Coloured-noise-induced transport in a model of the thermochemical reactor

In this paper, effects of coloured noise on the stochastic excitement in a model of the thermochemical flow reactor are studied. Transport phenomena associated with noise-induced generation of large-amplitude oscillations are investigated depending on the correlation time of coloured noise. We study how probability of the noise-induced excitement is related to the stochastic sensitivity of the system to coloured noise with certain correlation characteristics. Parameter zones of the high stochastic sensitivity are found and discussed in connection with occurrence of resonance. This article is part of the theme issue ‘Transport phenomena in complex systems (part 2)’.

Controlling Stochastic Sensitivity by Feedback Regulators in Nonlinear Dynamical Systems with Incomplete Information

The problem of synthesis of stochastic sensitivity for equilibrium modes in nonlinear randomly forced dynamical systems with incomplete information is considered. We construct a feedback regulator that uses noisy data on some system state coordinates. For parameters of the regulator providing assigned stochastic sensitivity, a quadratic matrix equation is derived. Attainability of the assigned stochastic sensitivity is reduced to the solvability of this equation. We suggest a constructive algorithm for solving this quadratic matrix equation. These general theoretical results are used to solve the problem of stabilizing equilibrium modes of nonlinear stochastic oscillators under conditions of incomplete information. Details of our approach are illustrated on the example of a van der Pol oscillator.

Research on Mechanical Properties and Parameter Identification of Beam-Column Joint with Gusset Plate Angle Using Experiment and Stochastic Sensitivity Analysis

Based on stochastic sensitivity analysis, a new style of joint structure with greater ductility and higher strength—the beam-column joint with gusset plate angle (JGA) steel—was proposed. Research on the static and hysteretic behavior of the JGA was performed using finite element analysis and experimental methods. The research results indicated that adding a seat angle could increase the positive and negative initial rotational stiffness and strength and provide a better energy consumption performance of the joint. An improved chaotic particle swarm optimization (ICPSO) neural network algorithm was used to study the stochastic sensitivity. Seven important parameters that influence the bending stiffness and strength of the JGA, namely, the beam height, beam flange width, beam web thickness, gusset plate thickness, connection angle steel thickness, connection angle steel width, and seat angle steel thickness, were investigated by stochastic sensitivity analysis. Moreover, the beam height, connection angle steel, and seat angle steel thickness, which had significant influences on the mechanical properties of the joints, were studied in depth by finite element analysis. Within the range of the parameters of the joint, the higher the beam height was, the larger the connection angle thickness was; the smaller the connection angle width was, the better the joint performance was. A reasonable design of the JGA is proposed: a beam with the SH2 section (250 × 125 × 6 × 9 mm) and a 10 mm thick and 75 mm long angle steel connection.

Stochastic sensitivity of bull and bear states

We study the price dynamics generated by a stochastic version of a Day–Huang type asset market model with heterogenous, interacting market participants. To facilitate the analysis, we introduce a methodology that allows us to assess the consequences of changes in uncertainty on the dynamics of an asset price process close to stable equilibria. In particular, we focus on noise-induced transitions between bull and bear states of the market under additive as well as parametric noise. Our results are obtained by combining the stochastic sensitivity function (SSF) approach, a mixture of analytical and numerical techniques, due to Mil’shtein and Ryashko (1995) with concepts and techniques from the study of non-smooth 1D maps. We find that the stochastic sensitivity of the respective bull and bear equilibria in the presence of additive noise is higher than under parametric noise. Thus, recurrent transitions are likely to be observed already for relatively low intensities of additive noise.