اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدDynamics of a map with power-law tail
125
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We analyze a one-dimensional piecewise continuous discrete model proposed originally in studies on population ecology. The map is composed of a linear part and a power-law decreasing piece, and has three parameters. The system presents both regular and chaotic behavior. We study numerically and, in part, analytically different bifurcation structures. Particularly interesting is the description of the abrupt transition order-to-chaos mediated by an attractor made of an infinite number of limit cycles with only a finite number of different periods. It is shown that the power-law piece in the map is at the origin of this type of bifurcation. The system exhibits interior crises and crisis-induced intermittency.
قيم البحث
اقرأ أيضاً
We use symbolic dynamics to study discrete-time dynamical systems with multiple time delays. We exploit the concept of avoiding sets, which arise from specific non-generating partitions of the phase space and restrict the occurrence of certain symbol
sequences related to the characteristics of the dynamics. In particular, we show that the resulting forbidden sequences are closely related to the time delays in the system. We present two applications to coupled map lattices, namely (1) detecting synchronization and (2) determining unknown values of the transmission delays in networks with possibly directed and weighted connections and measurement noise. The method is applicable to multi-dimensional as well as set-valued maps, and to networks with time-varying delays and connection structure.
Analytically tractable dynamical systems exhibiting a whole range of normal and anomalous deterministic diffusion are rare. Here we introduce a simple non-chaotic model in terms of an interval exchange transformation suitably lifted onto the whole re
al line which preserves distances except at a countable set of points. This property, which leads to vanishing Lyapunov exponents, is designed to mimic diffusion in non-chaotic polygonal billiards that give rise to normal and anomalous diffusion in a fully deterministic setting. As these billiards are typically too complicated to be analyzed from first principles, simplified models are needed to identify the minimal ingredients generating the different transport regimes. For our model, which we call the slicer map, we calculate all its moments in position analytically under variation of a single control parameter. We show that the slicer map exhibits a transition from subdiffusion over normal diffusion to superdiffusion under parameter variation. Our results may help to understand the delicate parameter dependence of the type of diffusion generated by polygonal billiards. We argue that in different parameter regions the transport properties of our simple model match to different classes of known stochastic processes. This may shed light on difficulties to match diffusion in polygonal billiards to a single anomalous stochastic process.
We study the statistics of the amplitude of the synchronization error in chaotic electronic circuits coupled through linear feedback. Depending on the coupling strength, our system exhibits three qualitatively different regimes of synchronization: we
ak coupling yields independent oscillations; moderate to strong coupling produces a regime of intermittent synchronization known as attractor bubbling; and stronger coupling produces complete synchronization. In the regime of moderate coupling, the probability distribution for the sizes of desynchronization events follows a power law, with an exponent that can be adjusted by changing the coupling strength. Such power-law distributions are interesting, as they appear in many complex systems. However, most of the systems with such a behavior have a fixed value for the exponent of the power law, while here we present an example of a system where the exponent of the power law is easily tuned in real time.
We report the detection of pulsed gamma-ray emission from the Geminga pulsar (PSR J0633+1746) between $15,$GeV and $75,$GeV. This is the first time a middle-aged pulsar has been detected up to these energies. Observations were carried out with the MA
GIC telescopes between 2017 and 2019 using the low-energy threshold Sum-Trigger-II system. After quality selection cuts, $sim 80,$hours of observational data were used for this analysis. To compare with the emission at lower energies below the sensitivity range of MAGIC, $11$ years of Fermi-LAT data above $100,$MeV were also analysed. From the two pulses per rotation seen by Fermi-LAT, only the second one, P2, is detected in the MAGIC energy range, with a significance of $6.3,sigma$. The spectrum measured by MAGIC is well-represented by a simple power law of spectral index $Gamma= 5.62pm0.54$, which smoothly extends the Fermi-LAT spectrum. A joint fit to MAGIC and Fermi-LAT data rules out the existence of a sub-exponential cut-off in the combined energy range at the $3.6,sigma$ significance level. The power-law tail emission detected by MAGIC is interpreted as the transition from curvature radiation to Inverse Compton Scattering of particles accelerated in the northern outer gap.
We point out the joint occurrence of Pascal triangle patterns and power-law scaling in the standard logistic map, or more generally, in unimodal maps. It is known that these features are present in its two types of bifurcation cascades: period and ch
aotic- band doubling of attractors. Approximate Pascal triangles are exhibited by the sets of lengths of supercycle diameters and by the sets of widths of opening bands. Additionally, power-law scaling manifests along periodic attractor supercycle positions and chaotic band splitting points. Consequently, the attractor at the mutual accumulation point of the doubling cascades, the onset of chaos, displays both Gaussian and power-law distributions. Their combined existence implies both ordinary and exceptional statistical-mechanical descriptions of dynamical properties.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
