By Yoko Yamaguchi
By Yoko Yamaguchi
By Denis Sidorov
By H Scott Dumas
This is a semi-popular arithmetic publication aimed toward a extensive readership of mathematically literate scientists, specifically mathematicians and physicists who're no longer specialists in classical mechanics or KAM conception, and scientific-minded readers. components of the publication must also attract much less mathematically proficient readers with an curiosity within the heritage or philosophy of science.
The scope of the publication is extensive: it not just describes KAM idea in a few aspect, but in addition offers its historic context (thus displaying why it used to be a “breakthrough”). additionally mentioned are functions of KAM idea (especially to celestial mechanics and statistical mechanics) and the elements of arithmetic and physics during which KAM conception is living (dynamical structures, classical mechanics, and Hamiltonian perturbation theory).
Although a few assets on KAM conception are actually on hand for specialists, this e-book makes an attempt to fill a long-standing hole at a extra descriptive point. It sticks out very essentially from current guides on KAM thought since it leads the reader via an available account of the speculation and areas it in its right context in arithmetic, physics, and the background of science.
Readership: Undergraduates, graduates, and researchers commonly attracted to Hamiltonian perturbation idea, statistical mechanics, ergodic conception, Nekhoroshev concept, Arnold diffusion, nonlinear dynamics, dynamical structures, chaos idea, classical mechanics, and the historical past of those subjects.
By Ahmed G. Radwan,Mohammed E. Fouda
This booklet introduces the elemental basics, versions, emulators and analyses of mem-elements within the circuit concept with purposes. The ebook starts off reviewing the literature on mem-elements, versions and their fresh functions. It offers mathematical types, numerical effects, circuit simulations, and experimental effects for double-loop hysteresis habit of mem-elements. The authors introduce a generalized memristor version within the fractional-order area below assorted enter and various designs for emulator-based mem-elements, with circuit and experimental results. The easy proposal of memristive-based relaxation-oscillators within the circuit concept is usually coated. The reader will in addition locate during this publication info on memristor-based multi-level electronic circuits, memristor-based multi-level multiplier and memcapacitor-based oscillators and synaptic circuits.
By Pierre Collet,M. Courbage,S. Métens,A. Neishtadt,G. Zaslavsky
By Christos H. Skiadas,Charilaos Skiadas
Offers either commonplace and Novel techniques for the Modeling of Systems
Examines the attention-grabbing habit of specific sessions of Models
Chaotic Modelling and Simulation: Analysis of Chaotic versions, Attractors and Forms provides the most versions built by means of pioneers of chaos thought, in addition to new extensions and diversifications of those types. utilizing greater than 500 graphs and illustrations, the authors express the way to layout, estimate, and try out an array of models.
Requiring little earlier wisdom of arithmetic, the e-book makes a speciality of classical kinds and attractors in addition to new simulation equipment and methods. principles essentially development from the main uncomplicated to the main complex. The authors conceal deterministic, stochastic, logistic, Gaussian, hold up, Hénon, Holmes, Lorenz, Rössler, and rotation types. in addition they examine chaotic research as a device to layout types that seem in actual platforms; simulate advanced and chaotic orbits and paths within the sunlight process; discover the Hénon–Heiles, Contopoulos, and Hamiltonian platforms; and supply a compilation of attention-grabbing structures and diversifications of platforms, together with the very exciting Lotka–Volterra system.
Making a fancy subject obtainable via a visible and geometric type, this booklet may still encourage new advancements within the box of chaotic versions and inspire extra readers to get involved during this speedily advancing region.
By Christophe Letellier,Robert Gilmore
The e-book surveys how chaotic behaviors might be defined with topological instruments and the way this method happened in chaos conception. a few sleek functions are included.
The contents are almost always dedicated to topology, the most box of Robert Gilmore's works in dynamical platforms. They comprise a evaluation at the topological research of chaotic dynamics, works performed some time past in addition to the very newest concerns. lots of the individuals who released throughout the 90's, together with the very recognized scientists Otto Rössler, René Lozi and Joan Birman, have made an important influence on chaos idea, discrete chaos, and knot idea, respectively.
Very few books disguise the topological procedure for investigating nonlinear dynamical structures. the current booklet will offer not just a few ancient — no longer unavoidably well known — contributions (about the different sorts of chaos brought via Rössler and never simply the “Rössler attractor”; Gumowski and Mira's contributions in electronics; Poincaré's history in nonlinear dynamics) but in addition a few fresh functions in laser dynamics, biology, etc.
Readership: Graduate scholars and researchers attracted to topological research of nonlinear dynamical structures generating chaotic attractors.
By Gaetan Kerschen
Nonlinear approach Identification
By Jean-Pierre AUBIN,Alexandre M. Bayen,Patrick Saint-Pierre
By Jan G. De Gooijer
This ebook offers an outline of the present cutting-edge of nonlinear time sequence analysis, richly illustrated with examples, pseudocode algorithms and real-world functions. averting a “theorem-proof” structure, it exhibits concrete functions on a number of empirical time sequence. The book can be utilized in graduate classes in nonlinear time sequence and whilst additionally includes interesting fabric for extra complicated readers. notwithstanding it's mostly self-contained, readers require an figuring out of simple linear time sequence strategies, Markov chains and Monte Carlo simulation methods.
The e-book covers time-domain and frequency-domain equipment for the research of either univariate and multivariate (vector) time sequence. It makes a transparent contrast among parametric types at the one hand, and semi- and nonparametric models/methods at the different. this provides the reader the choice of concentrating completely on the sort of nonlinear time sequence research methods.
To make the publication as person pleasant as attainable, significant aiding options and really good tables are appended on the finish of every bankruptcy. additionally, each one bankruptcy concludes with a collection of key phrases and ideas, in addition to a precis of the most findings. finally, the ebook deals various theoretical and empirical workouts, with solutions supplied through the writer in an intensive suggestions manual.