On controlling stochastic sensitivity of oscillatory systems

For a nonlinear oscillatory stochastic system, we study the control problem for the variance of random trajectories around a deterministic cycle. To describe the range of random trajectories, we use the method of stochastic sensitivity functions. We consider the problem of designing a given stochastic sensitivity function, discuss problems of controllability and reachability. Complete stochastic controllability is only possible when the control's dimension coincides with the system's dimension. Otherwise, the design problem becomes ill-posed. To solve it, we propose a regularization method that lets us produce a given stochastic sensitivity function with any given precision. The efficiency of the proposed approach is demonstrated with the example of controlling stochastic oscillations in a brusselator model. © 2013 Pleiades Publishing, Ltd

Nonlinear dynamics of mushy layers induced by external stochastic fluctuations

The time-dependent process of directional crystallization in the presence of a mushy layer is considered with allowance for arbitrary fluctuations in the atmospheric temperature and friction velocity. A nonlinear set of mushy layer equations and boundary conditions is solved analytically when the heat and mass fluxes at the boundary between the mushy layer and liquid phase are induced by turbulent motion in the liquid and, as a result, have the corresponding convective form. Namely, the ‘solid phase–mushy layer’ and ‘mushy layer–liquid phase’ phase transition boundaries as well as the solid fraction, temperature and concentration (salinity) distributions are found. If the atmospheric temperature and friction velocity are constant, the analytical solution takes a parametric form. In the more common case when they represent arbitrary functions of time, the analytical solution is given by means of the standard Cauchy problem. The deterministic and stochastic behaviour of the phase transition process is analysed on the basis of the obtained analytical solutions. In the case of stochastic fluctuations in the atmospheric temperature and friction velocity, the phase transition interfaces (mushy layer boundaries) move faster than in the deterministic case. A cumulative effect of these noise contributions is revealed as well. In other words, when the atmospheric temperature and friction velocity fluctuate simultaneously due to the influence of different external processes and phenomena, the phase transition boundaries move even faster. This article is part of the theme issue ‘From atomistic interfaces to dendritic patterns’. 10.1098/rsta.2017.0216Ministry of Education and Science of the Russian Federation, Minobrnauka: 1.9527.2017/8.9Data accessibility. This article has no additional data. Authors’ contributions. All authors contributed equally to the present research article. Competing interests. We declare we have no competing interests. Funding. This work was supported by the Ministry of Education and Science of the Russian Federation (project no. 1.9527.2017/8.9)

Stochastic Analysis and Control in Kinetics of Multistable Chemical Reactor

We consider a model of thermochemical reactor proposed by Nowakowski. Stochastic effects in the bistability zone are studied. A parametric analysis of noise-induced transitions between coexisting equilibria is carried out on the basis of the stochastic sensitivity technique and confidence ellipses method. We solve the problem of stabilization of the equilibrium regime under incomplete information. The feedback regulator which reduces the stochastic sensitivity and stabilizes the randomly forced equilibrium is constructed. © 201

Analysis of multimodal stochastic oscillations in a biochemical reaction model

This paper studies the dynamics of the two-dimensional biochemical Goldbeter model under the influence of random disturbances. The model describes an enzymatic reaction with nonlinear recirculation of a product into a substrate. We investigate parametric zones where the system exhibits the phenomenon of bistability: the coexistence of two stable periodic regimes or the coexistence of a stable equilibrium and a stable limit cycle. The noise-induced transitions of stochastic trajectories between deterministic attractors resulting in multimodal oscillations are demonstrated via the direct numerical simulation. It is shown how the effect of noise on the system changes the frequency and amplitude characteristics of stochastic self-oscillations. © 2019 Udmurt State University. All right reserved.Russian Science Foundation, RSF: 16–11–10098Funding. This work was supported by the Russian Science Foundation (project no. 16–11–10098)

Solidification dynamics under random external-temperature fluctuations

The nonlinear dynamic mechanisms of solid-phase formation with a phase transition region are studied under periodic and random fluctuations of the cooling-boundary temperature. It is theoretically shown that a mushy zone can form even at close liquid and cooling-boundary temperatures due to random temperature field fluctuations. The growth of a solid phase with the mushy zone is investigated as a function of the autocovariance characteristics of random noises. © 2013 Pleiades Publishing, Ltd

Sea Ice Dynamics Induced by External Stochastic Fluctuations

The influence of stochastic fluctuations in the atmosphere and in the ocean caused by different occasional phenomena (noises) on dynamic processes of sea ice growth with a mushy layer is studied. It is shown that atmospheric temperature variances substantially increase the sea ice thickness, whereas dispersion variations of turbulent flows in the ocean to a great extent decrease the ice content produced by false bottom evolution. © 2013 Springer Basel

Stochastic multimodal oscillations in nonlinear biochemical model

We consider the influence of random noise on the dynamic regimes of one nonlinear biochemical model with nonlinear recycling of product into substrate. In the deterministic case this model admits either mono- or bistable zones. In the monostable zone, random disturbances result in mixed-mode stochastic oscillations. For a constructive research of noise-induced phenomena, we apply a direct numerical simulations and statistics of stochastic oscillations. © 2019 Author(s)

Stochastic multimodal oscillations in nonlinear biochemical model

We consider the influence of random noise on the dynamic regimes of one non-linear biochemical model. The model admits either mono- or bistable zones. In the monosta-ble zone stochastic excitability arise resulting in large-amplitude oscillations. In the bistable zone noise-induced transitions between the attractors are of interest. For a constructive research of these phenomena, we apply a theoretical approach using confidence domains method and stochastic sensitivity analysis.The work was supported by Russian Science Foundation (№16-11-10098)