Search results for "chao"
showing 10 items of 402 documents
Magnetic field dynamos and magnetically triggered flow instabilities
2017
The project A2 of the LIMTECH Alliance aimed at a better understanding of those magnetohydrodynamic instabilities that are relevant for the generation and the action of cosmic magnetic fields. These comprise the hydromagnetic dynamo effect and various magnetically triggered flow instabilities, such as the magnetorotational instability and the Tayler instability. The project was intended to support the experimental capabilities to become available in the framework of the DREsden Sodium facility for DYNamo and thermohydraulic studies (DRESDYN). An associated starting grant was focused on the dimensioning of a liquid metal experiment on the newly found magnetic destabilization of rotating flow…
PageRank model of opinion formation on Ulam networks
2013
We consider a PageRank model of opinion formation on Ulam networks, generated by the intermittency map and the typical Chirikov map. The Ulam networks generated by these maps have certain similarities with such scale-free networks as the World Wide Web (WWW), showing an algebraic decay of the PageRank probability. We find that the opinion formation process on Ulam networks have certain similarities but also distinct features comparing to the WWW. We attribute these distinctions to internal differences in network structure of the Ulam and WWW networks. We also analyze the process of opinion formation in the frame of generalized Sznajd model which protects opinion of small communities.
Random Walk in a N-cube Without Hamiltonian Cycle to Chaotic Pseudorandom Number Generation: Theoretical and Practical Considerations
2017
Designing a pseudorandom number generator (PRNG) is a difficult and complex task. Many recent works have considered chaotic functions as the basis of built PRNGs: the quality of the output would indeed be an obvious consequence of some chaos properties. However, there is no direct reasoning that goes from chaotic functions to uniform distribution of the output. Moreover, embedding such kind of functions into a PRNG does not necessarily allow to get a chaotic output, which could be required for simulating some chaotic behaviors. In a previous work, some of the authors have proposed the idea of walking into a $\mathsf{N}$-cube where a balanced Hamiltonian cycle has been removed as the basis o…
Bifurcation analysis of a TaO memristor model
2019
This paper presents a study of bifurcation in the time-averaged dynamics of TaO memristors driven by narrow pulses of alternating polarities. The analysis, based on a physics-inspired model, focuses on the stable fixed points and on how these are affected by the pulse parameters. Our main finding is the identification of a driving regime when two stable fixed points exist simultaneously. To the best of our knowledge, such bistability is identified in a single memristor for the first time. This result can be readily tested experimentally, and is expected to be useful in future memristor circuit designs.
Quantifying non-periodicity of non-stationary time series through wavelets
2019
In this paper, we introduce a new wavelet tool for studying the degree of non-periodicity of time series that is based on some recently defined tools, such as the \textit{windowed scalogram} and the \textit{scale index}. It is especially appropriate for non-stationary time series whose characteristics change over time and so, it can be applied to a wide variety of disciplines. In addition, we revise the concept of the scale index and pose a theoretical problem: it is known that if the scale index of a function is not zero then it is non-periodic, but if the scale index of a function is zero, then it is not proved that it has to be periodic. This problem is solved for the particular case of …
Parameter Switching Synchronization
2016
In this paper we show how the Parameter Switching algorithm, utilized initially to approximate attractors of a general class of nonlinear dynamical systems, can be utilized also as a synchronization-induced method. Two illustrative examples are considered: the Lorenz system and the Rabinovich-Fabrikant system.
Porosities and dimensions of measures satisfying the doubling condition
1999
Summary of a talk at the conference The Chaotic Universe in Rome, Feb, 1999
On differences and similarities in the analysis of Lorenz, Chen, and Lu systems
2015
Currently it is being actively discussed the question of the equivalence of various Lorenz-like systems and the possibility of universal consideration of their behavior (Algaba et al., 2013a,b, 2014b,c; Chen, 2013; Chen and Yang, 2013; Leonov, 2013a), in view of the possibility of reduction of such systems to the same form with the help of various transformations. In the present paper the differences and similarities in the analysis of the Lorenz, the Chen and the Lu systems are discussed. It is shown that the Chen and the Lu systems stimulate the development of new methods for the analysis of chaotic systems. Open problems are discussed.
A new approach to fuzzy sets: Application to the design of nonlinear time-series, symmetry-breaking patterns, and non-sinusoidal limit-cycle oscillat…
2017
It is shown that characteristic functions of sets can be made fuzzy by means of the $\mathcal{B}_{\kappa}$-function, recently introduced by the author, where the fuzziness parameter $\kappa \in \mathbb{R}$ controls how much a fuzzy set deviates from the crisp set obtained in the limit $\kappa \to 0$. As applications, we present first a general expression for a switching function that may be of interest in electrical engineering and in the design of nonlinear time-series. We then introduce another general expression that allows wallpaper and frieze patterns for every possible planar symmetry group (besides patterns typical of quasicrystals) to be designed. We show how the fuzziness parameter…
Horseshoe-shaped maps in chaotic dynamics of long Josephson junction driven by biharmonic signals
2000
Abstract A collective coordinate approach is applied to study chaotic responses induced by an applied biharmonic driven signal on the long Josephson junction influenced by a constant dc-driven field with breather initial conditions. We derive a nonlinear equation for the collective variable of the breather and a new version of the Melnikov method is then used to demonstrate the existence of Smale horseshoe-shaped maps in its dynamics. Additionally, numerical simulations show that the theoretical predictions are well reproduced. The subharmonic Melnikov theory is applied to study the resonant breathers. Results obtained using this approach are in good agreement with numerical simulations of …