In the last decade, there has been a growing body of literature addressing the utilization of complex network methods for the characterization of dynamical systems based on time series. While both ...nonlinear time series analysis and complex network theory are widely considered to be established fields of complex systems sciences with strong links to nonlinear dynamics and statistical physics, the thorough combination of both approaches has become an active field of nonlinear time series analysis, which has allowed addressing fundamental questions regarding the structural organization of nonlinear dynamics as well as the successful treatment of a variety of applications from a broad range of disciplines. In this report, we provide an in-depth review of existing approaches of time series networks, covering their methodological foundations, interpretation and practical considerations with an emphasis on recent developments. After a brief outline of the state-of-the-art of nonlinear time series analysis and the theory of complex networks, we focus on three main network approaches, namely, phase space based recurrence networks, visibility graphs and Markov chain based transition networks, all of which have made their way from abstract concepts to widely used methodologies. These three concepts, as well as several variants thereof will be discussed in great detail regarding their specific properties, potentials and limitations. More importantly, we emphasize which fundamental new insights complex network approaches bring into the field of nonlinear time series analysis. In addition, we summarize examples from the wide range of recent applications of these methods, covering rather diverse fields like climatology, fluid dynamics, neurophysiology, engineering and economics, and demonstrating the great potentials of time series networks for tackling real-world contemporary scientific problems. The overall aim of this report is to provide the readers with the knowledge how the complex network approaches can be applied to their own field of real-world time series analysis.
•A DNA-based color image encryption method is proposed by using three 1D chaotic systems with excellent performance and easy implementation.•The key streams used for encryption are related to both ...the secret keys and the plain-image.•To improve the security and sensitivity, a division-shuffling process is introduced.•Transforming the plain-image and the key streams into the DNA matrices randomly can further enhance the security of the cryptosystem.•The presented scheme has a good robustness for some common image processing operations and geometric attack.
This paper proposes a new encryption scheme for color images based on Deoxyribonucleic acid (DNA) sequence operations and multiple improved one-dimensional (1D) chaotic systems with excellent performance. Firstly, the key streams are generated from three improved 1D chaotic systems by using the secret keys and the plain-image. Transform randomly the key streams and the plain-image into the DNA matrices by the DNA encoding rules, respectively. Secondly, perform the DNA complementary and XOR operations on the DNA matrices to get the scrambled DNA matrices. Thirdly, decompose equally the scrambled DNA matrices into blocks and shuffle these blocks randomly. Finally, implement the DNA XOR and addition operations on the DNA matrices obtained from the previous step and the key streams, and then convert the encrypted DNA matrices into the cipher-image by the DNA decoding rules. Experimental results and security analysis show that the proposed encryption scheme has a good encryption effect and high security. Moreover, it has a strong robustness for the common image processing operations and geometric attack.
The stability of synchronised networked systems is a multi-faceted challenge for many natural and technological fields, from cardiac and neuronal tissue pacemakers to power grids. For these, the ...ongoing transition to distributed renewable energy sources leads to a proliferation of dynamical actors. The desynchronisation of a few or even one of those would likely result in a substantial blackout. Thus the dynamical stability of the synchronous state has become a leading topic in power grid research. Here we uncover that, when taking into account physical losses in the network, the back-reaction of the network induces new exotic solitary states in the individual actors and the stability characteristics of the synchronous state are dramatically altered. These effects will have to be explicitly taken into account in the design of future power grids. We expect the results presented here to transfer to other systems of coupled heterogeneous Newtonian oscillators.
The human brain power grids, arrays of coupled lasers and the Amazon rainforest, are all characterized by multistability. The likelihood that these systems will remain in the most desirable of their ...many stable states depends on their stability against significant perturbations, particularly in a state space populated by undesirable states. Here we claim that the traditional linearization-based approach to stability is too local to adequately assess how stable a state is. Instead, we quantify it in terms of basin stability, a new measure related to the volume of the basin of attraction. Basin stability is non-local, nonlinear and easily applicable, even to high-dimensional systems. It provides a long-sought-after explanation for the surprisingly regular topologies of neural networks and power grids, which have eluded theoretical description based solely on linear stability. We anticipate that basin stability will provide a powerful tool for complex systems studies, including the assessment of multistable climatic tipping elements.
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