Results 1 - 10 of 102
Results 1 - 10 of 102. Search took: 0.026 seconds
|Sort by: date | relevance|
[en] We use the Melnikov method to identify chaotic behavior in geodesic motion perturbed by the minimal length effects around a Schwarzschild black hole. Unlike the integrable unperturbed geodesic motion, our results show that the perturbed homoclinic orbit, which is a geodesic joining the unstable circular orbit to itself, becomes chaotic in the sense that Smale horseshoes chaotic structure is present in phase space.
[en] Complexity analysis of fractional-order chaotic systems is an interesting topic of recent years. In this paper, the fractional symbolic network entropy measure algorithm is designed in which the symbol networks are built and fractional generalized information is introduced. Complexity of the fractional-order chaotic systems is analyzed. It shows that the proposed algorithm is effective for measure complexity of different pseudo random sequences. Complexity decreases with the decrease of derivative order in the fractional-order discrete chaotic system while changes with the derivative order in the fractional-order continuous chaotic system. Moreover, basin of attraction is also determined by the derivative order. It provides a basis for parameter choice of the fractional-order chaotic systems in the real applications. (paper)
[en] This study investigates the reconstruction of self-similar chaotic attractors and virtual functions by mean of fractal interpolation function by choosing vertical scaling parameter as a continuous function on the interval of interpolation. We describe a procedure for the reconstruction of Lorenz attractor and claim that the flexibility on the choice of vertical scaling produce smoother and non-smooth fractal functions which reconstruct the self-affine Lorenz attractor. Apart from approximation and visualization, this paper facilitates fractal function to interact with chaotic systems for proper mild conditions on scaling parameter of fractal functions. (paper)
[en] Chaotic encryption is one of hot topics in cryptography, which has received increasing attention. Among many encryption methods, chaotic map is employed as an important source of pseudo-random numbers (PRNS). Although the randomness and the butterfly effect of chaotic map make the generated sequence look very confused, its essence is still the deterministic behavior generated by a set of deterministic parameters. Therefore, the unceasing improved parameter estimation technology becomes one of potential threats for chaotic encryption, enhancing the attacking effect of the deciphering methods. In this paper, for better analyzing the cryptography, we focus on investigating the condition of chaotic maps to resist parameter estimation. An improved particle swarm optimization (IPSO) algorithm is introduced as the estimation method. Furthermore, a new piecewise principle is proposed for increasing estimation precision. Detailed experimental results demonstrate the effectiveness of the new estimation principle, and some new requirements are summarized for a secure chaotic encryption system. (paper)
[en] Pairs of numerically computed trajectories of a chaotic system may coalesce because of finite arithmetic precision. We analyse an example of this phenomenon, showing that it occurs surprisingly frequently. We argue that our model belongs to a universality class of chaotic systems where this numerical coincidence effect can be described by mapping it to a first-passage process. Our results are applicable to aggregation of small particles in random flows, as well as to numerical investigation of chaotic systems. (paper)
[en] The economic and financial systems consist of many nonlinear factors that make them behave as the complex systems. Recently many chaotic finance systems have been proposed to study the complex dynamics of finance as a noticeable problem in economics. In fact, the intricate structure between financial institutions can be obtained by using a network of financial systems. Therefore, in this paper, we consider a ring network of coupled symmetric chaotic finance systems, and investigate its behavior by varying the coupling parameters. The results show that the coupling strength and range have significant effects on the behavior of the coupled systems, and various patterns such as the chimera and multi-chimera states are observed. Furthermore, changing the parameters’ values, remarkably influences on the oscillators attractors. When several synchronous clusters are formed, the attractors of the synchronized oscillators are symmetric, but different from the single oscillator attractor. (paper)
[en] Aiming to solve the problems of low accuracy of multi-step prediction and difficulty in determining the maximum number of prediction steps of chaotic time series, a multi-step time series prediction model based on the dilated convolution network and long short-term memory (LSTM), named the dilated convolution-long short-term memory (DC-LSTM), is proposed. The dilated convolution operation is used to extract the correlation between the predicted variable and correlational variables. The features extracted by dilated convolution operation and historical data of predicted variable are input into LSTM to obtain the desired multi-step prediction result. Furthermore, cross-correlation analyses (CCA) are applied to calculate the reasonable maximum prediction steps of chaotic time series. Actual applications of multi-step prediction were studied to demonstrate the effectiveness of the proposed model which has superiorities in RMSE, MAE and prediction accuracy because of the extraction of correlation between the predicted variable and correlational variables. Moreover, the proposed DC-LSTM model provides a new method for prediction of chaotic time series and lays a foundation for scientific data analysis of chaotic time series monitoring systems.
[en] Quantum Chaos has been investigated for about a half century. It is an old yet vigorous interdisciplinary field with new concepts and interesting topics emerging constantly. Recent years have witnessed a growing interest in quantum chaos in relativistic quantum systems, leading to the still developing field of relativistic quantum chaos. The purpose of this paper is not to provide a thorough review of this area, but rather to outline the basics and introduce the key concepts and methods in a concise way. A few representative topics are discussed, which may help the readers to quickly grasp the essentials of relativistic quantum chaos. A brief overview of the general topics in quantum chaos has also been provided with rich references. (topical review)
[en] In this paper, by employing an occasionally coupling scheme in a two-species bosonic Josephson junction, it is found that for nonlocal measure synchronized states appearing in the two dynamic modes, known as 0-phase mode and π phase mode, their broken-symmetry can be restored. Nevertheless, there are dramatic differences for the results. For 0-phase mode, we can restore the broken symmetry by turning the nonlocal MS state into a conventional quasiperiodic MS state. However, for the π-phase mode, the broken symmetry is restored accompanied by the appearance of chaotic MS states. (paper)
[en] Using an Er-doped fiber laser as a test bed, here we for the first time experimentally demonstrate the simultaneous effect of the fast scale (round-trip time) and slow scale (thousands round-trip time) instabilities on the emergence of breathers similar to the Akhmediev breathers, Peregrine solitons, and partially mode-locked chaotic solitons. The anomalous statistics of the laser output power justifies the connection of the observed spatiotemporal structures with bright and dark rogue waves. Apart from the interest in laser physics for revealing mechanisms of the multiscale dynamics, the obtained results can be of fundamental interest for studying spatiotemporal patterns induced by the interplay of the mechanisms mentioned above in various distributed systems. (letter)