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Analysis of an on-off intermittency system with adjustable state levels

Shi-Jian Cang, Zeng-Qiang Chen, Zhu Zhi Yuan (2008)

Kybernetika

We consider a chaotic system with a double-scroll attractor proposed by Elwakil, composing with a second-order system, which has low-dimensional multiple invariant subspaces and multi-level on-off intermittency. This type of composite system always includes a skew-product structure and some invariant subspaces, which are associated with different levels of laminar phase. In order for the level of laminar phase be adjustable, we adopt a nonlinear function with saturation characteristic to tune the...

Analysis of singularities and of integrability of ODE's by algorithms of Power Geometry

Alexander D. Bruno (2011)

Banach Center Publications

Here we present basic ideas and algorithms of Power Geometry and give a survey of some of its applications. In Section 2, we consider one generic ordinary differential equation and demonstrate how to find asymptotic forms and asymptotic expansions of its solutions. In Section 3, we demonstrate how to find expansions of solutions to Painlevé equations by this method, and we analyze singularities of plane oscillations of a satellite on an elliptic orbit. In Section 4, we consider the problem of local...

Analysis of the accuracy and convergence of equation-free projection to a slow manifold

Antonios Zagaris, C. William Gear, Tasso J. Kaper, Yannis G. Kevrekidis (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

In [C.W. Gear, T.J. Kaper, I.G. Kevrekidis and A. Zagaris, SIAM J. Appl. Dyn. Syst. 4 (2005) 711–732], we developed a class of iterative algorithms within the context of equation-free methods to approximate low-dimensional, attracting, slow manifolds in systems of differential equations with multiple time scales. For user-specified values of a finite number of the observables, the mth member of the class of algorithms ( m = 0 , 1 , ... ) finds iteratively an approximation of the appropriate zero of the (m+1)st...

Analysis of The Impact of Diabetes on The Dynamical Transmission of Tuberculosis

D.P. Moualeu, S. Bowong, J.J. Tewa, Y. Emvudu (2012)

Mathematical Modelling of Natural Phenomena

Tuberculosis (TB) remains a major global health problem. A possible risk factor for TB is diabetes (DM), which is predicted to increase dramatically over the next two decades, particularly in low and middle income countries, where TB is widespread. This study aimed to assess the strength of the association between TB and DM. We present a deterministic model for TB in a community in order to determine the impact of DM in the spread of the disease....

Analysis of two step nilsequences

Bernard Host, Bryna Kra (2008)

Annales de l’institut Fourier

Nilsequences arose in the study of the multiple ergodic averages associated to Furstenberg’s proof of Szemerédi’s Theorem and have since played a role in problems in additive combinatorics. Nilsequences are a generalization of almost periodic sequences and we study which portions of the classical theory for almost periodic sequences can be generalized for two step nilsequences. We state and prove basic properties for two step nilsequences and give a classification scheme for them.

Analytic enclosure of the fundamental matrix solution

Roberto Castelli, Jean-Philippe Lessard, Jason D. Mireles James (2015)

Applications of Mathematics

This work describes a method to rigorously compute the real Floquet normal form decomposition of the fundamental matrix solution of a system of linear ODEs having periodic coefficients. The Floquet normal form is validated in the space of analytic functions. The technique combines analytical estimates and rigorous numerical computations and no rigorous integration is needed. An application to the theory of dynamical system is presented, together with a comparison with the results obtained by computing...

Analytic invariants for the 1 : - 1 resonance

José Pedro Gaivão (2013)

Annales de l’institut Fourier

Associated to analytic Hamiltonian vector fields in 4 having an equilibrium point satisfying a non semisimple 1 : - 1 resonance, we construct two constants that are invariant with respect to local analytic symplectic changes of coordinates. These invariants vanish when the Hamiltonian is integrable. We also prove that one of these invariants does not vanish on an open and dense set.

Analytic torsions on contact manifolds

Michel Rumin, Neil Seshadri (2012)

Annales de l’institut Fourier

We propose a definition for analytic torsion of the contact complex on contact manifolds. We show it coincides with Ray–Singer torsion on any 3 -dimensional CR Seifert manifold equipped with a unitary representation. In this particular case we compute it and relate it to dynamical properties of the Reeb flow. In fact the whole spectral torsion function we consider may be interpreted on CR Seifert manifolds as a purely dynamical function through Selberg-like trace formulae, that hold also in variable...

Analytical derivation of time spectral rigidity for thermodynamic traffic gas

Milan Krbálek (2010)

Kybernetika

We introduce an one-dimensional thermodynamical particle model which is efficient in predictions about a microscopical structure of animal/human groups. For such a model we present analytical calculations leading to formulae for time clearance distribution as well as for time spectral rigidity. Furthermore, the results obtained are reformulated in terms of vehicular traffic theory and consecutively compared to experimental traffic data.

Anisotropic Hölder and Sobolev spaces for hyperbolic diffeomorphisms

Viviane Baladi, Masato Tsujii (2007)

Annales de l’institut Fourier

We study spectral properties of transfer operators for diffeomorphisms T : X X on a Riemannian manifold X . Suppose that Ω is an isolated hyperbolic subset for T , with a compact isolating neighborhood V X . We first introduce Banach spaces of distributions supported on V , which are anisotropic versions of the usual space of C p functions C p ( V ) and of the generalized Sobolev spaces W p , t ( V ) , respectively. We then show that the transfer operators associated to  T and a smooth weight g extend boundedly to these spaces, and...

Anosov flows and non-Stein symplectic manifolds

Yoshihiko Mitsumatsu (1995)

Annales de l'institut Fourier

We simplify and generalize McDuff’s construction of symplectic 4-manifolds with disconnected boundary of contact type in terms of the linking pairing defined on the dual of 3-dimensional Lie algebras. This leads us to an observation that an Anosov flow gives rise to a bi-contact structure, i.e. a transverse pair of contact structures with different orientations, and the construction turns out to work for 3-manifolds which admit Anosov flows with smooth invariant volume. Finally, new examples of...

Currently displaying 441 – 460 of 557