By Qingjie Cao,Alain Léger
This is the 1st ebook to introduce the irrational elliptic functionality sequence, offering a theoretical remedy for the graceful and discontinuous process and beginning a brand new department of utilized arithmetic. the invention of the sleek and discontinuous (SD) oscillator and the SD attractors mentioned during this publication represents one more milestone in nonlinear dynamics, following at the discovery of the Ueda attractor in 1961 and Lorenz attractor in 1963.
This specific approach bears major similarities to the Duffing oscillator, displaying the normal dynamics ruled via the hyperbolic constitution linked to the desk bound nation of the double good. despite the fact that, there's a mammoth departure in nonlinear dynamics from typical dynamics on the discontinuous degree. The developed irrational elliptic functionality sequence, which bargains how to at once process the character dynamics analytically for either soft and discontinuous behaviours together with the unperturbed periodic motions and the perturbed chaotic attractors with none truncation, is of specific interest.
Readers also will achieve a deeper knowing of the particular nonlinear phenomena by way of an easy mechanical version: the speculation, method, and the functions in numerous interlinked disciplines of sciences and engineering. This booklet bargains a invaluable source for researchers, pros and postgraduate scholars in mechanical engineering, non-linear dynamics, and comparable components, equivalent to nonlinear modelling in a variety of fields of arithmetic, physics and the engineering sciences.
Read or Download A Smooth and Discontinuous Oscillator: Theory, Methodology and Applications (Springer Tracts in Mechanical Engineering) PDF
Similar chaos & systems books
The second one legislation, a cornerstone of thermodynamics, governs the typical course of dissipative, non-equilibrium techniques. however it says not anything approximately their real charges or the chance of fluctuations concerning the regular. This interdisciplinary publication, written and peer-reviewed by way of overseas specialists, offers contemporary advances within the look for new non-equilibrium rules past the second one legislations, and their functions to a variety of platforms throughout physics, chemistry and biology.
The slime mildew Physarum polycephalum is a big cellphone noticeable via the unaided eye. It behaves as an clever nonlinear spatially prolonged energetic medium encapsulated in an elastic membrane. The phone optimises its development styles in configurations of attractants and repellents. This behaviour is interpreted as computation.
This ebook comprises evaluate articles on mathematical body structure that take care of heavily comparable subject matters yet have been written and will be learn independently. the 1st article reports the fundamental concept of calcium oscillations (common to just about all cellphone types), together with spatio-temporal behaviors comparable to waves.
This textbook provides the movement of natural nonlinear oscillatory structures and diverse resolution strategies which provide the approximate options of the robust nonlinear oscillator equations. It offers the author’s original method for the analytical answer process of the natural nonlinear oscillator process.
Extra resources for A Smooth and Discontinuous Oscillator: Theory, Methodology and Applications (Springer Tracts in Mechanical Engineering)