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  • Artikel  (846)
  • Springer  (846)
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  • 2019  (846)
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  • Nonlinear Dynamics  (140)
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  • 1
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    Analysing the dynamics of digital chaotic maps via a new period search algorithm (2019)
    Springer
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    Publikationsdatum: 2019
    Beschreibung: 〈h3〉Abstract〈/h3〉 〈p〉The dynamics of chaotic maps are severely inhibited by the limited precision of the computational device that is used to implement them, and thus, their applications in cryptography and secure communications are seriously limited. To evaluate the degree of degradation of digital chaotic maps, we designed a fast period search algorithm (FPSA) that is based on a tree structure for analysing the periodicities of digital chaotic maps from a new perspective. FPSA can calculate the maximal transient length, fixed points and periodic limit cycles of digital chaotic maps in finite-precision domains quickly and accurately. Furthermore, based on this algorithm, the security of 1-D logistic maps and 2-D Arnold maps in engineering applications is analysed to demonstrate the versatility and effectiveness of our proposed algorithm. This algorithm plays an active role in analysing the structures of the functional graphs of digital chaotic maps in digital computers.〈/p〉
    Print ISSN: 0924-090X
    Digitale ISSN: 1573-269X
    Thema: Mathematik
    Publiziert von Springer
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  • 2
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    Stability criteria of stochastic nonlinear systems with asynchronous impulses and switchings (2019)
    Springer
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    Publikationsdatum: 2019
    Beschreibung: 〈h3〉Abstract〈/h3〉 〈p〉The problem of stability analysis of stochastic nonlinear systems with asynchronous impulses and switchings is addressed in this paper. The obvious distinctions between the previous results and ours are that the impulses are not simultaneous with the switchings and the jump maps are different and dependent on the impulsive instants. By introducing the concepts of mode-independent(dependent) average impulsive interval and average dwell time to describe the impulsive and switching signals, respectively, sufficient conditions ensuring global asymptotic stability and almost sure stability are provided. Meanwhile, some new results for stochastic impulsive/switching nonlinear systems are established. In the end, two illustrative examples are given to show the applicability of our theoretical results.〈/p〉
    Print ISSN: 0924-090X
    Digitale ISSN: 1573-269X
    Thema: Mathematik
    Publiziert von Springer
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  • 3
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    Mechanical-electromagnetic coupling elastic vibration instability of symmetrical three-phase external rotor induction motor (2019)
    Springer
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    Publikationsdatum: 2019
    Beschreibung: 〈h3〉Abstract〈/h3〉 〈p〉The work investigates the elastic vibration instability induced by rotating electromagnetic load in symmetrical three-phase external rotor induction motor with compliant rotor and stator. The investigation is based on a mechanical-electromagnetic coupling dual-ring model undergoing flexural and extensional deformations. The model is established in a field-synchronous coordinates such that the time variance of electromagnetic load can be eliminated. The dependence of electromagnetic load on pole pair count and wavenumber is classified into typical cases. The eigenvalues are calculated by simple vibration theory such that unstable behaviors can be accurately estimated. The estimation is independent of weak-parametric source assumption. For verification purpose, a time-variant model is constructed in the inertial frame, based on which typical cases of the time-variant electromagnetic load are classified in terms of the pole pair count and wavenumber. Numerical calculations are performed by using Floquét theory, and transition curves between stable and unstable regions are identified. The results in field-synchronous and inertial frames are well compared with each other.〈/p〉
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    Thema: Mathematik
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  • 4
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    Interaction and energy transition between the breather and rogue wave for a generalized nonlinear Schrödinger system with two higher-order dispersion operators in optical fibers (2019)
    Springer
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    Publikationsdatum: 2019
    Beschreibung: 〈h3〉Abstract〈/h3〉 〈p〉A generalized nonlinear Schrödinger system is investigated, which can be used to describe the optical pulse propagation in inhomogeneous optical fibers with the fourth- and third-order dispersions operators. The Darboux transformation method is extended to construct a mixed breather and rogue wave solution for the system. The interaction behaviors between the breather and rogue wave are studied. As a novel result, the energy transition between the breather and rogue wave is observed. Furthermore, the impacts of the different operators on the mixed solution are analyzed.〈/p〉
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    Thema: Mathematik
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  • 5
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    Generalized Wright stability for distributed fractional-order nonlinear dynamical systems and their synchronization (2019)
    Springer
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    Publikationsdatum: 2019
    Beschreibung: 〈h3〉Abstract〈/h3〉 〈p〉In this article, we present a generalization of stability theorems for Caputo fractional derivative to the distributed fractional-order (DFO) case by using the Laplace transform and the asymptotical expansion of the generalized Mittag–Leffler function. We propose the definition of the generalized Wright stability to study the stability of DFO nonlinear dynamical system using Lyapunov direct method. The linear feedback control is used to stabilize a class of chaotic DFO nonlinear dynamical systems. Using Lyapunov direct method, we study the synchronization between two identical chaotic systems and between two other different in the linear terms. The chaotic DFO Lorenz system is given as an example to achieve the linear feedback control technique. Another two examples which are chaotic DFO complex Chen and Lü systems are used to show the validity and feasibility of our proposed synchronization scheme. Numerical simulations are implemented to verify the results of these investigations.〈/p〉
    Print ISSN: 0924-090X
    Digitale ISSN: 1573-269X
    Thema: Mathematik
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  • 6
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    Comments on “Discrete fractional logistic map and its chaos” [Nonlinear Dyn. 75, 283–287 (2014)] (2019)
    Springer
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    Publikationsdatum: 2019
    Beschreibung: 〈h3〉Abstract〈/h3〉 〈p〉In this note, two comments are pointed out to the paper (Wu and Baleanu in Nonlinear Dyn 75:283–287, 〈span〉2014〈/span〉). It is confirmed that the equation of fractional logistic map proposed by Wu and Baleanu cannot be called the “fractional logistic map,” because the map does not converge to the classical logistic map in one dimension, and the analysis of bifurcation diagrams also exist problem. So, the revised equation and the correct bifurcation diagrams are presented in this note. Due to the high impact of the Wu and Baleanu’s paper, we believe that these comments will be helpful for the fractional community in the further research.〈/p〉
    Print ISSN: 0924-090X
    Digitale ISSN: 1573-269X
    Thema: Mathematik
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  • 7
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    Bistable vibration energy harvester and SECE circuit: exploring their mutual influence (2019)
    Springer
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    Publikationsdatum: 2019
    Beschreibung: 〈h3〉Abstract〈/h3〉 〈p〉The present work focuses on vibration energy harvesting to replace chemical batteries as power supplies in wireless autonomous sensors. More particularly, this article deals with nonlinear inertial oscillators and more precisely bistable harvesters, which offer a wide bandwidth compared to linear structures. These harvesters require AC–DC electronic interface to be able to supply wireless sensors or small intermediate storage elements (used to smooth the power demand). However, few studies have investigated the influence of AC–DC circuits on bistable harvesters. This work therefore focuses on developing the first analytical model able to predict the frequency response of a bistable harvester coupled to one of these interfaces: the SECE (synchronized electric charge extraction) circuit. This mathematical model includes subharmonic behaviors, stability analyses to small disturbances and the analyses of the stability robustness of high orbits characterizing their capability to handle external disturbances in real conditions without falling on a low orbit. The model is then validated experimentally with a buckled beam bistable harvester with piezoelectric conversion. The latter shows that the use of SECE circuit leads to multiply the mean extracted power from 1.3 to 2.2 compared to a direct connection to the load. The reachable frequency range is nevertheless divided by 1.55. 〈/p〉
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    Thema: Mathematik
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  • 8
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    Dynamic relationship analysis between NAFTA stock markets using nonlinear, nonparametric, non-stationary methods (2019)
    Springer
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    Publikationsdatum: 2019
    Beschreibung: 〈h3〉Abstract〈/h3〉 〈p〉This paper seeks to investigate the dynamic relationship between daily stock market indices in NAFTA countries from 8 November 1991 to 16 March 2018, using for the first time nonlinear, nonparametric, non-stationary methods. We apply two novel nonlinear, nonparametric, non-stationary dynamic correlation techniques—rolling window Spearman correlation and wavelet coherence—to study the relationships between the three pairwise comparisons. We apply a nonlinear, nonparametric causality test to four specific sub-periods and to the full period of these indices to check the direction of causality. Our results show the following: (1) the correlation between the indices increases from 2000 to 2011, but that correlation increase is interrupted around 2011/2012 and then falls noticeably, picking up again from 2015 onwards. (2) The pairs that show the lowest correlation are those involving the IPC. (3) The causality test reveals nonlinear bidirectional causality for all three indices and all the intervals analysed, indicating that there is a strong interrelationship between NAFTA members. These results are relevant to obtain a better understanding of the complex dynamical system formed by NAFTA stock markets and have direct implications for hedging and portfolio diversification policies.〈/p〉
    Print ISSN: 0924-090X
    Digitale ISSN: 1573-269X
    Thema: Mathematik
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  • 9
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    Enhancement of the entanglement generation via randomly perturbed series of external pulses in a nonlinear Bose–Hubbard dimer (2019)
    Springer
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    Publikationsdatum: 2019
    Beschreibung: 〈h3〉Abstract〈/h3〉 〈p〉We discuss a model of a short Bose–Hubbard dimer involving two anharmonic quantum oscillators mutually coupled with the use of the linear interaction and additionally driven by a series of ultra-short external pulses. We show that under some conditions the system behaves as a two-qubit one, and contrary to its continuously driven counterpart can be a source of maximally entangled states (MES). We discuss the cases when the system is excited only in one mode and in both ones, and additionally when the cross-Kerr-type interaction is present or omitted. We show that the generation of maximally (or almost maximally) entangled states depends on the time of free evolution of oscillators and hence, the proper steering of the changes of the time between subsequent pulses can increase the effectiveness of MES generation. Moreover, we show the influence of the timing between two series of pulses (corresponding to the two modes) on such a process. What is relevant, thanks to the presence of additional randomness in the timings, the states with stronger entanglement can be achieved than for the situation when the time between consecutive pulses remains ideally fixed.〈/p〉
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    Thema: Mathematik
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  • 10
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    Modelling and dynamic analysis of an anti-stall tool in a drilling system including spatial friction (2019)
    Springer
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    Publikationsdatum: 2019
    Beschreibung: 〈h3〉Abstract〈/h3〉 〈p〉This paper investigates the effects of a down-hole anti-stall tool (AST) in deviated wells on the drilling performance of a rotary drilling system. Deviated wells typically induce frictional contact between the drill-string and the borehole, which affects the drill-string dynamics. In order to study the influence of such frictional effects on the effectiveness of the AST in improving the rate-of-penetration and drilling efficiency, a model-based approach is proposed. A dynamic model with coupled axial and torsional dynamics of a drilling system including the down-hole tool in an inclined well is constructed. Furthermore, the frictional contact between the drill-string and the borehole is modelled by a set-valued spatial Coulomb friction law affecting both the axial and torsional dynamics. These dynamics are described by state-dependent delay differential inclusions. Numerical analysis of this model shows that the rate-of-penetration and drilling efficiency increases by inclusion of the AST, both in the case with and without spatial Coulomb friction. Furthermore, a parametric design study of the AST in different inclined drilling scenarios is performed. This study reveals a design for the AST, which gives optimal drilling efficiency, robustly over a broad range of inclined drilling scenarios.〈/p〉
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    Thema: Mathematik
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