One of the fundamental open questions in plasma physics is the role of non-thermal particles distributions in poorly collisional plasma environments, a system that is commonly found throughout the Universe, e.g., the solar wind and the Earth’s magnetosphere correspond to natural plasma physics laboratories in which turbulent phenomena can be studied. Our study perspective is born from the method of Horizontal Visibility Graph (HVG) that has been developed in the last years to analyze time series avoiding the tedium and the high computational cost that other methods offer. Here, we build a complex network based on directed HVG technique applied to magnetic field fluctuations time series obtained from Particle In Cell (PIC) simulations of a magnetized collisionless plasma to distinguish the degree distributions and calculate the Kullback–Leibler Divergence (KLD) as a measure of relative entropy of data sets produced by processes that are not in equilibrium. First, we analyze the connectivity probability distribution for the undirected version of HVG finding how the Kappa distribution for low values of κ tends to be an uncorrelated time series, while the Maxwell–Boltzmann distribution shows a correlated stochastic processes behavior. Subsequently, we investigate the degree of temporary irreversibility of magnetic fluctuations that are self-generated by the plasma, comparing the case of a thermal plasma (described by a Maxwell–Botzmann velocity distribution function) with non-thermal Kappa distributions. We have shown that the KLD associated to the HVG is able to distinguish the level of reversibility that is associated to the thermal equilibrium in the plasma, because the dissipative degree of the system increases as the value of κ parameter decreases and the distribution function departs from the Maxwell–Boltzmann equilibrium.

We focus on characterizing the high-energy emission mechanisms of blazars by analyzing the variability in the radio band of the light curves of more than a thousand sources. We are interested in assigning complexity parameters to these sources, modeling the time series of the light curves with the method of the Horizontal Visibility Graph (HVG), which allows us to obtain properties from degree distributions, such as a characteristic exponent to describe its stochasticity and the Kullback–Leibler Divergence (KLD), presenting a new perspective to the methods commonly used to study Active Galactic Nuclei (AGN). We contrast these parameters with the excess variance, which is an astronomical measurement of variability in light curves; at the same time, we use the spectral classification of the sources. While it is not possible to find significant correlations with the excess variance, the degree distributions extracted from the network are detecting differences related to the spectral classification of blazars. These differences suggest a chaotic behavior in the time series for the BL Lac sources and a correlated stochastic behavior in the time series for the FSRQ sources. Our results show that complex networks may be a valuable alternative tool to study AGNs according to the variability of their energy output.

Context. The solar wind develops a highly turbulent character during its expansion, where plasma and electromagnetic fluctuations coexist. Considering the presence of turbulence in the plasma as a complex system, the turbulence in the solar wind in general has been measured and studied using different techniques from a systems science point of view. These techniques provide the opportunity to obtain preliminary information even before much of the physics can be assimilated and integrated. Aims. We describe this plasma as a complex system in order to understand solar wind dynamics from a new perspective. Several missions provide a wide range of data concerning critical astrophysical phenomena. This poses a challenge to implement new effective methods to complement the characterization of the constantly new, and sometimes highly reduced information, especially when dealing with observational data with intermittent gaps. Methods. We work with magnetic fluctuation time series data obtained from the Wind mission at 1 AU in order to characterize the fast and slow solar wind behavior during solar cycles 23 (SC23) and 24 (SC24). We applied the horizontal visibility graph (HVG) method to obtain the evolution of measurements of Kullback-Leibler divergence (KLD), D, and the characteristic exponent, γ, over time. Both are complexity parameters extracted from the degree distributions of the networks. Results. By contrasting our complexity parameters, γ and D, with solar activity characterized by the number of sunspots and solar wind speed, we obtain significant intercorrelations among them during both cycles and ascending, descending, minimum, and maximum phases. According to γ values, the magnetic fluctuations of the solar wind are a correlated stochastic time series at 1 AU. Also, the divergence D recognizes SC23 as the most dissipative and identifies the slow wind as more variable than the fast wind, with a better anti-correlation in the minima phases. This study reveals that in terms of solar phases γmin > γdes > γasc > γmax, and Dmin < Ddes < Dasc < Dmax. We show that the HVG technique leads to results that are consistent with the complex nature of solar wind turbulence.

We focus on characterizing the high-energy emission mechanisms of blazars by analyzing the variability in the radio band of the light curves of more than a thousand sources. We are interested in assigning complexity parameters to these sources, modeling the time series of the light curves with the method of the Horizontal Visibility Graph (HVG), which allows us to obtain properties from degree distributions, such as a characteristic exponent to describe its stochasticity and the Kullback-Leibler Divergence (KLD), presenting a new perspective to the methods commonly used to study Active Galactic Nuclei (AGN). We contrast these parameters with the excess variance, an astronomical measurement of variability in light curves, at the same time we use the spectral classification of the sources. While it is not possible to find significant correlations with the excess variance, the degree distributions extracted from the network are detecting differences related to the spectral classification of blazars. These differences suggest a chaotic behavior in the time series for the BL Lac sources and a correlated stochastic behavior in the time series for the FSRQ sources. Our results show that complex networks may be a valuable alternative tool to study AGNs according to the variability of their energy output.