scholarly journals Exact Stationary Solution Method for the Wadati-Konno-Ichikawa-Shimizu (WKIS) Equation

2012 ◽  
Vol 128 (5) ◽  
pp. 993-999 ◽  
Author(s):  
R. A. V. Gorder
Keyword(s):  
Stationary Solution ◽  
Solution Method ◽  
Exact Stationary Solution

Atom in a resonant elliptically polarized field: the exact stationary solution

2002 ◽  
Author(s):  
A. V. Taichenachev ◽  
A. M. Tumaikin ◽  
V. I. Yudin ◽  
G. Nienhuis
Keyword(s):  
Stationary Solution ◽  
Exact Stationary Solution ◽  
Elliptically Polarized

MATHEMATICAL DESCRIPTION OF A SIMPLE AGING MODEL

2005 ◽  
Vol 16 (04) ◽  
pp. 571-576
Author(s):  
MINGFENG HE ◽  
HUI YUE
Keyword(s):  
Stationary Solution ◽  
Difference Equations ◽  
Mathematical Description ◽  
Biological Aging ◽  
Aging Model ◽  
Exact Stationary Solution

We present difference equations for the simple biological aging model, which is called Stauffer model, and obtain the corresponding expression of the exact stationary solution. Considering numerically iterated solutions to those difference equations, we find that the result of iterated simulations is similar to the simulations of Stauffer model.

An Aggregation/Disaggregation Algorithm for Stochastic Automata Networks

1997 ◽  
Vol 11 (2) ◽  
pp. 229-253 ◽  
Author(s):  
Peter Buchholz
Keyword(s):  
Markov Chains ◽  
Stationary Solution ◽  
Solution Method ◽  
Compact Representation ◽  
Generator Matrix ◽  
Iterative Techniques ◽  
Stochastic Automata ◽  
Loosely Coupled ◽  
Automata Networks ◽  
Solution Methods

Stochastic automata networks (SANs) have recently received much attention in the literature as a means to analyze complex Markov chains in an efficient way. The main advantage of SANs over most other paradigms is that they allow a very compact description of the generator matrix by means of much smaller matrices for single automata. This representation can be exploited in different iterative techniques to compute the stationary solution. However, the set of applicable solution methods for SANs is restricted, because a solution method has to respect the specific representation of the generator matrix to exploit the compact representation. In particular, aggregation/disaggregation (a/d) methods cannot be applied in their usual realization for SANs without losing the possibility to exploit the compact representation of the generator matrix.In this paper, a new a/d algorithm for SANs is introduced. The algorithm differs significantly from standard a/d methods because the parts to be aggregated are defined in a completely different way, exploiting the structure of the generator matrix of a SAN. Aggregation is performed with respect to single automata or sets of automata, which are the basic parts generating a SAN. It is shown that the new algorithm is efficient even if the automata are not loosely coupled.

Sign in / Sign up

Export Citation Format

Share Document