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- Slaven Peles, Brian Munsky, Mustafa Khammash
- The Journal of chemical physics
- 2006

The dynamics of chemical reaction networks often takes place on widely differing time scales--from the order of nanoseconds to the order of several days. This is particularly true for gene regulatory networks, which are modeled by chemical kinetics. Multiple time scales in mathematical models often lead to serious computational difficulties, such as… (More)

Considerable recent experimental evidence suggests that significant stochastic fluctuations are present in gene regulatory networks. The investigation of stochastic properties in genetic systems involves the formulation of a mathematical representation of molecular noise and devising efficient computational algorithms for computing the relevant statistics… (More)

We present a general approach to the study of synchrony in networks of weakly nonlinear systems described by singularly perturbed equations of the type x′′ + x + f(x, x′) = 0. By performing a perturbative calculation based on normal form theory we analytically obtain an O( ) approximation to the Floquet multipliers that determine the stability of the… (More)

- Sunil Ahuja, Slaven Peles
- CDC
- 2013

Gene network dynamics often involves processes that take place on widely differing time scales – from the order of nanoseconds to the order of several days. Multiple time scales in mathematical models often lead to serious computational difficulties, such as numerical stiffness in the case of differential equations or excessively redundant Monte Carlo… (More)

- Slaven Peles, Stefan Klus
- ArXiv
- 2015

Most numerical solvers and libraries nowadays are implemented to use mathematical models created with language-specific built-in data types (e.g. real in Fortran or double in C) and their respective elementary algebra implementations. However, built-in elementary algebra typically has limited functionality and often restricts flexibility of mathematical… (More)

We present a general approach to the study of synchrony in networks of weakly nonlinear, quasi-harmonic oscillators, described by equations of the type x′′ + x + f(x, x′) = 0. By performing a perturbative calculation based on normal form theory we analytically obtain an O( ) approximation to the eigenvalues that determine the stability of the synchronous,… (More)

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