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[en] Let be rotations on the unit circle and define as for , , where is the shift, and and are rotational angles. It is first proved that the system exhibits maximal distributional chaos for any (no assumption of ), generalizing Theorem 1 in Wu and Chen (Topol. Appl. 162:91–99, 2014). It is also obtained that is cofinitely sensitive and -sensitive and that is densely chaotic if and only if .
[en] We consider a class of nonideal oscillating (by Sommerfeld and Kononenko) dynamical systems and establish the existence of two types of hyperchaotic attractors in these systems. The scenarios of transitions from regular to chaotic ones attractors and the scenarios of transitions between chaotic attractors of different types are described.
[en] Slow Slip Events (SSEs) are episodic slip events that play a significant role in the moment budget along a subduction megathrust. They share many similarities with regular earthquakes, and have been observed in major subduction regions like, for example, Cascadia, Japan, Mexico, New Zealand. They show striking regularity, suggesting that it might be possible to forecast their size and timing, but the prediction of their extension and exact timing is still yet to come.
[en] Let , and let G be a locally compact group. Let A be a unital -algebra. We give a sufficient and necessary condition for a sequence of weighted translations on the -algebra-valued Lebesgue space to be topologically transitive in terms of the Haar measure, the weight functions, and an aperiodic sequence in G. Chaos, topological mixing, supercyclicity and dual hypercyclicity for such a sequence are also discussed.
[en] The effects of inertial terms on the dynamics of the dc+ac driven Frenkel-Kontorova model were examined. As the mass of particles was varied, the response of the system to the driving forces and appearance of the Shapiro steps were analyzed in detail. Unlike in the overdamped case, the increase of mass led to the appearance of the whole series of subharmonic steps in the staircase of the average velocity as a function of average driving force in any commensurate structure. At certain values of parameters, the subharmonic steps became separated by chaotic windows while the whole structure retained scaling similar to the original staircase. The mass of the particles also determined their sensitivity to the forces governing their dynamics. Depending on their mass, they were found to exhibit three types of dynamics, from dynamical mode-locking with chaotic windows, through to a typical dc response, to essentially a free-particle response. Examination of this dynamics in both the upforce and downforce directions showed that the system may not only exhibit hysteresis, but also that large Shapiro steps may appear in the downforce direction, even in cases for which no dynamical mode-locking occurred in the upforce direction. © 2019 American Physical Society.
[en] Peculiarities of the formation of multistability in a microwave generator with delayed reflection from the load have been studied. Characteristic scenarios of the appearance and evolution of multistable states are determined. The influence of nonisochronism on the scenario of transition to chaos is revealed.
[en] We argue that the problem of calculating retention time scales in young black holes is a problem of relative state complexity. In particular, we suggest that Alice’s ability to estimate the time scale for a perturbed black hole to release the extra html-italic>n qubits comes down to her decoding the Hilbert space of the Hawking radiation. We then demonstrate the decoding task Alice faces is very difficult, and in order to calculate the relative state complexity she would either need to act with an exponentially complex unitary operator or apply an extremely fine-tuned future precursor operator to the perturbed state in .
[en] In this paper, we propose a novel quantum secret image-sharing scheme which constructs m quantum secret images into m+1 quantum share images. A chaotic image generated by the logistic map is utilized to assist in the construction of quantum share images first. The chaotic image and secret images are expressed as quantum image representation by using the novel enhanced quantum representation. To enhance the confidentiality, quantum secret images are scrambled into disordered images through the Arnold transform. Then the quantum share images are constructed by performing a series of quantum swap operations and quantum controlled-NOT operations. Because all quantum operations are invertible, the original quantum secret images can be reconstructed by performing a series of inverse operations. Theoretical analysis and numerical simulation proved both the security and low computational complexity of the scheme, which has outperformed its classical counterparts. It also provides quantum circuits for sharing and recovery processes. (paper)
[en] This manuscript deals with a new insight into multi-switching combination–combination synchronization among different chaotic systems for fully unknown parameters. The suitable controllers and parameter update laws are designed by employing adaptive control and Lyapunov stability approach, to achieve asymptotically stable synchronization states for two drive and two response systems. In order to demonstrate the proposed methodology, an example of Lorenz system, Lu system, Chen–Lee system and Wang system is considered where Lorenz system and Lu system are taken as drive systems and Chen–Lee system and Wang system are taken as response systems. Numerical results are performed to justify the theoretical approach. Computational and theoretical results are in excellent agreement.
[en] We present a model—a modified standard map. This model has interesting properties that allow quantum–classical correspondences to be studied. For some range of parameters in the classical phase space of this model, there exist large accelerator modes. We can create a family of maps that have large accelerator modes.