Search results for "dynamical systems"
showing 10 items of 476 documents
Post-Double Hopf Bifurcation Dynamics and Adaptive Synchronization of a Hyperchaotic System
2012
In this paper a four-dimensional hyperchaotic system with only one equilibrium is considered and its double Hopf bifurcations are investigated. The general post-bifurcation and stability analysis are carried out using the normal form of the system obtained via the method of multiple scales. The dynamics of the orbits predicted through the normal form comprises possible regimes of periodic solutions, two-period tori, and three-period tori in parameter space. Moreover, we show how the hyperchaotic synchronization of this system can be realized via an adaptive control scheme. Numerical simulations are included to show the effectiveness of the designed control.
Symbolic dynamics in a binary asteroid system
2020
We highlight the existence of a topological horseshoe arising from a a--priori stable model of the binary asteroid dynamics. The inspection is numerical and uses correctly aligned windows, as described in a recent paper by A. Gierzkiewicz and P. Zgliczy\'nski, combined with a recent analysis of an associated secular problem.
Iterated function systems and well-posedness
2009
Abstract Fractals and multivalued fractals play an important role in biology, quantum mechanics, computer graphics, dynamical systems, astronomy and astrophysics, geophysics, etc. Especially, there are important consequences of the iterated function (or multifunction) systems in several topics of applied sciences [see for example: El Naschie MS. Iterated function systems and the two-slit experiment of quantum mechanics. Chaos, Solitons & Fractals 1994;4:1965–8; Iovane G. Cantorian spacetime and Hilbert space: Part I-Foundations. Chaos, Solitons & Fractals 2006;28:857–78; Iovane G. Cantorian space-time and Hilbert space: Part II-Relevant consequences. Chaos, Solitons & Fractals 2006;29:1–22;…
Universality of Schmidt decomposition and particle identity
2017
Schmidt decomposition is a widely employed tool of quantum theory which plays a key role for distinguishable particles in scenarios such as entanglement characterization, theory of measurement and state purification. Yet, it is held not to exist for identical particles, an open problem forbidding its application to analyze such many-body quantum systems. Here we prove, using a newly developed approach, that the Schmidt decomposition exists for identical particles and is thus universal. We find that it is affected by single-particle measurement localization and state overlap. We study paradigmatic two-particle systems where identical qubits and qutrits are located in the same place or in sep…
Model Identification of a Network as Compressing Sensing
2013
In many applications, it is important to derive information about the topology and the internal connections of dynamical systems interacting together. Examples can be found in fields as diverse as Economics, Neuroscience and Biochemistry. The paper deals with the problem of deriving a descriptive model of a network, collecting the node outputs as time series with no use of a priori insight on the topology, and unveiling an unknown structure as the estimate of a "sparse Wiener filter". A geometric interpretation of the problem in a pre-Hilbert space for wide-sense stochastic processes is provided. We cast the problem as the optimization of a cost function where a set of parameters are used t…
Almost sure rates of mixing for i.i.d. unimodal maps
2002
International audience; It has been known since the pioneering work of Jakobson and subsequent work by Benedicks and Carleson and others that a positive measure set of quadratic maps admit an absolutely continuous invariant measure. Young and Keller-Nowicki proved exponential decay of its correlation functions. Benedicks and Young, and Baladi and Viana studied stability of the density and exponential rate of decay of the Markov chain associated to i.i.d. small perturbations. The almost sure statistical properties of the sample stationary measures of i.i.d. itineraries are more difficult to estimate than the "averaged statistics". Adapting to random systems, on the one hand partitions associ…
A New Wavelet Tool to Quantify Non-Periodicity of Non-Stationary Economic Time Series
2020
We introduce a new wavelet tool, the windowed scale index, to study the degree of non-periodicity of time series. The windowed scale index is based on some recently defined tools, such as the windowed scalogram and the scale index. This novel measure is appropriate for non-stationary time series whose characteristics change over time and, therefore, it can be applied to a wide variety of disciplines. Furthermore, we revise the concept of the scale index and pose a theoretical problem: it is known that if the scale index of a function is not zero then it is non-periodic, but if the scale index of a function is zero, then it is not proved that it has to be periodic. This problem is solved for…
Long time behavior for a dissipative shallow water model
2013
We consider the two-dimensional shallow water model derived by Levermore and Sammartino (Nonlinearity 14,2001), describing the motion of an incompressible fluid, confined in a shallow basin, with varying bottom topography. We construct the approximate inertial manifolds for the associated dynamical system and estimate its order. Finally, considering the whole domain R^2 and under suitable conditions on the time dependent forcing term, we prove the L^2 asymptotic decay of the weak solutions.
Information Decomposition in Multivariate Systems: Definitions, Implementation and Application to Cardiovascular Networks
2016
The continuously growing framework of information dynamics encompasses a set of tools, rooted in information theory and statistical physics, which allow to quantify different aspects of the statistical structure of multivariate processes reflecting the temporal dynamics of complex networks. Building on the most recent developments in this field, this work designs a complete approach to dissect the information carried by the target of a network of multiple interacting systems into the new information produced by the system, the information stored in the system, and the information transferred to it from the other systems; information storage and transfer are then further decomposed into amou…
Hysteresis Model of Unconscious-Conscious Interconnection: Exploring Dynamics on m-Adic Trees
2015
The theoretical model outlined in this paper, has been experimentally validated by: H. Kim ,J-Y. Moon ,G.A. Mashour & U. Lee, ''Mechanisms of hysteresis in human brain networks during transitions of consciousness and unconsciousness: Theoretical principles and empirical evidence'', PLOS-Computational Biology, August 30, 2018, https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1006424; International audience; In this brief note, we focus attention on a possible implementation of a basic hysteretic pattern (the Preisach one), suitably generalized, into a formal model of unconscious-conscious interconnection and based on representation of mental entities by m-adic numbers. …