Complex Dynamics and Morphogenesis : An Introduction to Nonlinear Science / by Chaouqi Misbah.

Format:

Book

Author/Creator:

Misbah, Chaouqi., Author.

Language:

English

Subjects (All):

Statistical physics.

Physics.

System theory.

Biophysics.

Applications of Nonlinear Dynamics and Chaos Theory.

Mathematical Methods in Physics.

Complex Systems.

Biological and Medical Physics, Biophysics.

Local Subjects:

Applications of Nonlinear Dynamics and Chaos Theory.

Mathematical Methods in Physics.

Complex Systems.

Biological and Medical Physics, Biophysics.

Physical Description:

1 online resource (XIX, 463 p. 179 illus.)

Edition:

1st ed. 2017.

Place of Publication:

Dordrecht : Springer Netherlands : Imprint: Springer, 2017.

Summary:

This book offers an introduction to the physics of nonlinear phenomena through two complementary approaches: bifurcation theory and catastrophe theory. Readers will be gradually introduced to the language and formalisms of nonlinear sciences, which constitute the framework to describe complex systems. The difficulty with complex systems is that their evolution cannot be fully predicted because of the interdependence and interactions between their different components. Starting with simple examples and working toward an increasing level of universalization, the work explores diverse scenarios of bifurcations and elementary catastrophes which characterize the qualitative behavior of nonlinear systems. The study of temporal evolution is undertaken using the equations that characterize stationary or oscillatory solutions, while spatial analysis introduces the fascinating problem of morphogenesis. Accessible to undergraduate university students in any discipline concerned with nonlinear phenomena (physics, mathematics, chemistry, geology, economy, etc.), this work provides a wealth of information for teachers and researchers in these various fields. Chaouqi Misbah is a senior researcher at the CNRS (National Centre of Scientific Research in France). His work spans from pattern formation in nonlinear science to complex fluids and biophysics. In 2002 he received a major award from the French Academy of Science for his achievements and in 2003 Grenoble University honoured him with a gold medal. Leader of a group of around 40 scientists, he is a member of the editorial board of the French Academy of Science since 2013 and also holds numerous national and international responsibilities.

Contents:

1. Presentation of Main Ideas

2. Basic Introduction to Bifurcations in 1-D

3. The Other Generic Bifurcations

4. Classification of the 7 Elementary Catastrophes

5. Hopf Bifurcation

6. Amplitude Equation for the Hopf Bifurcation

7. Parametric Instabilities and Other Nonlinear Behaviors

8. Introduction to Chaos

9. Pattern Formation in One Dimension

10. Universality in the Vicinity of the Threshold

11. Fronts between Domains

12. Order and Disorder both Spatial and Temporal

13. Two Dimensional Patterns

14. Wavelength Selection

15. Conclusion

16. Solutions to Exercises

Bibliography. .

Notes:

Includes bibliographical references and index.

ISBN:

9789402410204

9402410201

OCLC:

1499721361