Attractors, Bifurcations, and Chaos: Nonlinear Phenomena in by Tönu Puu

By Tönu Puu

Attractors, Bifurcations, & Chaos - now in its moment version - begins with an creation to mathematical equipment in smooth nonlinear dynamics and bargains with differential equations. Phenomena equivalent to bifurcations and deterministic chaos are given enormous emphasis, either within the methodological half, and within the moment half, containing a number of purposes in economics and in local technological know-how. Coexistence of attractors and the multiplicity of improvement paths in nonlinear structures are relevant themes. The purposes specialize in matters corresponding to company cycles, oligopoly, interregional alternate dynamics, and financial improvement conception.

Show description

Read or Download Attractors, Bifurcations, and Chaos: Nonlinear Phenomena in Economics PDF

Best urban & regional books

Transport Developments and Innovations in an Evolving World

Advances in Spatial ScienceThis sequence of books is devoted to reporting on fresh advances in spatial technology. It comprises clinical experiences targeting spatial phenomena, making use of theoretical frameworks, analytical tools, and empirical strategies in particular designed for spatial research. The sequence brings jointly leading edge spatial study employing recommendations, views, and techniques with a relevance to either simple technological know-how and coverage making.

Advanced Cultural Districts: Innovative Approaches to Organizational Design

Complex Cultural Districts explores the organisational layout concerns in the cultural background area, with specific specialise in the complex sorts of cultural districts for neighborhood socio-economic improvement.

Spatial Econometric Interaction Modelling

This contributed quantity applies spatial and space-time econometric how you can spatial interplay modeling. the 1st a part of the booklet addresses common state of the art methodological questions in spatial econometric interplay modeling, which hindrance points similar to coefficient interpretation, limited estimation, and scale results.

Cracking the Carbon Code: The Key to Sustainable Profits in the New Economy

Holds severe details that's wanted through someone who desires to know the way to earn a living from 'green' expertise and the way to prevent investments that would quickly be afflicted by hidden carbon liabilities. Readers will learn how to de-code a very important element of this new financial motive force - carbon credit, the world's first universal foreign money.

Additional info for Attractors, Bifurcations, and Chaos: Nonlinear Phenomena in Economics

Example text

54). With increasing time the second term in the denominator simply vanishes and we have x = cos( cp adding, we get x 2 + y2 t), Y = sin( cp - t) . Taking squares and =1, which defines the unit circle which is the limit cycle. Note that Fig. 13 has a certain likeness to both Figs. 3. There is a closed orbit as in Fig. 1, but only one, not a concentric family. The rest of the curves are spirals, as in Fig. 3. They, however, do not spiral towards a fixed point, but towards the limit cycle. The limit cycle thus is a new sort of attractor present in two dimensions along with the fixed points.

These methods still are most useful for understanding nonlinear differential equations. We already encountered the concept of perturbation in the context of structural stability, but now the use is slightly different. 38 2 Differential Equations: Ordinary The idea is to regard a nonlinear equation as a slight modification of a linear equation whose solution we know. Suppose we deal with the equation for the pendulum x + sin x = 0 . We take the two first terms of the Taylor series for the sine: sin x "" x - X 3 / 6 , and rescale the variable x by multiplication with 16 .

We will next use the second equation for determining these slowly varying coefficients, though we will not even attempt to solve that equation itself. It can be done, though, and for details the reader is referred to Kevorkian and Cole. 109): a2Xo dA. 111) results in cubic expressions in the sines and cosines. To reduce such powers to the basic oscillation frequency and its harmonics we need the following trigonometric identities: cos 3 t = (3/4) cos t + (1/4) cos 3t and sin 3 t = (3/4) sin t - (1 /4) sin 3t.

Download PDF sample

Rated 4.20 of 5 – based on 33 votes