scholarly journals A Sharp Threshold for a Modified Bootstrap Percolation with Recovery

2014 ◽  
Vol 157 (3) ◽  
pp. 531-570 ◽  
Author(s):  
Tom Coker ◽  
Karen Gunderson
Keyword(s):  
Bootstrap Percolation ◽  
Sharp Threshold

scholarly journals The sharp threshold for bootstrap percolation in all dimensions

2012 ◽  
Vol 364 (5) ◽  
pp. 2667-2701 ◽  
Author(s):  
József Balogh ◽  
Béla Bollobás ◽  
Hugo Duminil-Copin ◽  
Robert Morris
Keyword(s):  
Bootstrap Percolation ◽  
Sharp Threshold

Transport through bootstrap percolation clusters

1991 ◽  
Vol 1 (5) ◽  
pp. 685-692 ◽  
Author(s):  
Muhammad Sahimi ◽  
Tane S. Ray
Keyword(s):  
Bootstrap Percolation ◽  
Percolation Clusters

scholarly journals Uniform persistence and almost periodic solutions of a nonautonomous patch occupancy model

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Hui Zhou ◽  
Jehad Alzabut ◽  
Shahram Rezapour ◽  
Mohammad Esmael Samei
Keyword(s):  
Differential Inequality ◽  
Almost Periodic Solution ◽  
Rocky Intertidal ◽  
Uniform Persistence ◽  
Almost Periodic ◽  
Patch Occupancy ◽  
Sharp Threshold ◽  
Intertidal Community ◽  
Patch Occupancy Model ◽  
Inequality Techniques

Abstract In this paper, a nonlinear nonautonomous model in a rocky intertidal community is studied. The model is composed of two species in a rocky intertidal community and describes a patch occupancy with global dispersal of propagules and occupy each other by individual organisms. Firstly, we study the uniform persistence of the model via differential inequality techniques. Furthermore, a sharp threshold of global asymptotic stability and the existence of a unique almost periodic solution are derived. To prove the main results, we construct an appropriate Lyapunov function whose conditions are easily verified. The assumptions of the model are reasonable, and the results complement previously known ones. An example with specific values of parameters is included for demonstration of theoretical outcomes.

A multigroup model for cholera dynamics and control

2015 ◽  
Vol 09 (01) ◽  
pp. 1650001 ◽  
Author(s):  
Drew Posny ◽  
Chairat Modnak ◽  
Jin Wang
Keyword(s):  
Reproduction Number ◽  
Vaccination Strategy ◽  
Sharp Threshold ◽  
Indirect Transmission ◽  
Dynamics And Control ◽  
Simulation Results ◽  
Transmission Pathways ◽  
And Control ◽  
Control Study ◽  
The Basic Reproduction Number

We propose a general multigroup model for cholera dynamics that involves both direct and indirect transmission pathways and that incorporates spatial heterogeneity. Under biologically feasible conditions, we show that the basic reproduction number R0 remains a sharp threshold for cholera dynamics in multigroup settings. We verify the analysis by numerical simulation results. We also perform an optimal control study to explore optimal vaccination strategy for cholera outbreaks.

Comparison of bootstrap percolation models

1989 ◽  
Vol 22 (7) ◽  
pp. L297-L301 ◽  
Author(s):  
J Adler ◽  
D Stauffer ◽  
A Aharony
Keyword(s):  
Bootstrap Percolation

Bootstrap percolation on certain branching media

1983 ◽  
Vol 16 (32) ◽  
pp. 6263-6274 ◽  
Author(s):  
Y S Yang ◽  
Z Q Zhang
Keyword(s):  
Bootstrap Percolation

scholarly journals Bootstrap Percolation on a Graph with Random and Local Connections

2015 ◽  
Vol 160 (5) ◽  
pp. 1249-1276 ◽  
Author(s):  
Tatyana S. Turova ◽  
Thomas Vallier
Keyword(s):  
Bootstrap Percolation

scholarly journals THRESHOLD VALUE OF THREE-DIMENSIONAL BOOTSTRAP PERCOLATION

2003 ◽  
Vol 14 (04) ◽  
pp. 529-536 ◽  
Author(s):  
DIRK KURTSIEFER
Keyword(s):  
Present Article ◽  
Three Dimensional ◽  
Threshold Value ◽  
Critical Value ◽  
Bootstrap Percolation ◽  
Infinite Lattice

The present article deals with the critical value pc of the three-dimensional bootstrap percolation. We will check the behavior of pc for different lengths of the lattice and additionally we will scale pc in the limit of an infinite lattice.

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