Effects Of Internal Fluctuations Research Articles

Mathematical modeling of spatial-temporal structures in a heterogeneous catalytic system

The article focuses on mathematical modeling of the spatial-temporal structures that appear in a heterogeneous catalytic reaction on the surface of a catalyst. A system of consistent mathematical models has been developed for a three-component reaction, describing self-organization phenomena on macro, meso, and micro levels. Qualitative analysis of the solutions of the ODE system (macro level) produces the existence regions of spatial-temporal structures of various types in distributed meso- and micro-level models. A point model is applied to predict the shape of traveling impulses and fronts; the switching direction in a bistable medium is determined analytically. Solutions constructed and investigated for a PDE multicomponent reaction-diffusion system describe trigger waves, single traveling impulses, phase and spiral waves. Spatial-temporal structures on the atomic level are investigated by the Monte Carlo method. Direct and inverse trigger waves are implemented, as well as single traveling impulses and spiral waves. The effect of internal fluctuations in the reaction system is investigated.

Global stability analysis and robust design of multi-time-scale biological networks under parametric uncertainties

Biological networks are prone to internal parametric fluctuations and external noises. Robustness represents a crucial property of these networks, which militates the effects of internal fluctuations and external noises. In this paper biological networks are formulated as coupled nonlinear differential systems operating at different time-scales under vanishing perturbations. In contrast to previous work viewing biological parametric uncertain systems as perturbations to a known nominal linear system, the perturbed biological system is modeled as nonlinear perturbations to a known nonlinear idealized system and is represented by two time-scales (subsystems). In addition, conditions for the existence of a global uniform attractor of the perturbed biological system are presented. By using an appropriate Lyapunov function for the coupled system, a maximal upper bound for the fast time-scale associated with the fast state is derived. The proposed robust system design principles are potentially applicable to robust biosynthetic network design. Finally, two examples of two important biological networks, a neural network and a gene regulatory network, are presented to illustrate the applicability of the developed theoretical framework.

Oscillatory Dynamics of CO Oxidation on Platinum-Group Metal Catalysts

Rate oscillations are theoretically studied for the CO + O2 reaction proceeding according to a modified Langmuir-Hinshelwood mechanism on a platinum-group metal catalyst. A new hierarchical system of consistent mathematical models is suggested for the identification of oscillatory regimes in the stochastic model. This system includes the stochastic model based on the Monte Carlo method and a point deterministic model in the medium field approximation. Three fundamentally different types of oscillatory behavior of the stochastic model are revealed and studied. These are kinetic oscillations corresponding to autooscillations of the point model, fluctuation-induced oscillations occurring in an excitable medium in the region of the unique stable stationary solution of the point model, and fluctuation-induced random phase transitions between stable stationary solutions of the point model in the bistability region. The effect of internal fluctuations (which are inherent in stochastic models) on the oscillatory dynamics of the reaction is studied.

Effects of internal fluctuations on the spreading of Hantavirus

We study the spread of Hantavirus over a host population of deer mice using a population dynamics model. We show that taking into account the internal fluctuations in the mouse population due to its discrete character strongly alters the behavior of the system. In addition to the familiar transition present in the deterministic model, the inclusion of internal fluctuations leads to the emergence of an additional deterministically hidden transition. We determine parameter values that lead to maximal propagation of the disease and discuss some implications for disease prevention policies.

Numerical schemes for continuum models of reaction-diffusion systems subject to internal noise

We present numerical schemes to integrate stochastic partial differential equations which describe the spatio-temporal dynamics of reaction-diffusion problems under the effect of internal fluctuations. The schemes conserve the non-negativity of the solutions and incorporate the Poissonian nature of internal fluctuations at small densities, their performance being limited by the level of approximation of density fluctuations at small scales. We apply the schemes to two different aspects of the Reggeon model, namely, the study of its nonequilibrium phase transition and the dynamics of fluctuating pulled fronts. In the latter case, our approach allows us to reproduce microscopic properties quantitatively within the continuum model.

Internal fluctuations in a model of chemical chaos.

The effect of internal fluctuations in chaotic systems is studied for the case of the Williamowski-R\"ossler model. In this system the strange attractor coexists with a stable fixed point, and it is shown that internal fluctuations may induce a transition between these two situations. Simulations are performed with the stochastic method due to Gillespie [J. Comput. Phys. 22, 403 (1976); J. Phys. Chem. 81, 2340 (1977)], and the conclusions are verified by representing the intrinsic fluctuations in the form of a multiplicative external noise.

Microscopic spatial correlations induced by external noise in a reaction-diffusion system

The reversible single species reaction scheme X ↔ 2X has long served as an example of a system with nonlinear macroscopic dynamics. In recent years a microscopic version of this interacting particle system, namely the diffusion-controlled limit, has been solved exactly in one spatial dimension. The effects of internal fluctuations, correlations arising in nonequilibrium situations, and external noise can all be studied in this model diffusion-reaction system without approximation. Here we review some recent results, focusing on an exact treatment of the effect of spatially homogeneous temporal fluctuations in the growth rate of the process (the rate for the X → 2X process). We find that the nonequilibrium steady state possesses new microscopic length scales resulting from the nonequilibrium constraints, demonstrating that spatially homogeneous external noise can introduce spatial correlations.

Effect of Internal Fluctuations and Scanning on Clutter Attenuation in MTI Radar

The approximate effect of internal fluctuations and scanning on clutter attenuation in MTI radar is derived and the results presented on two charts. It is proposed that derivative antenna patterns be used to increase the clutter attenuation when scanning. The theoretical improvement from the use of derivatives is appreciable, as shown on the second chart.