scholarly journals Graph Constructions for the Contact Process with a Prescribed Critical Rate

2021 ◽  
Author(s):  
Stein Andreas Bethuelsen ◽  
Gabriel Baptista da Silva ◽  
Daniel Valesin
Keyword(s):  
Contact Process ◽  
Critical Value ◽  
Critical Rate ◽  
Bounded Degree ◽  
One Dimensional ◽  
Local Survival ◽  
The One ◽  
Global And Local

AbstractWe construct graphs (trees of bounded degree) on which the contact process has critical rate (which will be the same for both global and local survival) equal to any prescribed value between zero and $$\lambda _c({\mathbb {Z}})$$ λ c ( Z ) , the critical rate of the one-dimensional contact process. We exhibit both graphs in which the process at this target critical value survives (locally) and graphs where it dies out (globally).

On the critical infection rate of the one-dimensional basic contact process: numerical results

1988 ◽  
Vol 25 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Herbert Ziezold ◽  
Christian Grillenberger
Keyword(s):  
Markov Process ◽  
Infected Cell ◽  
Infection Rate ◽  
Lower Bounds ◽  
Contact Process ◽  
Critical Value ◽  
Critical Values ◽  
One Dimensional ◽  
The One ◽  
The Right

Instead of the basic contact process on with infection rate λ we consider for m ≧ 0 the Markov process starting with ξ0(k) = 1 for k ≧ 0 and ξ0(k)= 0 for k < 0 and with changing only those k which are at most m places to the right of the left-most infected cell. For m = 0, 1,· ··, 14 direct computations give critical values which are lower bounds for the critical value of the original basic contact process.

CORRELATION IDENTITIES FOR NEAREST-PARTICLE SYSTEMS AND THEIR APPLICATIONS TO ONE-DIMENSIONAL CONTACT PROCESS

1991 ◽  
Vol 05 (02) ◽  
pp. 151-159 ◽  
Author(s):  
NORIO KONNO ◽  
MAKOTO KATORI
Keyword(s):  
Order Parameter ◽  
Particle System ◽  
Contact Process ◽  
Critical Value ◽  
Particle Systems ◽  
Approximation Formula ◽  
One Dimensional ◽  
Renewal Measure ◽  
First Approximation ◽  
The One

A series of identities of correlation functions K(n1, n2, …, nN) are given in the nearest-particle system. The above correlation identities are applied to the one-dimensional contact process. The decoupling induced by a renewal measure yields the first approximation: [Formula: see text] for the critical value and [Formula: see text] for the order parameter, which makes a rigorous bound as proved by Holley and Liggett. Furthermore, introducing a new decoupling procedure, improved estimations of [Formula: see text] and [Formula: see text] are calculated.

On the critical infection rate of the one-dimensional basic contact process: numerical results

1988 ◽  
Vol 25 (01) ◽  
pp. 1-8 ◽  
Author(s):  
Herbert Ziezold ◽  
Christian Grillenberger
Keyword(s):  
Markov Process ◽  
Infected Cell ◽  
Infection Rate ◽  
Lower Bounds ◽  
Contact Process ◽  
Critical Value ◽  
Critical Values ◽  
One Dimensional ◽  
The One ◽  
The Right

Instead of the basic contact process on with infection rate λ we consider for m ≧ 0 the Markov process starting with ξ 0(k) = 1 for k ≧ 0 and ξ 0(k)= 0 for k &lt; 0 and with changing only those k which are at most m places to the right of the left-most infected cell. For m = 0, 1,· ··, 14 direct computations give critical values which are lower bounds for the critical value of the original basic contact process.

Large-density fluctuations for the one-dimensional supercritical contact process

1989 ◽  
Vol 55 (3-4) ◽  
pp. 639-648 ◽  
Author(s):  
Antonio Galves ◽  
Fabio Martinelli ◽  
Enzo Olivieri
Keyword(s):  
Contact Process ◽  
Density Fluctuations ◽  
One Dimensional ◽  
Large Density ◽  
The One

A Note on Hidden Transient Chaos in the Lorenz System

2017 ◽  
Vol 18 (5) ◽  
pp. 427-434 ◽  
Author(s):  
Quan Yuan ◽  
Fang-Yan Yang ◽  
Lei Wang
Keyword(s):  
Rayleigh Number ◽  
Lorenz System ◽  
Critical Value ◽  
Transient Chaos ◽  
Topological Horseshoe ◽  
One Dimensional ◽  
Dynamical Behaviors ◽  
The Lorenz System ◽  
The One

AbstractIn this paper, the classic Lorenz system is revisited. Some dynamical behaviors are shown with the Rayleigh number $\rho $ somewhat smaller than the critical value 24.06 by studying the basins characterization of attraction of attractors and tracing the one-dimensional unstable manifold of the origin, indicating some interesting clues for detecting the existence of hidden transient chaos. In addition, horseshoes chaos is verified in the famous system for some parameters corresponding to the hidden transient chaos by the topological horseshoe theory.

On a semilinear equation in ℝ2 involving bounded measures

1983 ◽  
Vol 95 (3-4) ◽  
pp. 181-202 ◽  
Author(s):  
Juan L. Vazquez
Keyword(s):  
Real Function ◽  
Radon Measure ◽  
Existence Of Solutions ◽  
Critical Value ◽  
Existence Of A Solution ◽  
One Dimensional ◽  
Semilinear Equation ◽  
The One

SynopsisWe study the semilinear equation –Δu + β(u) = f in ℝ2, where β is a continuous increasing real function with β(0) = 0 and f is a bounded Radon measure. We show the existence of a solution, which is unique in the appropriate class, provided that each of the point masses contained in f does not exceed some critical value denned in terms of the growth of (β at ∞ This condition is shown to be necessary for the existence of solutions, even locally. The one-dimensional situation is also discussed.

scholarly journals Edge Fluctuations for the One Dimensional Supercritical Contact Process

1987 ◽  
Vol 15 (3) ◽  
pp. 1131-1145 ◽  
Author(s):  
Antonio Galves ◽  
Errico Presutti
Keyword(s):  
Contact Process ◽  
One Dimensional ◽  
The One

scholarly journals Revisiting the one-dimensional diffusive contact process

2007 ◽  
Vol 2007 (08) ◽  
pp. P08009-P08009 ◽  
Author(s):  
W G Dantas ◽  
M J de Oliveira ◽  
J F Stilck
Keyword(s):  
Contact Process ◽  
One Dimensional ◽  
The One
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