Spreading-vanishing dichotomy in information diffusion in online social networks with intervention

Ren, Jing; Zhu, Dandan; Wang, Haiyan

doi:10.3934/dcdsb.2018240

Cited by 9 publications

(13 citation statements)

References 24 publications

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“…Multiplying both sides of equation (5) by u(t) and integrating over the interval [0, ω]. Similar to equations (11) and (12), we obtain…”

Section: µ ≤ −2mentioning

confidence: 94%

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Positive periodic solution for generalized Basener-Ross model

Cheng¹,

Cui²

2017

Discrete &Amp; Continuous Dynamical Systems - B

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This paper is devoted to the existence of at least one positive periodic solution for generalized Basener-Ross model with time-dependent coefficients. Our proof is based on Manásevich-Mawhin continuation theorem, Leray-Schauder alternative principle, fixed point theorem in cones. Moreover, we obtain that there are at least two positive periodic solutions for this model.2010 Mathematics Subject Classification. Primary: 34B16, 34B18; Secondary: 34C25.

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“…Multiplying both sides of equation (5) by u(t) and integrating over the interval [0, ω]. Similar to equations (11) and (12), we obtain…”

Section: µ ≤ −2mentioning

confidence: 94%

“…It is obvious that a, c, h, k are positive constants. According to model (1), residents will survive rely on the existing resources on the island [11,13] . If resources are used excessively, humans will increase rapidly in a short time and eventually disappear.…”

mentioning

confidence: 99%

Positive periodic solution for generalized Basener-Ross model

Cheng¹,

Cui²

2017

Discrete &Amp; Continuous Dynamical Systems - B

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“…Difference operators play a very important role in solving functional differential equations, which derived from some practical problems, such as biology, economics and population models [11,20,25]. In the 1970s, Hale [10] gave a definition for a functional differential equations of an operator.…”

Section: Introductionmentioning

confidence: 99%

Linear difference operator with multiple variable parameters and applications to second-order differential equations

Yao

et al. 2020

Bound Value Probl

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In this article, we first investigate the linear difference operator (Ax)(t) := x(t)-n i=1 c i (t)x(t-δ i (t)) in a continuous periodic function space. The existence condition and some properties of the inverse of the operator A are explicitly pointed out. Afterwards, as applications of properties of the operator A, we study the existence of periodic solutions for two kinds of second-order functional differential equations with this operator. One is a kind of second-order functional differential equation, by applications of Krasnoselskii's fixed point theorem, some sufficient conditions for the existence of positive periodic solutions are established. Another one is a kind of second-order quasi-linear differential equation, we establish the existence of periodic solutions of this equation by an extension of Mawhin's continuous theorem.

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“…and Holland (2012), Georgelin and Loeuille (2014), Rojas-Nossa, Sanchez, and Navarro (2016), Souza, Nepi, Machado, and Guimaraes (2017), Ren, Zhu, and Wang (2019), Tan, Wang, and Wu (2019), Wang (2019), Wang and Wu (2019), and so forth. Revilla (2015) established a model to describe pollination-mutualisms, in which plant, nectar, and pollinator are included.…”

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confidence: 98%

Persistence of pollination‐mutualisms under the effect of intermediary resource

Yuan

Wang

et al. 2020

Natural Resource Modeling

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This paper considers pollination-mutualism systems, including intermediary resources, which are represented by nectar for convenience. In the plant-nectar-pollinator system, we focus on the case in which the plant cannot persist without pollination and the pollinator can live independently. When nectar is assumed to rapidly approach a steady state, the plant-nectar-pollinator system can be described by its approximate plant-pollinator equations. Using dynamical system theory, we exhibit conditions under which the three-dimensional system persists and provide rigorous proof for global dynamics of the approximate equations. The analysis demonstrates mechanisms by which the decay rate of nectar, the nectar-consumption rate by a pollinator, the nectarproduction cost, and the rate of the plant can result in the persistence of pollination-mutualisms. As an example, (a) when the decay rate is low, the plant survives in the system and pollination-mutualisms persist, in which the pollinator approaches an enhanced density.(b) When the decay rate is intermediary, the plant can survive in the system only if the initial density of nectar is not below a threshold. (c) When the decay rate is large, the plant goes to extinction even though the pollinator persists. A novel finding in comparing the plant-nectarpollinator system and its approximate plant-pollinator equations is that varying the initial value of nectar can lead to the persistence/extinction of pollinationmutualisms. Our results are consistent with real observations, and numerical simulations confirm and extend the results. Considerations for managementTaking into account findings, management considerations may include:1. Mechanisms how pollination-mutualisms persist through intermediary resources are demonstrated.2. The plant's cost for nectar production plays a role in the persistence. 3. The decay rate of nectar, the nectar-consumption rate by a pollinator, and the nectar-production rate of the plant are crucial to the persistence. K E Y W O R D S coexistence, cooperation, mutualism, stability, uniform persistence 2 0 0 0 M S C 34C12; 34C28; 37G20; 37N25 | INTRODUCTIONFlowering plants interact with pollinators through pollination-mutualisms. In the mutualisms, a plant provides food (e.g., nectar and pollen) for its pollinator and the pollinator supplies pollination service for its host plant in return. Pollination-mutualisms indirectly support the survival of most species in natural environments (Holland & DeAngelis, 2010;McCall & Irwin, 2006). For example, herbivores consume plant leaves for survival, while most plant species depend on pollination service for reproduction. Although a series of models has been formed to characterize pollination-mutualisms, many of them have not considered the effect of intermediary resources on plant-pollinator associations (Morales, Morris, & Wilson, 2008). For convenience, the intermediary resources are represented by nectar in this study. Vannette, Gauthier, and Fukami (2013) performed experiments and exhibited that it is neces...

show abstract

Spreading-vanishing dichotomy in information diffusion in online social networks with intervention

Cited by 9 publications

References 24 publications

Positive periodic solution for generalized Basener-Ross model

Positive periodic solution for generalized Basener-Ross model

Linear difference operator with multiple variable parameters and applications to second-order differential equations

Persistence of pollination‐mutualisms under the effect of intermediary resource

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