12 research outputs found
Suppression of growth by multiplicative white noise in a parametric resonant system
The author studied the growth of the amplitude in a Mathieu-like equation
with multiplicative white noise. The approximate value of the exponent at the
extremum on parametric resonance regions was obtained theoretically by
introducing the width of time interval, and the exponents were calculated
numerically by solving the stochastic differential equations by a symplectic
numerical method. The Mathieu-like equation contains a parameter that
is determined by the intensity of noise and the strength of the coupling
between the variable and the noise. The value of was restricted not to
be negative without loss of generality. It was shown that the exponent
decreases with , reaches a minimum and increases after that. It was
also found that the exponent as a function of has only one minimum at
on parametric resonance regions of . This minimum
value is obtained theoretically and numerically. The existence of the minimum
at indicates the suppression of the growth by multiplicative
white noise.Comment: The title and the description in the manuscript are change
The interplay of intrinsic and extrinsic bounded noises in genetic networks
After being considered as a nuisance to be filtered out, it became recently
clear that biochemical noise plays a complex role, often fully functional, for
a genetic network. The influence of intrinsic and extrinsic noises on genetic
networks has intensively been investigated in last ten years, though
contributions on the co-presence of both are sparse. Extrinsic noise is usually
modeled as an unbounded white or colored gaussian stochastic process, even
though realistic stochastic perturbations are clearly bounded. In this paper we
consider Gillespie-like stochastic models of nonlinear networks, i.e. the
intrinsic noise, where the model jump rates are affected by colored bounded
extrinsic noises synthesized by a suitable biochemical state-dependent Langevin
system. These systems are described by a master equation, and a simulation
algorithm to analyze them is derived. This new modeling paradigm should enlarge
the class of systems amenable at modeling.
We investigated the influence of both amplitude and autocorrelation time of a
extrinsic Sine-Wiener noise on: the Michaelis-Menten approximation of
noisy enzymatic reactions, which we show to be applicable also in co-presence
of both intrinsic and extrinsic noise, a model of enzymatic futile cycle
and a genetic toggle switch. In and we show that the
presence of a bounded extrinsic noise induces qualitative modifications in the
probability densities of the involved chemicals, where new modes emerge, thus
suggesting the possibile functional role of bounded noises
Gene switching rate determines response to extrinsic perturbations in the self-activation transcriptional network motif
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