Nonlinear dynamics, chaos and fractals with applications to geological systems

Cover of: Nonlinear dynamics, chaos and fractals with applications to geological systems |

Published by Geological Association of Canada in St. John"s, Nfld .

Written in English

Read online


  • Geology -- Mathematics.,
  • Dynamics.,
  • Nonlinear theories.,
  • Fractals.,
  • Chaotic behavior in systems.

Edition Notes

Book details

Statementeditor, G.V. Middleton ; authors, John Chadam ... [et al.].
SeriesShort course notes (Geological Association of Canada) -- v.9
ContributionsGeological Association of Canada.
LC ClassificationsQE"33.2"M3"N66"1991
The Physical Object
Paginationviii, 235 p. :
Number of Pages235
ID Numbers
Open LibraryOL21027203M
ISBN 100919216471

Download Nonlinear dynamics, chaos and fractals with applications to geological systems

Additional Physical Format: Online version: Nonlinear dynamics, chaos and fractals with applications to geological systems. John's, Nfld.: Geological Association of Canada, Download Citation | Social Networks in Nonlinear Dynamics, Chaos and Fractals | We show how the seeds of twentieth century mathematical Chaos Theory grew.

This is an attempt to analyze the current lithospheric stress pattern in the Baikal rift in terms of nonlinear dynamics as an open self-organizing system in order to gain more insights into the. Nonlinear dynamics, chaos and fractals with applications to geological Gerard V.

Middleton Not In Library. Read. Borrow. Accessible bookChaotic behavior in systems, Congresses, Mathematical models. I was reading through a book on chaos theory and geology and I just found this line funny.

Chaos in a time series, in Middleton, G.V., Ed., Nonlinear dynamics, chaos and fractals with applications to geological systems,Short Course Notes, V. 9: Toronto, Ontario, Geological Association of Canada, p. The paper mainly focuses on a novel hyperchaotic system. The local stability of equilibrium is analyzed and existence of Hopf bifurcation is established.

Moreover, formulas for determining the stability and direction of bifurcating periodic solutions are derived by center manifold theorem and normal form by: 4. Nonlinear dynamics and chaos with applications to to hydrodynamics and hydrological modelling Slavco Velickov A hydroinformatics system represents an electronic knowledge encapsulator that models part of the real world and can be used for the simulation and analysis of physical, chemical and biological processes in water systems, in order to.

The book provides a detailed description of the current research on the application of fractal concepts, nonlinear dynamics and disordered systems in chemical engineering, with emphasis on interdisciplinary connections with related fields, such as control theory of nonlinear systems, dynamic theory of fractals, transport theory and physical.

This paper has dedicated to study the control of chaos when the system dynamics is unknown and there are some limitations on measuring states.

There are many chaotic systems with these features occurring in many biological, economical and mechanical : Hojjat Kaveh, Hassan Salarieh. They address the rich panoply of manifold applications of fractal geometry available for study and research in science and industry: i.e., remote sensing, mapping, texture creations, pattern recognition, image compression, aeromechanical systems, cryptography and financial analysis.

The chapters relate to many fields of chaos including Dynamical and Nonlinear Systems, Attractors and Fractals, Hydro-Fluid Dynamics and Mechanics, Chaos in Meteorology and Cosmology, Chaos in Biology and Genetics, Chaotic Control, Chaos in Economy and Markets, and Computer Composition and Chaotic Simulations, including related applications.

Chadam, J. () “Geochemical self—organization: An application of nonlinear dynamics”, in: Nonlinear Dynamics, Chaos and Fractals with Applications to Geological Systems(G.V.

Middleton, Ed.): 83–96, Geological Association of Canada, Toronto. Google Scholar. Nonlinear dynamics, chaos and fractals: with applications to geological systems by Gerard V.

Middleton Wavelets and Fractals in Earth System Sciences by E. Chandrasekhar next ›. Rundle JB, Turcotte DL, Shcherbakov R, Klein W, Sammis C () Statistical physics approach to understanding the multiscale dynamics of earthquake fault systems. Rev Geophys Google Scholar Schertzer D, Lovejoy S () The dimension and intermittency of atmospheric dynamics multifractal cascade dynamics and turbulent intermittency.

BOOK REVIEWS Kruhl, J. Fractals and Dynamic Systems in Geoscience. Berlin (Springer-Verlag) Price DM vi + pp. ISBN X. The general subject area of fractals and dynamical systems has recently found a wide variety of practical applications in the Earth Sciences, following the publication of Benoit Mandelbrot's books on the fractal geometry Author: Main, I.

Applications range from classical problems such as the buckling of cylindrical shells, twisted rods and pipelines, to the folding of geological strata, the failure of sandwich structures and the propagation of solitary waves in suspended beam systems.

Contents: The Strut on an Elastic Foundation; Numerics and Discretization; Twisted Rods. It becomes frighteningly evident that no matter how many super computers we have grinding away, it will take more than chaos theory, classical dynamics, and geological models to predict erosion.

For fractals to be of any practical use in predicting erosion, they would need to be examined in a nonlinear context. The SCOPUS database provides searching of author affiliations within their broad interdisciplinary journal coverage. View journal articles with SXU as the author affiliation.

You can sort the results by Date, Citation, etc. on the top right corner of the results page.; The left column provides facets for viewing SXU publications by author, subject, date, and journal (Source Title). Summary: Chaos theory is a mathematical theory that can be used to explain complex systems such as weather, astronomy, politics, and economics The chaos theory pdf.

Although many complex systems appear to behave in a random manner, chaos theory shows that, in reality, there is an underlying order that is difficult to see.

The chaos theory pdf. Chaos theory is concerned with unpredictable courses of events. The irregular and unpredictable time evolution of many nonlinear and complex linear systems has been named chaos. Chaos is best illustrated by Lorentz’ famous butterfly effect: the notion that a butterfly stirring the air in Hong Kong today can transform storm systems in New York next month.

ory, chaos, fractals, and other (then) unconventional approaches. Again, he was far ahead of main-stream thinking in applying multidisciplinary nonlinear dynamics to geological and cosmological processes.

As a measure of his rapidly expanding intellectual horizons at that time, in. [41] Processes generating nonlinear dynamics in flow through unsaturated fractured porous media can be divided into two categories: (1) the complex geometry of flow paths and (2) nonlinear liquid flow and chemical transport through fractures and surrounding matrix.

A key question is, What is the role of internal factors associated with the Cited by: Chaos, Fractals, and Dynamics: Computer Experiments in Mathematics Robert L.

Devaney / Paperback / Published Coping With Chaos: Analysis of Chaotic Data and the Exploitation of Chaotic Systems (Wiley Series in Nonlinear Science) Edward Ott(Editor), et al / Paperback / Published Discrete Dynamical Systems: Theory and Applications.

Dragon king (DK) is a double metaphor for an event that is both extremely large in size or impact (a "king") and born of unique origins (a "dragon") relative to its peers (other events from the same system).

DK events are generated by / correspond to mechanisms such as positive feedback, tipping points, bifurcations, and phase transitions, that tend to occur in nonlinear and complex.

Math Introduction to Dynamics and Chaos Mathematics. The course is an introduction to nonlinear dynamics and chaos theory. It will cover stability in nonlinear systems of differential equations, bifurcation theory, chaos, strange attractors, iteration of nonlinear mappings, fractals, and applications.

Chaos, Solitons & Fractals() Building a puzzle to solve a riddle: A multi-scale disaggregation approach for multivariate stochastic processes with any marginal distribution and correlation by: Chaos, Fractals, Dynamic Systems Combinatorics Nonlinear & Complex Systems Nuclear & High Energy Physics Optics & Photonics Particle Physics Physics Special Topics Physics & Astronomy.

Featured Products View All. More related products available. Physics, 10th Edition. Complex nonlinear dynamic systems are ubiquitous in the landscapes and phenomena studied by earth sciences in general and by geomorphology in particular.

Many natural landscape features have an aspect such as fractals. In the many geomorphologic phenomena such as river networks and coast lines this is visible.

In recent years fractal geometry offers as an option for modeling Cited by: 4. In et al. (eds.), Applications of Nonlinear Dynamics, Understanding Complex Systems, c Springer-Verlag Berlin Heidelberg DOI / 2, 15 16 H.B.

Chan and C. Stambaugh half the modulation frequency. The phase of the oscillation can take on either one of two values that differ from each other by π. In a sense, one might say this is (almost) the whole of mathematics. Commonly, however, this notion is associated with ideas of chaos, fractals, solitons, self-organizing, synergetics, etc.

The book obviously concentrates only on a few aspects of nonlinear mathematics, mainly deterministic chaos and nonlinear dynamics, and several applications.

Unfortunately, this book can't be printed from the OpenBook. Visit to get more information about this book, to buy it in print, or to download it as a free PDF. Despite of many years of studies, predicting fluid flow, heat, and chemical transport in fractured-porous media remains a challenge for scientists and engineers worldwide.

This monograph is the third in a series on the dynamics of fluids and transport in fractured rock published by the American Geophysical Union (Geophysical Monograph Series, Vol.; and. Continuum mechanics underlies many geological and geophysical phenomena, from earthquakes and faults to the fluid dynamics of the Earth.

This interdisciplinary book provides geoscientists, physicists and applied mathematicians with a class-tested, accessible overview of Cited by: 6.

Chaos, Solitons and Fractals, 43, () L. Zavala Sanson, A. Provenzale. The effects of abrupt topography on plankton dynamics, Theoretical Population Dynamics, 76, (). Natural systems also produce fractal behavior over time or in dynamics. Earthquakes are a common example. There are many more small earthquakes.

Sections include multifractal analysis, iterated function systems, random processes, network traffic analysis, fractals and waves, image compression, and applications in physics. Fractals in Engineering emphasizes the connection between fractal analysis research and applications to : Jacques Levy Vehel.

Christopher C. Barton is Professor of Earth and Environmental Sciences and founder and leader of the Complexity Research Group at Wright State University since He is a pioneer in the identification and quantification of nonlinear dynamics and complexity in earth, environmental, human, and economic systems.

Chen, G. Rangarajan and M. Ding, Stability of synchronized dynamics and pattern formation in coupled systems: Review of some recent results, Communications in Nonlinear Science and Numerical Simulat (). quantify the dynamics and chemistry of solids and uids in nature. Mathematical topics to be introduced include linear algebra, vectors and tensors, di erential equations, dynamical systems, eigenvalues and eigenvectors, empirical orthogonal functions, fractals, chaos, and statistics.

Applications include waves in. Christopher C. Barton is Founder and Leader of the Complexity Research Group, Professor of Earth and Environmental Sciences at Wright State University since He is a pioneer in the identification and quantification of nonlinear dynamics and complexity in earth, environmental, human, and economic systems.

A brief introduction to the discovery of chaos theory and its applications to understanding human awareness and behavior. The mathematics of deterministic chaos underlies the growth patterns of nature and our nature. There is an implicate order in chaos.

But we don't need to understand the math to see that expression in our physiology and psychology.Chaos, Solitons & Fractals() An analysis of a two-cell coupled nonlinear chemical oscillator. Dynamics and Stability of SystemsCited by: Fractals occur in complex or nonlinear systems.

Such systems characteristically have feedback, and each successive state depends on the previous state. We can model a nonlinear system with a simple equation, say Y=AX (X+B), where A and B are constants, which gives us a simple curve with Y steeply increasing as X increases.

10901 views Friday, October 30, 2020