Connectivity of growing networks with link constraints

Jin, Ke; Li, Pengyue; Chen, X.-S.; Lin, Zhenkun; Zheng, Yizhuang

doi:10.1140/epjb/e2009-00211-7

Cited by 1 publication

(1 citation statement)

References 25 publications

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“…[42] Recently, Ke et al proposed a controlled particle deposition model for cluster growth on the substrate surface and then presented exact results for the cluster size distribution. [28] Furthermore, Ben-Naim et al studied models for the development of disparate social classes in a competitive population, where individuals advance their fitness by competing against those in lower classes, and in parallel, individuals decline due to inactivity. [43,44] Moreover, researchers have carried out many studies in terms of infection.…”

Section: Introductionmentioning

confidence: 99%

Dynamic models of pest propagation and pest control

Yin¹,

Zhang²,

Ke³

2011

Chinese Phys. B

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This paper proposes a pest propagation model to investigate the evolution behaviours of pest aggregates. A pest aggregate grows by self-monomer birth, and it may fragment into two smaller ones. The kinetic evolution behaviours of pest aggregates are investigated by the rate equation approach based on the mean-field theory. For a system with a self-birth rate kernel I(k) = Ik and a fragmentation rate kernel L(i, j) = L, we find that the total number M A 0 (t) and the total mass of the pest aggregates M A 1 (t) both increase exponentially with time if L = 0. Furthermore, we introduce two catalysis-driven monomer death mechanisms for the former pest propagation model to study the evolution behaviours of pest aggregates under pesticide and natural enemy controlled pest propagation. In the pesticide controlled model with a catalyzed monomer death rate kernel J 1 (k) = J 1 k, it is found that only when I < J 1 B 0 (B 0 is the concentration of catalyst aggregates) can the pests be killed off. Otherwise, the pest aggregates can survive. In the model of pest control with a natural enemy, a pest aggregate loses one of its individuals and the number of natural enemies increases by one. For this system, we find that no matter how many natural enemies there are at the beginning, pests will be eliminated by them eventually.

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