Librería Portfolio

Enriched with a vast range of exercises and solved problems

Featuring a Foreword by Jacques Villain

Introduces bifurcations and the language of nonlinear sciences with simple, visual examples

Spans from elementary bifurcations to the origin of form and shape in nature

Uses elementary mathematical language, accessible to all undergraduate students

Provides detailed calculations of many problems of nonlinear physics, gathered in a single volume


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.