Nonlinear time series analysis of palaeoclimate proxy records

Identifying and characterising dynamical regime shifts, critical transitions or potential tipping points in palaeoclimate time series is relevant for improving the understanding of often highly nonlinear Earth system dynamics. Beyond linear changes in time series properties such as mean, variance, or trend, these nonlinear regime shifts can manifest as changes in signal predictability, regularity, complexity, or higher-order stochastic properties such as multi-stability.In recent years, several classes of methods have been put forward to study these critical transitions in time series data that are based on concepts from nonlinear dynamics, complex systems science, information theory, and stochastic analysis. These includeapproaches such as phase space-based recurrence plots and recurrence networks, visibility graphs, order pattern-based entropies, and stochastic modelling.Here, we review and compare in detail several prominent methods from these fields by applying them to the same set of marine palaeoclimate proxy records of African climate variations during the past 5~million years. Applying these methods, we observe notable nonlinear transitions in palaeoclimate dynamics in these marine proxy records and discuss them in the context of important climate events and regimes such as phases of intensified Walker circulation, marine isotope stage M2, the onset of northern hemisphere glaciation and the mid-Pleistocene transition. We find that the studied approaches complement each other by allowing us to point out distinct aspects of dynamical regime shifts in palaeoclimate time series.We also detect significant correlations of these nonlinear regime shift indicators with variations of Earth's orbit, suggesting the latter as potential triggers of nonlinear transitions in palaeoclimate.Overall, the presented study underlines the potentials of nonlinear time series analysis approaches to provide complementary information on dynamical regime shifts in palaeoclimate and their driving processes that cannot be revealed by linear statistics or eyeball inspection of the data alone.

Image Encryption with Fusion of Two Maps

In this paper, we propose a fusion technique for image encryption combining two maps and generate a new optimized map by fusing Hartley and Duffing chaotic oscillators. In order to measure and quantify the amount of chaos present in data sequences, the resultant map is tested by a new method of nonlinear time series analysis. This test ensures its robustness during its use to construct an encrypted image when combined with some mathematical function that we have designed. The cryptosystem was tested on images such as Lena, Barbara, Mandrill, and Man. The results were compared to those in the literature and proved satisfactory.

Ordinal partition transition network based complexity measures for climate data analysis

<p>Complex network approaches have been recently emerging as novel and complementary concepts of nonlinear time series analysis which are able to unveil many features that are hidden to more traditional analysis methods. In this talk, we focus on one particular approach of ordinal pattern transition networks (OPTNs) for characterizing time series data. In particular, we introduce a suite of OPTN based complexity measures to infer the coupling direction between two dynamical systems from pairs of time series. For several examples of both coupled stochastic processes and chaotic Henon maps, we demonstrate that our approach is able to successfully identify interaction delays of both unidirectional and bidirectional coupling configurations.</p><p>Furthermore, we focus on applying these methods to characterize the recent extreme drought events in the semiarid region of Northeast Brazil (NEB) where has been experiencing a continuous dry condition since 2012. Therefore, we propose a three-step strategy to establish the episodic coupling directions on intraseasonal time scales from the surrounding ocean to the precipitation patterns in the NEB, focusing on the distinctive roles of the oceans during the recent extreme drought events of 2012-2013 and 2015-2016. Our algorithm involves: (i) computing drought period length from daily precipitation anomalies to capture extreme drought events, (ii) characterizing the episodic coupling delays from the surrounding oceans to the precipitation by applying Kullback-Leibler divergence (KLD) of complexity measure which is based on OPTN representation of time series, and (iii) calculating the ratio of high temperature in the ocean during the extreme drought events with proper time lags that are identified by KLD measures. From the viewpoint of climatology, our analysis provides data-based evidence of showing significant influence from the North Atlantic in 2012-2013 to the NEB, but in 2015-2016 the Pacific played a dominant role than that of the Atlantic. The episodic intra-seasonal time scale properties are potential for monitoring and forecasting droughts in the NEB, in order to propose strategies for drought impacts reduction.</p><p>In conclusion, our results suggest that ordinal partition transition networks can be used as complementary tools for causal inference tasks and provide insights into the potentials and theoretical foundations of time series networks.</p><p>References:</p><p>[1] H. Y. Wu, Y. Zou, L. M. Alves, E. E. N. Macau, G. Sampaio, and J. A. Marengo. Uncovering episodic influence of oceans on extreme drought events in Northeast Brazil by ordinal partition network approaches. Chaos, 30, 053104, 2020.</p><p>[2] Y. J. Ruan, R. V. Donner, S. G. Guan, and Y. Zou. Ordinal partition transition network based complexity measures for inferring coupling direction and delay from time series. Chaos, 29, 043111, 2019.</p><p>[3] Y. Zou, R. V. Donner, N. Marwan, J. F. Donges, and J. Kurths. Complex network approaches to nonlinear time series analysis. Physics Reports, 787, 1 – 97, 2019.</p>

Searching for signatures of chaos in γ-ray light curves of selected Fermi-LAT blazars

ABSTRACT Blazar variability appears to be stochastic in nature. However, a possibility of low-dimensional chaos was considered in the past, but with no unambiguous detection so far. If present, it would constrain the emission mechanism by suggesting an underlying dynamical system. We rigorously searched for signatures of chaos in Fermi-Large Area Telescope light curves of 11 blazars. The data were comprehensively investigated using the methods of nonlinear time-series analysis: phase-space reconstruction, fractal dimension, and maximal Lyapunov exponent (mLE). We tested several possible parameters affecting the outcomes, in particular the mLE, in order to verify the spuriousness of the outcomes. We found no signs of chaos in any of the analysed blazars. Blazar variability is either truly stochastic in nature or governed by high-dimensional chaos that can often resemble randomness.

A MATHEMATICAL STUDY OF RAIN DROP SOUND

In this work we first download the recorded sound of drizzling rain and convert them to digits using Octave. Then we analyze this time series formed to interpret the rain data. We find that his data is nonlinear and yet have the similarity of being a linear data. We perform both linear and nonlinear time series analysis here in our work using the computational tool TISEAN. We present our results in this paper.