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### "Dynamic processes in geology: Introduction to nonlinear systems"

E-textbook (in Russian)
(electronic version of textbook with demonstrative executable modules # Summary

The purpose of this E-textbook:
- To acquaint the reader with nonlinear dynamic systems;
- To learn of working with computer models of some dynamic geological phenomena.

The geology investigates of the Earth as a dynamic system. Any object on the Earth in any time interval is part of this whole dynamic system.

The overwhelming majority of interactions in nature geological processes are nonlinear - response is not proportional to the input. The analysis of behavior of systems with nonlinear interplay during time is a subject of this E-textbook.

The E-textbook represents the introducing to concepts and methods used at analysis of dynamic systems. The linear and nonlinear systems are reviewed, and the examples of dynamic systems in geology are considered. An intimate relationship between nonlinear systems and fractals is demonstrated.

Some numerical methods of a solution of the differential equations and least squares method are presented in "Appendix".

The E-textbook is hypertext and is realized in a WinHelp format. The major concepts and terms are explained in the dictionary. To study behavior of dynamic systems the author's demonstration programs are include. They allow, not going out from the E-textbook, to investigate influence of controlling parameters and/or initial conditions on model dynamic. All demonstration programs provide for operating instructions.

The list of the advisable literature includes 54 names, the 21 Internet links are added.

The E-textbook is intended to the students and postgraduate students of geologic specialities. The students should know basic mathematician and physics courses.

Key words: geological processes, dynamic system, nonlinear processes, chaotic dynamics, deterministic chaos, fractals.

# Contents

Introduction

Chapter 1. Linear dynamic systems

1.1 Definition of a dynamic system
1.2 Linear first order system
1.3 Linear systems of the second order
1.4 Oscillating motion

Chapter 2. Examples of nonlinear dynamic systems

2.1 Nonlinear system with a limit cycle
2.2 Simplest nonlinear system with complicated behavior
2.3 Two-dimensional system
2.4 Three-dimensional system

Chapter 3. Dynamic models of a "predator - victim" type (Lotka-Volterra system)

3.1 Formulation of a problem and the main equations
3.2 Modeling of interplay of polar ice and warm stream
3.3 Analyzing of a system
3.4 Results of numerical simulation of a system "predator - victim"
3.4 The importance of such problems for geology

Chapter 4. Models of geologic systems with dry friction

4.1 Block-spring system with dry friction
4.2 Three-disk models with dry friction
4.3 "Train"-model
4.4 Model of block dynamics in foredeep basins

Chapter 5. Dynamic systems and fractal geometry

5.1 Fractal objects
5.2 Fractal dimension
5.3 Examples of fractal objects and their dimensions

Chapter 6. Fractals and geology

6.1 Fractal properties of coast line
6.2 Fractal properties of a topographic profile
6.3 Fractal properties of geologic objects
6.4 Fractal characteristics of rocks fractures process
6.5 Fractal characteristics of seismicity
6.6 Fractal characteristics of processes in magmatic chamber
6.7 Plumes and fractals
6.8 Climate and fractals
6.9 Magnitostratigraphy and fractals

Appendix

A.1 Methods of a solution of the differential equations
A.2 Concept of a finite differences method
A.3 Methods of a Cauchy problem solving
A.4 Least squares method

Conclusion

Literature

For more information concerning the E-textbook "Dynamic processes in geology: Introduction to nonlinear systems" refer to the authors. 