Bifurcation and Chaos: Analysis, Algorithms, Applications by Eugene L. Allgower, Klaus Böhmer, Mei Zhen (auth.), R.

By Eugene L. Allgower, Klaus Böhmer, Mei Zhen (auth.), R. Seydel, F. W. Schneider, T. Küpper, H. Troger (eds.)

This quantity includes the complaints of a convention held in Wiirzburg, August 20-24, 1990. The subject matter of the convention used to be Bifurcation and Chaos: research, Algorithms, Ap­ plications. greater than a hundred scientists from 21 nations awarded eighty contributions. some of the result of the convention are defined within the forty nine refereed papers that stick to. The convention was once backed through the Deutsche Forschungsgemeinschaft, and through the Deutscher Akademischer Austauschdienst. We gratefully recognize the help from those agen­ cies. The technology of nonlinear phenomena is evolving speedily. during the last 10 years, the emphasis has been steadily moving. How developments range will be visible by means of evaluating those complaints with earlier ones, specifically with the convention held in Dortmund 1986 (proceedings released in ISNM 79). in regards to the diversity of phenomena, chaos has joined the bifurcation eventualities. As anticipated, the recognition of chaos is much less emotional between execs, than it's been in a few well known guides. A nalytical equipment seem to have reached a nation during which simple result of singularities, symmetry teams, or common varieties are daily adventure instead of intriguing information. equally, numerical algorithms for widespread occasions at the moment are good validated. applied in numerous applications, such algorithms became regular potential for attacking nonlinear difficulties. The sophisti­ cation that analytical and numerical equipment have reached helps the energetic pattern to an increasing number of functions. Pioneering equations as these named after Duffing, Van der Pol, or Lorenz, aren't any longer completely the nation of art.

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Extra resources for Bifurcation and Chaos: Analysis, Algorithms, Applications

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The analytical investigations are carried out for the case of infinite activation energy, while the numerical investigations are carried out for finite, though large, activation energies. A high resolution of the reaction zones is necessary to accurately describe the structure and dynamics of the solution. Since the location of the reaction zone is not know a-priori, but in fact moves during the course of combustion, in a possibly oscillatory manner, the task of its accurate resolution is a challenge to numerical methods.

Of Engineering Sciences and Applied Mathematics Northwestern University Evanston, IL 60208, U. S. A. 1. Introduction. We study problems in the dynamics and pattern formation of both solid and gaseous fuel combustion. Our goal is to understand the basic mechanisms affecting the combustion process, which is a necessary prerequisite to controlling it. A related goal is to describe the spatio-temporal patterns that are observed experimentallyas well as to predict new dynamical behavior, as yet unobserved.

Thus, a chaotic attractor becomes tangent to the stable manifold of a saddle-type fixed point or periodic orbit, which defines the basin boundary of the chaotic attractor. In many cases, the tangency occurs simultaneously with the collision of the attractor with the saddle itself [2]. Many examples of systems exhibiting crises have been reported and studied in the literature. These include forced damped pendulum [3], Lorenz equations [4], Josephson junction [5], Duffing's equation [6], and Belousov - Zhabotinskii reaction [7].

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