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Furthermore, the time-varying characteristics of high-dimensional transformed waves are investigated by analyzing the geometric properties (angle and distance) of two characteristic lines of waves, which do not exist in (1+1)-dimensional systems. Based on the high-order breath-wave solutions, the interactions between those transformed nonlinear waves are investigated, such as the completely elastic mode, semi-elastic mode, inelastic mode, and collision-free mode. We reveal that the diversity of transformed waves, time-varying property, and shape-changed collision mainly appear as a result of the difference of phase shifts of the solitary wave and periodic wave components. Isoproterenol sulfate Such phase shifts come from the time evolution as well as the collisions. Finally, the dynamics of the double shape-changed collisions are presented.We explore the influence of precision of the data and the algorithm for the simulation of chaotic dynamics by neural network techniques. For this purpose, we simulate the Lorenz system with different precisions using three different neural network techniques adapted to time series, namely, reservoir computing [using Echo State Network (ESN)], long short-term memory, and temporal convolutional network, for both short- and long-time predictions, and assess their efficiency and accuracy. Our results show that the ESN network is better at predicting accurately the dynamics of the system, and that in all cases, the precision of the algorithm is more important than the precision of the training data for the accuracy of the predictions. This result gives support to the idea that neural networks can perform time-series predictions in many practical applications for which data are necessarily of limited precision, in line with recent results. It also suggests that for a given set of data, the reliability of the predictions can be significantly improved by using a network with higher precision than the one of the data.The effect of chaotic dynamical states of agents on the coevolution of cooperation and synchronization in a structured population of the agents remains unexplored. With a view to gaining insights into this problem, we construct a coupled map lattice of the paradigmatic chaotic logistic map by adopting the Watts-Strogatz network algorithm. The map models the agent's chaotic state dynamics. In the model, an agent benefits by synchronizing with its neighbors, and in the process of doing so, it pays a cost. The agents update their strategies (cooperation or defection) by using either a stochastic or a deterministic rule in an attempt to fetch themselves higher payoffs than what they already have. Among some other interesting results, we find that beyond a critical coupling strength, which increases with the rewiring probability parameter of the Watts-Strogatz model, the coupled map lattice is spatiotemporally synchronized regardless of the rewiring probability. Moreover, we observe that the population does not desynchronize completely-and hence, a finite level of cooperation is sustained-even when the average degree of the coupled map lattice is very high. These results are at odds with how a population of the non-chaotic Kuramoto oscillators as agents would behave. Our model also brings forth the possibility of the emergence of cooperation through synchronization onto a dynamical state that is a periodic orbit attractor.We consider a self-oscillator whose excitation parameter is varied. The frequency of the variation is much smaller than the natural frequency of the oscillator so that oscillations in the system are periodically excited and decayed. Also, a time delay is added such that when the oscillations start to grow at a new excitation stage, they are influenced via the delay line by the oscillations at the penultimate excitation stage. Due to nonlinearity, the seeding from the past arrives with a doubled phase so that the oscillation phase changes from stage to stage according to the chaotic Bernoulli-type map. As a result, the system operates as two coupled hyperbolic chaotic subsystems. Varying the relation between the delay time and the excitation period, we found a coupling strength between these subsystems as well as intensity of the phase doubling mechanism responsible for the hyperbolicity. Due to this, a transition from non-hyperbolic to hyperbolic hyperchaos occurs. The following steps of the transition scenario are revealed and analyzed (a) an intermittency as an alternation of long staying near a fixed point at the origin and short chaotic bursts; (b) chaotic oscillations with frequent visits to the fixed point; (c) plain hyperchaos without hyperbolicity after termination visiting the fixed point; and (d) transformation of hyperchaos to the hyperbolic form.We construct an equivalent cellular automaton (CA) for a system of globally coupled sine circle maps with two populations and distinct values for intergroup and intragroup coupling. The phase diagram of the system shows that the coupled map lattice can exhibit chimera states with synchronized and spatiotemporally intermittent subgroups after evolution from random initial conditions in some parameter regimes, as well as to other kinds of solutions in other parameter regimes. The CA constructed by us reflects the global nature and the two population structure of the coupled map lattice and is able to reproduce the phase diagram accurately. The CA depends only on the total number of laminar and burst sites and shows a transition from co-existing deterministic and probabilistic behavior in the chimera region to fully probabilistic behavior at the phase boundaries. This identifies the characteristic signature of the transition of a cellular automaton to a chimera state. We also construct an evolution equation for the average number of laminar/burst sites from the CA, analyze its behavior and solutions, and correlate these with the behavior seen for the coupled map lattice. Our CA and methods of analysis can have relevance in wider contexts.Cellular automata models based on population dynamics, introduced by Von Neumann in the 1950s, has been successfully used to describe pattern development and front propagation in many applications, such as crystal growth, forest fires, fractal growth in biological media, etc. We, herein, explore the possibility of using a cellular automaton, based on the population dynamics of flamelets, as a low-order model to describe the dynamics of an expanding flame propagating in a turbulent environment. A turbulent flame is constituted by numerous flamelets, each of which interacts with their neighborhood composed of other flamelets, as well as unburned and burnt fluid particles. This local interaction leads to global flame dynamics. The effect of turbulence is simulated by introducing stochasticity in the local interaction and hence in the temporal evolution of the flamefront. Our results show that the model preserves various multifractal characteristics of the expanding turbulent flame and captures several characteristics of expanding turbulent flames observed in experiments. 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. 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.