The low-mass X-ray binary 4U1705-44 exhibits dramatic long-term X-ray time variability with a timescale of several hundred days. The All-Sky Monitor (ASM) aboard the Rossi X-ray Timing Explorer (RXTE) and the Japanese Monitor of All-sky X-ray Image (MAXI) aboard the International Space Station together have continuously observed the source from December 1995 through May 2014. The combined ASM-MAXI data provide a continuous time series over fifty times the length of the timescale of interest. Topological analysis can help us identify 'fingerprints' in the phase-space of a system unique to its equations of motion. The Birman-Williams theorem postulates that if such fingerprints are the same between two systems, then their equations of motion must be closely related. The phase-space embedding of the source light curve shows a strong resemblance to the double-welled nonlinear Duffing oscillator. We explore a range of parameters for which the Duffing oscillator closely mirrors the time evolution of 4U1705-44. We extract low period, unstable periodic orbits from the 4U1705-44 and Duffing time series and compare their topological information. The Duffing and 4U1705-44 topological properties are identical, providing strong evidence that they share the same underlying template. This suggests that we can look to the Duffing equation to help guide the development of a physical model to describe the long-term X-ray variability of this and other similarly behaved X-ray binary systems.

The advent of new time domain surveys and the imminent increase in astronomical data expose the shortcomings of traditional time series analysis (such as power spectra analysis) in characterising the abundantly varied, complex and stochastic light curves of Active Galactic Nuclei (AGN). Recent applications of novel methods from non-linear dynamics have shown promise in characterising higher modes of variability and time-scales in AGN. Recurrence analysis in particular can provide complementary information about characteristic time-scales revealed by other methods, as well as probe the nature of the underlying physics in these objects. Recurrence analysis was developed to study dynamical trajectories in phase space, which can be constructed from one-dimensional time series such as light curves. We apply the methods of recurrence analysis to two optical light curves of Kepler-monitored AGN. We confirm the detection and period of an optical quasi-periodic oscillation in one AGN, and confirm multiple other time-scales recovered from other methods ranging from 5 days to 60 days in both objects. We detect regions in the light curves that deviate from regularity, provide evidence of determinism and non-linearity in the mechanisms underlying one light curve (KIC 9650712), and determine realizations of a linear stochastic process describe the dominant variability in the other light curve (Zwicky 229–015). We discuss possible underlying processes driving the dynamics of the light curves and their diverse classes of variability.

We present results of recurrence analysis of 46 active galactic nuclei (AGN) using light curves from the 157-month catalog of the Swift Burst Alert Telescope (BAT) in the 14-150 keV band. We generate recurrence plots and compute recurrence plot metrics for each object. We use the surrogate data method to compare all derived recurrence-based quantities to three sets of stochastic light curves with identical power spectrum, flux distribution, or both, in order to determine the presence of determinism, non-linearity, entropy, and non-stationarity. We compare these quantities with known physical characteristics of each system, such as black hole mass, Eddington ratio, and bolometric luminosity, radio loudness, obscuration, and spectroscopic type. We find that almost all AGN in this sample exhibit substantial higher-order modes of variability than is contained in the power spectrum, with approximately half exhibiting nonlinear or non-stationary behavior. We find that Type 2 AGN are more likely to contain deterministic variability than Type 1 AGN while the same distinction is not found between obscured and unobscured AGN. The complexity of variability among Type 1 AGN is anticorrelated with Eddington ratio, while no relationship is found among Type 2 AGN. The connections between the recurrence properties and AGN class suggest that hard X-ray emission is a probe of distinct accretion processes among classes of AGN, which supports interpretations of changing-look AGN and challenges the traditional unification model that classifies AGN only on viewing angle.