Bifurcations and Chaos in the Dynamics of Two Point Vortices in an Acoustic Wave
In this paper, we consider a system governing the motion of two point vortices in a flow excited by an external acoustic forcing. It is known that the system of two vortices is integrable in the absence of acoustic forcing. However, the addition of the acoustic forcing makes the system much more complex, and the system becomes nonintegrable and loses the phase volume preservation property. The objective of our research is to study chaotic dynamics and typical bifurcations. Numerical analysis has shown that the reversible pitchfork bifurcation is typical. Also, we show that the existence of strange attractors is not characteristic for the system under consideration
The introduction describes the concept in the "hard"and "soft" sciences.
Der vorliegende Bank ist einer fuenf jaehrigen Projektarbeit zu Synergie-Konzepten. Synergie ist ein Schlüsselbegriff in Wissenschaft und Gesellschaft. Wie wird er historisch und gegenwärtig verwendet? Was zeichnet ihn als produktives Paradigma in interdisziplinären Forschungs- und Praxisfeldern aus? Als Modell einer holistischen Beschreibung der Wirklichkeit macht die synergetische Perspektive die aristotelische Einsicht fruchtbar, dass das Ganze mehr ist als bloß die Summe seiner Teile. Allgemeine Theorien des Zusammenwirkens (synérgeia) nehmen hier ihren Ausgangspunkt. Mit Blick auf kooperative Interaktionen und dynamische Strukturbildungen in Natur, Kunst und Gesellschaft untersuchen die Beiträge philosophie-, wissenschafts- und kulturgeschichtliche Konstellationen, in denen Synergie-Konzepte besondere Konjunktur haben, und fragen nach dem Zukunftspotenzial dieser transdisziplinären Denkfigur.
Sunspot number WN displays quasi-periodical variations that undergo regime changes. These irregularities could indicate a chaotic system and be measured by Lyapunov exponents. We define a functional l (an “irregularity index”) that is close to the (maximal) Lyapunov exponent for dynamical systems and well defined for series with a random component: this allows one to work with sunspot numbers. We compute l for the daily WN from 1850 to 2012 within 4-year sliding windows: l exhibit sharp maxima at solar minima and secondary maxima at solar maxima. This pattern is reflected in the ratio R of the amplitudes of the main vs secondary peaks. Two regimes have alternated in the past 150 years, R1 from 1850 to 1915 (large l and R values) and R2 from 1935 to 2005 (shrinking difference between main and secondary maxima, R values between 1 and 2). We build an autoregressive model consisting of Poisson noise plus an 11-yr cycle, and compute its irregularity index. The transition from R1 to R2 can be reproduced by strengthening the autocorrelation a of the model series. The features of the two regimes are stable for model and WN with respect to embedding dimension and delay. Near the time of the last solar minimum (~2008), the irregularity index exhibits a peak similar to the peaks observed before 1915. This might signal a regime change back from R2 to R1 and the onset of a significant decrease of solar activity.
The book describes the concepts of chaos and order in the "hard" and "soft" sciences.
The authors propose new approach to self-organization of complex distributed systems in logistics. That approach is based on combination of multi-agent paradigm with constraint satisfaction techniques. The proposed solution expresses major features of Swarm Intelligence approach and replaces traditional stochastic adaptation of the swarm of the autonomous agents by constraint-driven adaptation.
The monograph is devoted to the consideration of complex systems from the position of the end the 21st century. The considerable breakthrough in the understanding of complex systems is comprehensively analyzed. Such a breakthrough is connected with the use of the newest methods of nonlinear dynamics, of organization of the modern computational experiments. The book is meant for specialists in different fields of natural sciences and the humanities as well as for all readers who are interested in the recent advancements in science.
The work is devoted to fundamental aspects of the classical molecular dynamics method, which was developed half a century ago as a means of solving computational problems in statistical physics and has now become one of the most important numerical methods in the theory of condensed state. At the same time, the molecular dynamics method based on solving the equations of motion for a multiparticle system proved to be directly related to the basic concepts of classical statistical physics, in particular, to the problem of the occurrence of irreversibility. This paper analyzes the dynamic and stochastic properties of molecular dynamics systems connected with the local instability of trajectories and the errors of the numerical integration. The probabilistic nature of classical statistics is discussed. We propose a concept explaining the finite dynamic memory time and the emergence of irreversibility in real systems.
A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.
This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.