Chaos and Socio-Spatial Dynamics by Dimitrios S. Dendrinos, Michael Sonis

By Dimitrios S. Dendrinos, Michael Sonis

Presents a discrete in time-space common map of relative dynamics that's used to spread an in depth catalogue of dynamic occasions no longer formerly mentioned in mathematical or social technology literature. With emphasis at the chaotic dynamics which can occur, the ebook describes the evolution at the foundation of temporal and locational merits. It explains nonlinear discrete time dynamic maps basically via numerical simulations. those very wealthy qualitative dynamics are associated with evolution methods in socio-spatial structures. very important beneficial properties comprise: The analytical houses of the one-stock, - and three-location map; the numerical effects from the only- and two-stock, - and three-location dynamics; and the demonstration of the map's power applicability within the social sciences via simulating inhabitants dynamics of the U.S. areas over a two-century interval. furthermore, this booklet contains new findings: the Hopf an identical discrete time dynamics bifurcation; the Feigenbaum slope-sequences; the presence of wierd neighborhood attractors and bins; switching of utmost states; the presence of other kinds of turbulence; neighborhood and worldwide turbulence. meant for researchers and complicated graduate scholars in utilized arithmetic and an curiosity in dynamics and chaos. Mathematical social scientists in lots of different fields also will locate this ebook useful.

Show description

Read Online or Download Chaos and Socio-Spatial Dynamics PDF

Similar counting & numeration books

Linear Systems

In line with a streamlined presentation of the authors' profitable paintings Linear structures, this textbook offers an advent to structures conception with an emphasis on keep watch over. the fabric awarded is large sufficient to provide the reader a transparent photo of the dynamical habit of linear platforms in addition to their merits and barriers.

Statistical and Computational Inverse Problems (Applied Mathematical Sciences)

This booklet covers the statistical mechanics method of computational resolution of inverse difficulties, an cutting edge quarter of present learn with very promising numerical effects. The innovations are utilized to a few actual international purposes equivalent to constrained attitude tomography, snapshot deblurring, electical impedance tomography, and biomagnetic inverse difficulties.

Wavelets and Subbands: Fundamentals and Applications

Lately there was severe examine job with regards to wavelet and subband conception. specialists in various fields similar to arithmetic, physics, electric engineering, and photo processing have supplied unique and pioneering works and effects. yet this range, whereas wealthy and effective, has ended in a feeling of fragmentation, specially to these new to the sphere and to nonspecialists who're attempting to comprehend the connections among different facets of wavelet and subband conception.

Fitted Numerical Methods For Singular Perturbation Problems: Error Estimates in the Maximum Norm for Linear Problems in One and Two Dimensions

Because the first variation of this e-book, the literature on equipped mesh equipment for singularly perturbed difficulties has elevated considerably. Over the intervening years, geared up meshes were proven to be potent for an intensive set of singularly perturbed partial differential equations. within the revised model of this e-book, the reader will locate an advent to the elemental idea linked to outfitted numerical tools for singularly perturbed differential equations.

Extra info for Chaos and Socio-Spatial Dynamics

Example text

11) it obtains a maximum. The dynamics of the changes in the number of equilibria, and the dynamics of transitions from stability to instability will be demonstrated next for a special choice of the structural parameters a, b in the log-linear model, a > 1, b > 1. c. A SPECIAL CASE (a > 1, b > 1) The domain, a > 1, b > 1, is only one of 49 different domains of the possible ranges in the parameters a, b. Each is associated with different types of equilibria with distinct qualitative features. In this case the function 1(x*) has a minimum at point x*(+ 1) = (a + 1)/(a + b) and where Amin = A(+ 1) (see Figure 6).

The equilibria values x1,1, x2,1 move in the opposite direction toward the bifurcation state x*(+ 1) = (a + 1)/(a + b), so that they merge with x*(+1) at A = A(+ 1). If A > A(+ 1) then equilibria do not exist. a<-1 - a=-1 a>-1 A=1 b=1 A=1 A=1 A-1 A FIGURE 4. Graphical representation of the equilibria x* of the first iterate, as functions of A. B. Log-Linear Comparative Advantages Producing Functions 43 4. Geometric Description of the Iterative Process a. BEHAVIOR AT THE LIMITS Next we consider the behavior of the iterative process in the vicinity of the end points 0 and 1.

Briefly discussed was the one-stock, two-locaton case relating this universal algorithm to May's logistic prototype. A number of examples were provided in an effort to outline the social sciences and the geographic applications of our mapping. Spatiotemporal interdependencies of stocks, and periodicity in socio-spatial dynamics, were presented as the central elements for laying down the foundations of a universal map of socio-spatial evolution formed within a relative, discrete in time-space, framework.

Download PDF sample

Rated 4.12 of 5 – based on 37 votes