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For example, at low turbulence levels, an increase in global burning rate leads to an increase in the turbulence level, while beyond a critical turbulence level, the expanding flame becomes increasingly fragmented, and consequently, the total burning rate decreases with increasing turbulence. Furthermore, at an extremely high turbulence level, the ignition kernel quenches at its nascent state and consequently loses its ability to propagate as an expanding flame.This Focus Issue on instabilities and nonequilibrium structures includes invited contributions from leading researchers across many different fields. The issue was inspired in part by the "VII Instabilities and Nonequilibrium Structures 2019" conference that took place at the Pontifica Universidad Católica de Valparaiso, Chile in December 2019. The conference, which is devoted to nonlinear science, is one of the oldest conferences in South America (since December 1985). This session has an exceptional character since it coincides with the 80th anniversary of Professor Enrique Tirapegui. We take this opportunity to highlight Tirapegui's groundbreaking contributions in the field of random perturbations experienced by macroscopic systems and in the formation of spatiotemporal structures in such systems operating far from thermodynamic equilibrium. This issue addresses a cross-disciplinary area of research as can be witnessed by the diversity of systems considered from inert matter such as photonics, chemistry, and fluid dynamics, to biology.In this work, the multifractal properties of wind speed and solar radiation are studied in a small region in which a wide variety of micro-climates are concentrated. To achieve this, two years of hourly data are analyzed in Guadeloupe archipelago. The four selected stations for wind speed were chosen according to trade winds direction, while solar radiation is recorded at a representative location at the center of the island. First, the results of the multifractal detrended fluctuation analysis (MF-DFA) showed the multifractal and persistent behaviors of wind speed at all locations. Due to the continental effect that increases along the transect, the Hurst exponent (H) values decrease from east to west. In addition, the MF-DFA clearly highlighted the presence of a nocturnal radiative layer that weakens wind speed in the surface layer. The multifractality degree [Δh(q)] values confirm the peculiarity of wind speed regimes at the center of the island. Thereafter, the MF-DFA results of solar radiation exhibited its multifractal and persistent behavior. Due to the solar radiation planetary scale, its Δh(q) is lower than those obtained for wind speed, which strongly depends on synoptic and local scales. The source of multifractality of wind speed and solar radiation is due to correlations of small and large fluctuations. Finally, the results of the multifractal detrended cross-correlation analysis between wind speed and solar radiation pointed out that the multifractal cross-correlation degree [Δhxy(q)] is identical for each site, which is not the case for Hurst exponent values.The interfaces in the 2-dimensional (2D) ferromagnetic Ising system below and at the critical temperature Tc were numerically analyzed in the framework of discrete Loewner evolution. We numerically calculated Loewner driving forces corresponding to the interfaces in the 2D Ising system and analyzed them using nonlinear time series analyses. We found that the dynamics of the Loewner driving forces showed chaotic properties wherein their intermittency, sensitivity to initial condition, and autocorrelation change depending on the temperature T of the system. selleck inhibitor It is notable that while the Loewner driving forces have deterministic properties, they have Gaussian-type probability distributions whose variance increases as T→Tc, indicating that they are examples of the Gaussian chaos. Thus, the obtained Loewner driving forces can be considered a chaotic dynamical system whose bifurcation is dominated by the temperature of the Ising system. This perspective for the dynamical system was discussed in relation to the extension and/or generalization of the stochastic Loewner evolution.Motivated by the existing difficulties in establishing mathematical models and in observing state time series for some complex systems, especially for those driven by non-Gaussian Lévy motion, we devise a method for extracting non-Gaussian governing laws with observations only on the mean exit time. It is feasible to observe the mean exit time for certain complex systems. With such observations, we use a sparse regression technique in the least squares sense to obtain the approximated function expression of the mean exit time. Then, we learn the generator and further identify the governing stochastic differential equation by solving an inverse problem for a nonlocal partial differential equation and minimizing an error objective function. Finally, we verify the efficacy of the proposed method by three examples with the aid of the simulated data from the original systems. Results show that our method can apply to not only the stochastic dynamical systems driven by Gaussian Brownian motion but also those driven by non-Gaussian Lévy motion, including those systems with complex rational drift.We study active matter systems where the orientational dynamics of underlying self-propelled particles obey second-order equations. By primarily concentrating on a spatially homogeneous setup for particle distribution, our analysis combines theories of active matter and oscillatory networks. For such systems, we analyze the appearance of solitary states via a homoclinic bifurcation as a mechanism of the frequency clustering. By introducing noise, we establish a stochastic version of solitary states and derive the mean-field limit described by a partial differential equation for a one-particle probability density function, which one might call the continuum Kuramoto model with inertia and noise. By studying this limit, we establish second-order phase transitions between polar order and disorder. The combination of both analytical and numerical approaches in our study demonstrates an excellent qualitative agreement between mean-field and finite-size models.