The stationary distribution of a stochastic rumor spreading model

Chen, Chaodong; Gao, Dapeng; Guo, Peng

doi:10.3934/math.2021076

Cited by 6 publications

(2 citation statements)

References 13 publications

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“…The researchers in [25,39] contended that combining these two notions can assist us in developing a deep understanding of the natural world much more effectively because the fractal-fractional derivative can only acquire a small range of interrelated challenges while environmental noise can also capture multiple kinds of complexities in statistical theory. For further investigation on stochastic process and fractional calculus; see [40][41][42][43][44][45][46][47][48]. Additionally, the majority of earlier studies made the assumption that rumors circulate in an isolated circuit and that online social network densities are constant.…”

Section: Introductionmentioning

confidence: 99%

New insights of a stochastic nonlinear differential equations model with ergodic stationary distribution via fractal-fractional derivatives involving random perturbations

Chu

Sultana

Karim

et al. 2023

Preprint

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Rumor circulation has been a serious challenge to preserving the established societal structure. Recently, significant attempts have been made to explore the patterns of rumors using epidemic models, assuming that only rumor streams for a particular incident occur in the network. In this research, the rumor dynamics during catastrophes are discussed using a unique rumor spreading mechanism via the novel fractal-fractional derivative operators (Caputo and Caputo-Fabrizio) sense by proposing white noise in the system. By strengthening a comprehensive stochastic Lyapunov function, which gives us a reasonable representation of permanence. Furthermore, we established the existence-uniqueness of the non-negative solution of the model. Besides that, we are capable of demonstrating the necessary requirements for the persistence and exclusivity of an ergodic stationary distribution for the aforesaid model. Numerical configurations were investigated to illustrate the effect of model parameters, power law and exponential decay kernel with fractional-order and fractal-dimension on the rumor metastatic phenomenon. Finally, the corresponding management solutions with the fractal-fractional operators for preventing the proliferation of rumors during catastrophes are also covered in this research. AMS Subject Classification: 26A51; 26A33; 26D07; 26D10; 26D15.

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Section: Introductionmentioning

confidence: 99%

New insights of a stochastic nonlinear differential equations model with ergodic stationary distribution via fractal-fractional derivatives involving random perturbations

Chu

Sultana

Karim

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…It is worth noting that the above researchers studies the rumor propagation behavior with deterministic model, i.e., fixed parameters. However, due to the various interior and exterior noises on the propagation pro-cess, different stochastic models have been considered, such as Itô stochastic models, [24][25][26][27][28] stratonovich stochastic models, [8] and Levy process models. [29] Authors proved the dynamic property around equilibriums and the existence of stationary distribution.…”

Section: Introductionmentioning

confidence: 99%

Dynamics and intermittent stochastic stabilization of a rumor spreading model with guidance mechanism in heterogeneous network

Zhong¹,

Yang²,

Miao³

et al. 2022

Chinese Phys. B

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In this paper, we propose a novel rumor propagation model with guidance mechanism in heterogeneous complex networks. Firstly, the sharp threshold of rumor propagation, the global stability of the information-equilibrium and the information-prevailing-equilibrium under R 0 < 1 and R 0 > 1 are carried out by Lyapunov method and LaSalle’s invariant principle. Next, we design an aperiodically intermittent stochastic stabilization method to suppress rumor propagation. Using Itô formula and exponential martingale inequality, the expression of the minimum control intensity is calculated. This method can effectively stabilize rumor propagation by choosing a suitable perturb intensity and a perturb time ratio, while minimizing control cost. Finally, numerical examples are given to illustrate the analysis and method of the paper.

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Dynamical analysis of a stochastic Hyper-INPR competitive information propagation model

Xia,

Jiang,

Mei

et al. 2024

Chaos, Solitons & Fractals

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The stationary distribution of a stochastic rumor spreading model

Cited by 6 publications

References 13 publications

New insights of a stochastic nonlinear differential equations model with ergodic stationary distribution via fractal-fractional derivatives involving random perturbations

New insights of a stochastic nonlinear differential equations model with ergodic stationary distribution via fractal-fractional derivatives involving random perturbations

Dynamics and intermittent stochastic stabilization of a rumor spreading model with guidance mechanism in heterogeneous network

Dynamical analysis of a stochastic Hyper-INPR competitive information propagation model

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