Mathematical Models of Quasi-Species Theory and Exact Results for the Dynamics

2015 ◽  
pp. 121-139 ◽  
Author(s):  
David B. Saakian ◽  
Chin-Kun Hu
Keyword(s):  
Mathematical Models ◽  
Exact Results

scholarly journals DICHOTOMOUS MARKOV NOISE: EXACT RESULTS FOR OUT-OF-EQUILIBRIUM SYSTEMS

2006 ◽  
Vol 20 (20) ◽  
pp. 2825-2888 ◽  
Author(s):  
IOANA BENA
Keyword(s):  
Mathematical Models ◽  
White Noise ◽  
Gaussian White Noise ◽  
Stokes Drift ◽  
Nonequilibrium Systems ◽  
Exact Results ◽  
Asymptotic Regime ◽  
Practical Applications ◽  
Long Time ◽  
Physical And Mathematical Models

Nonequilibrium systems driven by additive or multiplicative dichotomous Markov noise appear in a wide variety of physical and mathematical models. We review here some prototypical examples, with an emphasis on analytically-solvable situations. In particular, it has escaped attention till recently that the standard results for the long-time properties of such systems cannot be applied when unstable fixed points are crossed in the asymptotic regime. We show how calculations have to be modified to deal with these cases and present a few relevant applications — the hypersensitive transport, the rocking ratchet, and the stochastic Stokes' drift. These results reinforce the impression that dichotomous noise can be put on par with Gaussian white noise as far as obtaining analytical results is concerned. They convincingly illustrate the interplay between noise and nonlinearity in generating nontrivial behaviors of nonequilibrium systems and point to various practical applications.

Handbook of Mathematical Models for Languages and Computation

2019 ◽  
Author(s):  
Alexander Meduna ◽  
Petr Horacek ◽  
Martin Tomko
Keyword(s):  
Mathematical Models

Erratum - Frustration in periodic systems : exact results for some 2D ising models

1979 ◽  
Vol 40 (10) ◽  
pp. 1024-1024
Author(s):  
G. André ◽  
R. Bidaux ◽  
J.-P. Carton ◽  
R. Conte ◽  
L. de Seze
Keyword(s):  
Ising Models ◽  
Periodic Systems ◽  
Exact Results
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