtain sufficient conditions for influenza extinction and persistence, which are related to the basic reproduction number in the corresponding deterministic model. Notably, the analytical expression of the probability density function of stationary distribution near the quasi-endemic equilibrium is obtained by solving the challenging Fokker–Planck equation. Finally, numerical simulations are performed to support the theoretical conclusions, and the effect of main parameters and environmental perturbations on influenza transmission are also investigated.

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Dynamical behavior of a stochastic Nicholson’s blowflies model with distributed delay and degenerate diffusion

Cited by 10 publications

References 17 publications

Dynamics in a Competitive Nicholson’s Blowflies Model with Continuous Time Delays

Dynamics in a Competitive Nicholson’s Blowflies Model with Continuous Time Delays

Stationary distribution, extinction, density function and periodicity of an n-species competition system with infinite distributed delays and nonlinear perturbations

Dynamical analysis and numerical simulation of a stochastic influenza transmission model with human mobility and Ornstein-Uhlenbeck process

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