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BOOK EXCERPT:
The authors prove that in systems undergoing Hopf bifurcations, the effects of periodic forcing can be amplified by the shearing in the system to create sustained chaotic behavior. Specifically, strange attractors with SRB measures are shown to exist. The analysis is carried out for infinite dimensional systems, and the results are applicable to partial differential equations. Application of the general results to a concrete equation, namely the Brusselator, is given.
Product Details :
Genre |
: Mathematics |
Author |
: Kening Lu |
Publisher |
: American Mathematical Soc. |
Release |
: 2013-06-28 |
File |
: 97 Pages |
ISBN-13 |
: 9780821884843 |
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BOOK EXCERPT:
Nonautonomous dynamics describes the qualitative behavior of evolutionary differential and difference equations, whose right-hand side is explicitly time dependent. Over recent years, the theory of such systems has developed into a highly active field related to, yet recognizably distinct from that of classical autonomous dynamical systems. This development was motivated by problems of applied mathematics, in particular in the life sciences where genuinely nonautonomous systems abound. The purpose of this monograph is to indicate through selected, representative examples how often nonautonomous systems occur in the life sciences and to outline the new concepts and tools from the theory of nonautonomous dynamical systems that are now available for their investigation.
Product Details :
Genre |
: Mathematics |
Author |
: Peter E. Kloeden |
Publisher |
: Springer |
Release |
: 2014-01-22 |
File |
: 326 Pages |
ISBN-13 |
: 9783319030807 |
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Product Details :
Genre |
: Medical |
Author |
: Joon Ha |
Publisher |
: Frontiers Media SA |
Release |
: 2023-01-27 |
File |
: 142 Pages |
ISBN-13 |
: 9782832512142 |
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BOOK EXCERPT:
In particular, for b = 1 and λ = 0, we find a sharp condition on h such that the origin is a removable singularity for all non-negative solutions of [[eqref]]one, thus addressing an open question of Vázquez and Véron.
Product Details :
Genre |
: Mathematics |
Author |
: Florica C. Cîrstea |
Publisher |
: American Mathematical Soc. |
Release |
: 2014-01-08 |
File |
: 97 Pages |
ISBN-13 |
: 9780821890226 |
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BOOK EXCERPT:
The authors study the Cauchy problem for the sine-Gordon equation in the semiclassical limit with pure-impulse initial data of sufficient strength to generate both high-frequency rotational motion near the peak of the impulse profile and also high-frequency librational motion in the tails. They show that for small times independent of the semiclassical scaling parameter, both types of motion are accurately described by explicit formulae involving elliptic functions. These formulae demonstrate consistency with predictions of Whitham's formal modulation theory in both the hyperbolic (modulationally stable) and elliptic (modulationally unstable) cases.
Product Details :
Genre |
: Mathematics |
Author |
: Robert J. Buckingham |
Publisher |
: American Mathematical Soc. |
Release |
: 2013-08-23 |
File |
: 148 Pages |
ISBN-13 |
: 9780821885451 |
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BOOK EXCERPT:
The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
Product Details :
Genre |
: Mathematics |
Author |
: Boyan Sirakov |
Publisher |
: World Scientific |
Release |
: 2019-02-27 |
File |
: 5393 Pages |
ISBN-13 |
: 9789813272897 |
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BOOK EXCERPT:
Advances in Nonlinear Geosciences is a set of contributions from the participants of “30 Years of Nonlinear Dynamics” held July 3-8, 2016 in Rhodes, Greece as part of the Aegean Conferences, as well as from several other experts in the field who could not attend the meeting. The volume brings together up-to-date research from the atmospheric sciences, hydrology, geology, and other areas of geosciences and presents the new advances made in the last 10 years. Topics include chaos synchronization, topological data analysis, new insights on fractals, multifractals and stochasticity, climate dynamics, extreme events, complexity, and causality, among other topics.
Product Details :
Genre |
: Science |
Author |
: Anastasios A. Tsonis |
Publisher |
: Springer |
Release |
: 2017-10-13 |
File |
: 708 Pages |
ISBN-13 |
: 9783319588957 |
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BOOK EXCERPT:
The aim of this paper is to analyze some of the relationships between oscillation theory for linear ordinary differential equations on the real line (shortly, ODE) and the geometry of complete Riemannian manifolds. With this motivation the authors prove some new results in both directions, ranging from oscillation and nonoscillation conditions for ODE's that improve on classical criteria, to estimates in the spectral theory of some geometric differential operator on Riemannian manifolds with related topological and geometric applications. To keep their investigation basically self-contained, the authors also collect some, more or less known, material which often appears in the literature in various forms and for which they give, in some instances, new proofs according to their specific point of view.
Product Details :
Genre |
: Mathematics |
Author |
: Bruno Bianchini |
Publisher |
: American Mathematical Soc. |
Release |
: 2013-08-23 |
File |
: 208 Pages |
ISBN-13 |
: 9780821887998 |
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BOOK EXCERPT:
We study the unconstrained (free) motion of an elastic solid B in a Navier-Stokes liquid L occupying the whole space outside B, under the assumption that a constant body force b is acting on B. More specifically, we are interested in the steady motion of the coupled system {B,L}, which means that there exists a frame with respect to which the relevant governing equations possess a time-independent solution. We prove the existence of such a frame, provided some smallness restrictions are imposed on the physical parameters, and the reference configuration of B satisfies suitable geometric properties.
Product Details :
Genre |
: Mathematics |
Author |
: Josef Bemelmans |
Publisher |
: American Mathematical Soc. |
Release |
: 2013-10-23 |
File |
: 102 Pages |
ISBN-13 |
: 9780821887738 |
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BOOK EXCERPT:
Recently, the old notion of causal boundary for a spacetime V has been redefined consistently. The computation of this boundary ∂V on any standard conformally stationary spacetime V=R×M, suggests a natural compactification MB associated to any Riemannian metric on M or, more generally, to any Finslerian one. The corresponding boundary ∂BM is constructed in terms of Busemann-type functions. Roughly, ∂BM represents the set of all the directions in M including both, asymptotic and "finite" (or "incomplete") directions. This Busemann boundary ∂BM is related to two classical boundaries: the Cauchy boundary ∂CM and the Gromov boundary ∂GM. The authors' aims are: (1) to study the subtleties of both, the Cauchy boundary for any generalized (possibly non-symmetric) distance and the Gromov compactification for any (possibly incomplete) Finsler manifold, (2) to introduce the new Busemann compactification MB, relating it with the previous two completions, and (3) to give a full description of the causal boundary ∂V of any standard conformally stationary spacetime. J. L. Flores and J. Herrera, University of Malaga, Spain, and M. Sánchez, University of Granada, Spain. Publisher's note.
Product Details :
Genre |
: Mathematics |
Author |
: Jose Luis Flores |
Publisher |
: American Mathematical Soc. |
Release |
: 2013-10-23 |
File |
: 88 Pages |
ISBN-13 |
: 9780821887752 |