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In this paper, we present a framework for investigating coloured noise in reaction-diffusion systems. We start by considering a deterministic reaction-diffusion equation and show how external forcing can cause temporally correlated or coloured noise. Here, the main source of external noise is considered to be fluctuations in the parameter values representing the inflow of particles to the system. First, we determine which reaction systems, driven by extrinsic noise, can admit only one steady state, so that effects, such as stochastic switching, are precluded from our analysis. To analyse the steady-state behaviour of reaction systems, even if the parameter values are changing, necessitates a parameter-free approach, which has been central to algebraic analysis in chemical reaction network theory. To identify suitable models, we use tools from real algebraic geometry that link the network structure to its dynamical properties. We then make a connection to internal noise models and show how power spectral methods can be used to predict stochastically driven patterns in systems with coloured noise. In simple cases, we show that the power spectrum of the coloured noise process and the power spectrum of the reaction-diffusion system modelled with white noise multiply to give the power spectrum of the coloured noise reaction-diffusion system.
This article was published in the following journal.
Name: Bulletin of mathematical biology
The stochastic nature of chemical reaction and impact of the stochasticity on their evolution is soundly documented. Both theoretical predictions and emerging experimental evidence indicate the influe...
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This study evaluates the effectiveness of stochastic resonance electric stimulation on neuromuscular control and proprioception in healthy and individuals with stroke.
The effect of noise is often underestimated but it is one of the most common occupational health hazards. Its health effects include; noise-induced hearing loss, sleep disturbance, interfe...
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A diagnostic technique that incorporates the measurement of molecular diffusion (such as water or metabolites) for tissue assessment by MRI. The degree of molecular movement can be measured by changes of apparent diffusion coefficient (ADC) with time, as reflected by tissue microstructure. Diffusion MRI has been used to study BRAIN ISCHEMIA and tumor response to treatment.
The use of diffusion ANISOTROPY data from diffusion magnetic resonance imaging results to construct images based on the direction of the faster diffusing molecules.
Noise present in occupational, industrial, and factory situations.
The tendency of a gas or solute to pass from a point of higher pressure or concentration to a point of lower pressure or concentration and to distribute itself throughout the available space. Diffusion, especially FACILITATED DIFFUSION, is a major mechanism of BIOLOGICAL TRANSPORT.
Noise associated with transportation, particularly aircraft and automobiles.