Characterizing chaos in a type of fractional duffing's equation

We characterize the chaos in a fractional Duffing’s equation computing the Lyapunov exponents and the dimension of the strange attractor in the effective phase space of the system. We develop a specific analytical method to estimate all Lyapunov exponents and check the results with the fiduciary orbit technique and a time series estimation method.

Multistability, chaos, and random signal generation in semiconductor superlattices

Peer reviewed

Chaos, but in voting and apportionments?

Mathematical chaos and related concepts are used to explain and resolve issues ranging from voting paradoxes to the apportioning of congressional seats.

Titration of chaos with added noise

Deterministic chaos has been implicated in numerous natural and man-made complex phenomena ranging from quantum to astronomical scales and in disciplines as diverse as meteorology, physiology, ecology, and economics. However, the lack of a definitive test of chaos vs. random noise in experimental time series has led to considerable controversy in many fields. Here we propose a numerical titration procedure as a simple “litmus test” for highly sensitive, specific, and robust detection of chaos in short noisy data without the need for intensive surrogate data testing. We show that the controlled addition of white or colored noise to a signal with a preexisting noise floor results in a titration index that: (i) faithfully tracks the onset of deterministic chaos in all standard bifurcation routes to chaos; and (ii) gives a relative measure of chaos intensity. Such reliable detection and quantification of chaos under severe conditions of relatively low signal-to-noise ratio is of great interest, as it may open potential practical ways of identifying, forecasting, and controlling complex behaviors in a wide variety of physical, biomedical, and socioeconomic systems.

Ecological chaos in the wake of invasion.

Irregularities in observed population densities have traditionally been attributed to discretization of the underlying dynamics. We propose an alternative explanation by demonstrating the evolution of spatiotemporal chaos in reaction-diffusion models for predator-prey interactions. The chaos is generated naturally in the wake of invasive waves of predators. We discuss in detail the mechanism by which the chaos is generated. By considering a mathematical caricature of the predator-prey models, we go on to explain the dynamical origin of the irregular behavior and to justify our assertion that the behavior we present is a genuine example of spatiotemporal chaos.

Temperature chaos in 3D Ising spin glasses is driven by rare events

Temperature chaos has often been reported in the literature as a rare-event–driven phenomenon. However, this fact has always been ignored in the data analysis, thus erasing the signal of the chaotic behavior (still rare in the sizes achieved) and leading to an overall picture of a weak and gradual phenomenon. On the contrary, our analysis relies on a largedeviations functional that allows to discuss the size dependences. In addition, we had at our disposal unprecedentedly large configurations equilibrated at low temperatures, thanks to the Janus computer. According to our results, when temperature chaos occurs its effects are strong and can be felt even at short distances.

Linear chaos for the Quick-Thinking-Driver model.

In recent years, the topic of car-following has experimented an increased importance in traffic engineering and safety research. This has become a very interesting topic because of the development of driverless cars (Google driverless cars, http://en.wikipedia.org/wiki/Google_driverless_car). Driving models which describe the interaction between adjacent vehicles in the same lane have a big interest in simulation modeling, such as the Quick-Thinking-Driver model. A non-linear version of it can be given using the logistic map, and then chaos appears. We show that an infinite-dimensional version of the linear model presents a chaotic behaviour using the same approach as for studying chaos of death models of cell growth.

Chemical Reactors. Problem 1: A simple ODE (chaos in the atmosphere) (2011-2012 Course)

Wording of problem 1: A simple ODE (chaos in the atmosphere).

Dynamic Visual Servoing With Chaos Control for Redundant Robots

This paper presents a new dynamic visual control system for redundant robots with chaos compensation. In order to implement the visual servoing system, a new architecture is proposed that improves the system maintainability and traceability. Furthermore, high performance is obtained as a result of parallel execution of the different tasks that compose the architecture. The control component of the architecture implements a new visual servoing technique for resolving the redundancy at the acceleration level in order to guarantee the correct motion of both end-effector and joints. The controller generates the required torques for the tracking of image trajectories. However, in order to guarantee the applicability of this technique, a repetitive path tracked by the robot-end must produce a periodic joint motion. A chaos controller is integrated in the visual servoing system and the correct performance is observed in low and high velocities. Furthermore, a method to adjust the chaos controller is proposed and validated using a real three-link robot.

Descent from banking union to political chaos. CEPS Commentary, 24 January 2014

To counteract the powerful anti-Europe sentiments swirling throughout the EU today and to motivate EU citizens to vote in a constructive spirit in the upcoming European elections, Karel Lannoo argues in this commentary that the functioning of the EU institutions needs to be openly discussed and proposals need to be aired for improving the decision-making process to render it more transparent and democratic. This process would encompass, in his view, the proper role and functioning of the European Commission, the European Parliament and the member states in the EU Council and the interrelationships between these institutions.

Bosniacki chaos. Zrodla kryzysu politycznego we wspolczesnej Bosni i Hercegowinie. Prace OSW 31/2009. = Bosnia's chaos. Causes of the political crisis in Bosnia and Herzegovina today. OSW Study 31/2009

A new form of 'transformational crisis' has been observed in Bosnia and Herzegovina since at least 2005. Politicians representing the three major ethno-political communities (Bosnians, Croats and Serbs) have successively been raising disputes and have employed various political tools to preserve the conflicts instead of resolving them. As a result, the central state institutions and organisations have been weakened and attempts to replace them with narrower ethnic structures have been made. This is increasingly paralysing the state, thus impeding its everyday operation and preventing its structures and legislation from being modernised; had this been achieved, it would have resulted in a real acceleration of the process of Bosnia's integration with the EU and NATO. The present crisis is also an effect of the disagreement between the key international players - the European Union, the United States and Russia - over the 'plan for Bosnia' and the role and duties of the Office of the High Representative, who acts on behalf of the international community in the country.

The debt, the stock market and the state-owned enterprises. The sources of chaos on the Chinese financial markets. OSW Commentary NUMBER 201/16.03.2016

The government’s extensive programme for stimulating the economy has enabled China to maintain high economic growth after the global financial crisis in 2008. However, this success has come at the price of a number of negative economic phenomena and the consequences they have had are the major challenge for the government today. The vast programme of investments in infrastructure, construction and fixed assets, which has been the main source of economic growth over the past few years, has caused a rapid increase in China’s debt from 158% of GDP in 2007 to 282% in 2014. Along with the local governments in charge of implementing the programme, the Chinese sector of state-owned enterprises (SOEs) has been heavily burdened by the stimulation policy. The sector’s profitability has fallen, its indebtedness has increased and management problems have been revealed.

Europe in limbo while the UK descends into chaos. EPC Post-Summit Commentary, 30 June 2016

The EU Summit and the separate meeting of the EU27 without the UK on 28/29 June 2016 demonstrated that the EU is in limbo. Following the initial shock, frustration and anger after the unexpected result of the UK ‘in/out’ referendum, the future relationship between the European Union (EU) and the United Kingdom (UK) monopolised the meetings of EU leaders. The EU has entered uncharted waters and leaders are struggling to figure out how exactly to deal with the manifold (potential) consequences of the ‘Brexit crisis’. Despite the many uncertainties, the EU27 managed to reach some common lines, trying to convey four key messages, although the final outcome of the crisis and its effects on the Union’s overall future are still very unclear:

A four moments theorem for Gamma limits on a Poisson chaos

This paper deals with sequences of random variables belonging to a fixed chaos of order q generated by a Poisson random measure on a Polish space. The problem is investigated whether convergence of the third and fourth moment of such a suitably normalized sequence to the third and fourth moment of a centred Gamma law implies convergence in distribution of the involved random variables. A positive answer is obtained for q = 2 and q = 4. The proof of this four moments theorem is based on a number of new estimates for contraction norms. Applications concern homogeneous sums and U-statistics on the Poisson space.