An information diffusion model in social networks with carrier compartment and delay

Du, Bo; Wang, Haiyan; Liu, Maoxing

doi:10.15388/na.2018.4.7

Cited by 6 publications

(5 citation statements)

References 33 publications

(42 reference statements)

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“…All the derived results and analysis ideas [41][42][43][44][45][46][47] cannot be applied to (3) to obtain the stability and the existence of Hopf bifurcation for (3). Although the authors of [36,48] analyzed the Hopf bifurcation, and the stability of integerorder malware propagation model, they did not consider the fractional-order case. From the point, the fruit of this article on the stability and the existence of Hopf bifurcation for 3is completely new and completes some earlier publications.…”

Section: Preliminary Resultsmentioning

confidence: 99%

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Bifurcation of a Fractional-Order Delayed Malware Propagation Model in Social Networks

Liao

2019

Discrete Dynamics in Nature and Society

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In recent years, with the rapid development of the Internet and the Internet of Things, network security is urgently needed. Malware becomes a major threat to network security. Thus, the study on malware propagation model plays an important role in network security. In the past few decades, numerous researchers put up various kinds of malware propagation models to analyze the dynamic interaction. However, many works are only concerned with the integer-order malware propagation models, while the investigation on fractional-order ones is very few. In this paper, based on the earlier works, we will put up a new fractional-order delayed malware propagation model. Letting the delay be bifurcation parameter and analyzing the corresponding characteristic equations of considered system, we will establish a set of new sufficient conditions to guarantee the stability and the existence of Hopf bifurcation of fractional-order delayed malware propagation model. The study shows that the delay and the fractional order have important effect on the stability and Hopf bifurcation of considered system. To check the correctness of theoretical analyses, we carry out some computer simulations. At last, a simple conclusion is drawn. The derived results of this paper are completely innovative and play an important guiding role in network security.

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Section: Preliminary Resultsmentioning

confidence: 99%

“…Up to now, there are few articles that focus on the effect of delays on the Hopf bifurcation of fractional-order delayed malware propagation model. In 2018, Du et al [36] investigated the following malware propagation model with delay:…”

Section: Introductionmentioning

confidence: 99%

Bifurcation of a Fractional-Order Delayed Malware Propagation Model in Social Networks

Liao

2019

Discrete Dynamics in Nature and Society

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“…From the form of Equation , we note that the right side of Equation contains both monotone increasing and decreasing nonautonomous terms, as the authors in Du et al pointed out that, the existence of almost periodic solutions to model cannot be solved by some classical nonlinear analysis methods . By applying mixed monotone operator fixed point theorem in an appropriate cone, the main aim of the present paper is to obtain some suitable criteria, which guarantee the existence of positive almost periodic solution for Equation .…”

Section: Introductionmentioning

confidence: 95%

“…A known example of such applications is the delay differential equation proposed by Mackey and Glass; they introduced and investigated the following nonlinear delay equation:

x^{'} false(t false) = - α x false(t false) + \frac{β}{1 + x^{n} false(t - τ false)},

where α , β , and τ are positive constants (see Mackey and Glass). Moreover, the qualitative properties and dynamic behaviors for Equation and some generalized forms of have been studied by many researchers, one can refer to the previous studies . Since then, some authors were interested in variable delays of hematopoiesis systems or their extended forms, some good results were obtained .…”

Section: Introductionmentioning

confidence: 99%

Existence and uniqueness of almost periodic solutions to discrete mixed monotone hematopoiesis model

Zhou

2019

Math Methods in App Sciences

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This paper is devoted to studying a generalized nonlinear discrete hematopoiesis model with delays. By applying mixed monotone operator fixed point theorem in an appropriate cone, we discuss the existence and uniqueness of positive almost periodic solution to this model. Four cases are classified based on parameters of the concerned model. The main results provided in the paper are more general than that of some previously known results, which are extended and complemented. Two particular examples are provided to illustrate that the obtained results, which are reasonable. KEYWORDS almost periodic solution, cone, discrete hematopoiesis model, mixed monotone operator MSC CLASSIFICATION 34C27; 34K14; 39A29 Math Meth Appl Sci. 2019;42:7471-7481. wileyonlinelibrary.com/journal/mma

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“…Facebook or ChatGPT), while user abandonment indicates discontinuation. References such as [8][9][10][11][12][13][14][15] focus on information diffusion, while others like [16][17][18][19][20][21] address user adoption and abandonment dynamics.…”

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confidence: 99%

Modelling the dynamics of product adoption and abandonment

Kong

2024

Proc. R. Soc. A.

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We introduce a new compartmental differential equation model to examine the dynamics of user adoption and abandonment within a product context. This model features a nonlinear adoption rate and encompasses two distinct abandonment dynamics: infectious abandonment stemming from interactions among current and past users, and non-infectious abandonment induced by mass media, advertisements or the emergence of new products. Our exploration encompasses discussions on the existence and stability of model equilibria, as well as the derivation of a critical threshold quantity that regulates the model dynamics. Additionally, we establish criteria for backward and forward bifurcations and various forms of Hopf bifurcation. Detailed scrutiny of an associated optimal control problem is undertaken, starting with the establishment of the existence of an optimal control pair, followed by the determination of the requisite system conditions for this control pair. Extensive numerical simulations are conducted to validate the theoretical findings. Finally, we showcase the model’s efficacy by fitting it to historical data on Facebook’s daily active users, employing the derived parameter values to predict future user counts.

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An information diffusion model in social networks with carrier compartment and delay

Cited by 6 publications

References 33 publications

Bifurcation of a Fractional-Order Delayed Malware Propagation Model in Social Networks

Bifurcation of a Fractional-Order Delayed Malware Propagation Model in Social Networks

Existence and uniqueness of almost periodic solutions to discrete mixed monotone hematopoiesis model

Modelling the dynamics of product adoption and abandonment

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