The Master's Degree in Nonlinear Dynamics and Complex Systems aims to help find the right path in a chaotic world

Life is made of choices, whose consequences cannot be predicted in the long term. Therefore, mathematical and computational techniques are needed to estimate the possible consequences, as well as the uncertainty generated as a result of our choices. Also the possibilities of adapting to changing scenarios are of fundamental importance. In this master's degree, a set of specialized tools is acquired, which are, at the same time, general enough to be applied to a wide class of physical, biological, economic, sociological and other complex systems found in nature and in the society. 

 

The Nonlinear Dynamics, Chaos Theory and Complex Systems group at the Rey Juan Carlos University offers its long experience to students of scientific disciplines to address the study of the dynamics of nonlinear systems, which is becoming an increasingly important field. in many branches of human knowledge. This discipline studies systems that evolve over time, called dynamical systems. The latter, clearly, can be found in physics, biology, sociology, economics, virology, among others. Dynamic systems are represented by one or more variables that can increase or decrease over time according to nonlinear functions, sometimes describing complicated and unexpected trajectories, which blurs the causal interpretation of many phenomena.

 

A dynamical system can evolve in a predictable way ending up at rest or performing periodic cycles. However, some systems can develop chaotic movements. This movement is not periodic and carries a sensitivity to initial conditions. Because of this, predictability is hampered in chaotic systems, since a small change (or uncertainty) in the initial state transforms into a large change over time.

 

Teaching how to establish the non-linear laws that govern phenomena, study them and understand them is the objective of this master's degree. In addition, it is proposed to introduce students to numerical methods for the simulation of complex networks, such as cellular automata or agent-based models that allow us to describe the evolution, otherwise indecipherable, of these sophisticated multicomponent systems.

 

Indeed, computing and mathematics have become the cornerstone of any rigorous inquiry and can help open up a broader range of career options for students. In this master you will learn to create a large number of computational tools in different programming languages, such as MATLAB, JULIA or C ++. These programming skills can give you the ability to study dynamic systems and solve complex problems.

 

Another point of strength is that this Master proposes to go beyond teaching nonlinear dynamics and how to investigate it. In fact, it is proposed to provide the necessary knowledge to be able to present the results obtained in scientific articles and in international talks.

 

In summary, the student will study in depth dynamic systems, both discrete and those based on differential equations, both deterministic and stochastic. He will also address the development and characterization of complex networks. Innovative modeling techniques, such as agent-based models and cellular automata, will make it possible to deal with complex dynamic systems of all kinds. Finally, you will study how to rigorously present your work to the scientific community.