852 research outputs found
Probing the local dynamics of periodic orbits by the generalized alignment index (GALI) method
As originally formulated, the Generalized Alignment Index (GALI) method of
chaos detection has so far been applied to distinguish quasiperiodic from
chaotic motion in conservative nonlinear dynamical systems. In this paper we
extend its realm of applicability by using it to investigate the local dynamics
of periodic orbits. We show theoretically and verify numerically that for
stable periodic orbits the GALIs tend to zero following particular power laws
for Hamiltonian flows, while they fluctuate around non-zero values for
symplectic maps. By comparison, the GALIs of unstable periodic orbits tend
exponentially to zero, both for flows and maps. We also apply the GALIs for
investigating the dynamics in the neighborhood of periodic orbits, and show
that for chaotic solutions influenced by the homoclinic tangle of unstable
periodic orbits, the GALIs can exhibit a remarkable oscillatory behavior during
which their amplitudes change by many orders of magnitude. Finally, we use the
GALI method to elucidate further the connection between the dynamics of
Hamiltonian flows and symplectic maps. In particular, we show that, using for
the computation of GALIs the components of deviation vectors orthogonal to the
direction of motion, the indices of stable periodic orbits behave for flows as
they do for maps.Comment: 17 pages, 9 figures (accepted for publication in Int. J. of
Bifurcation and Chaos
Perspectives on punitivity, victimisation and fear of crime: A student case study in the United Kingdom
`The dragon breathes smoke': cigarette counterfeiting in the People's Republic of China
This article aims at providing an account of the social organization of the cigarette counterfeiting business in the People's Republic of China—a business that has been feeding the cigarette black markets around the globe. Specifically, we aim to exhibit the scale and nature of cigarette counterfeiting in mainland China, describe the practices and actors in the different phases of the trade, and examine the role of corruption and violence in the particular business. We argue that cigarette counterfeiting is one of the side effects of China's reform and ‘opening up’ policy, and a feature of the country's economic development process
Nonlinear dynamics and onset of chaos in a physical model of a damper pressure relief valve
Hydraulic valves, for the purpose of targeted pressure relief and damping,
are a ubiquitous part of modern suspension systems. This paper deals with the
analytical computation of fixed points of the dynamical system of a
single-stage shock absorber valve, which can be applied for the direct
computation of its system variables at equilibrium without brute-force
numerical integration. The obtained analytical expressions are given for the
original dimensional version of the model derived from continuity and motion
equations for a realistic valve setup. Furthermore, a large part of the study
is devoted to a systematic sensitivity analysis of the model towards crucial
parameter changes. Numerical investigation of a potential loss of stability and
following nonlinear oscillations is performed in multi-dimensional parameter
spaces, which reveals sustained valve vibrations at increased valve mass and
applied pretension force. The dynamical behaviour is analysed by phase space
orbits, as well as Fourier-transformed valve displacement data to identify
dominant frequencies. Chaotic indicators, such as Lyapunov exponents and the
Smaller Alignment Index (SALI), are utilized to understand the nature of the
oscillatory motion and to distinguish between order and chaos
Unfolding the procedure of characterizing recorded ultra low frequency, kHZ and MHz electromagetic anomalies prior to the L'Aquila earthquake as pre-seismic ones. Part I
Ultra low frequency, kHz and MHz electromagnetic anomalies were recorded
prior to the L'Aquila catastrophic earthquake that occurred on April 6, 2009.
The main aims of this contribution are: (i) To suggest a procedure for the
designation of detected EM anomalies as seismogenic ones. We do not expect to
be possible to provide a succinct and solid definition of a pre-seismic EM
emission. Instead, we attempt, through a multidisciplinary analysis, to provide
elements of a definition. (ii) To link the detected MHz and kHz EM anomalies
with equivalent last stages of the L'Aquila earthquake preparation process.
(iii) To put forward physically meaningful arguments to support a way of
quantifying the time to global failure and the identification of distinguishing
features beyond which the evolution towards global failure becomes
irreversible. The whole effort is unfolded in two consecutive parts. We clarify
we try to specify not only whether or not a single EM anomaly is pre-seismic in
itself, but mainly whether a combination of kHz, MHz, and ULF EM anomalies can
be characterized as pre-seismic one
Labyrinth chaos: Revisiting the elegant, chaotic, and hyperchaotic walks
Labyrinth chaos was discovered by Otto Rössler and René Thomas in their endeavour to identify the necessary mathematical conditions for the appearance of chaotic and hyperchaotic motion in continuous flows. Here, we celebrate their discovery by considering a single labyrinth walks system and an array of coupled labyrinth chaos systems that exhibit complex, chaotic behaviour, reminiscent of chimera-like states, a peculiar synchronisation phenomenon. We discuss the properties of the single labyrinth walks system and review the ability of coupled labyrinth chaos systems to exhibit chimera-like states due to the unique properties of their space-filling, chaotic trajectories, what amounts to elegant, hyperchaotic walks. Finally, we discuss further implications in relation to the labyrinth walks system by showing that even though it is volume-preserving, it is not force-conservative
Dynamic tracking with model-based forecasting for the spread of the COVID-19 pandemic
In this paper, a susceptible-infected-removed (SIR) model has been used to track the evolution of the spread of COVID-19 in four countries of interest. In particular, the epidemic model, that depends on some basic character- istics, has been applied to model the evolution of the disease in Italy, India, South Korea and Iran. The economic, social and health consequences of the spread of the virus have been cataclysmic. Hence, it is imperative that math- ematical models can be developed and used to compare published datasets with model predictions. The predictions estimated from the presented methodology can be used in both the qualitative and quantitative analysis of the spread. They give an insight into the spread of the virus that the published data alone cannot, by updating them and the model on a daily basis. We show that by doing so, it is possible to detect the early onset of secondary spikes in infections or the development of secondary waves. We considered data from March to August, 2020, when different communities were affected severely and demonstrate predictions depending on the model’s parameters related to the spread of COVID-19 until the end of December, 2020. By comparing the published data with model results, we conclude that in this way, it may be possible to reflect better the success or failure of the adequate measures implemented by governments and authorities to mitigate and control the current pandemic
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