An introductory master to research on nonlinear dynamics, chaos theory and complex systems
Master on nonlinear dynamics and complex systems
A master is for life
Physical, biological or sociological systems, are permanently transforming as time goes by. Dynamical systems are represented by one or more variables that evolve with time in the space of possibilities (phase space). These variables can grow or decrease according to nonlinear functions, sometimes describing complicated and unexpected trajectories in the space of states. In particular, complex feed-back loops among different variables commonly take place in nonlinear systems, blurring the causal interpretation of many phenomena. Establishing the nonlinear laws that govern phenomena is the goal of Nonlinear Dynamics.
There are three main fates of a dynamical system. It can evolve in a predictable fashion ending at rest or performing periodic cycles. However, some systems, specially when the dimensionality is higher or equal than three, can develop chaotic motions. This motion is non-periodic and entails a sensitivity to initial conditions. In particular, predictability is hindered in chaotic systems, since a small change (uncertainty) in the state at some time transforms into an big change as times goes by. Chaos theory allows to understand these systems, which in turn allows to improve our control of them.
Dynamical systems are commonly composed of lots of elements which displace in space and which are interconnected among them forming complex networks. The interactions among the elements are constantly redefining, leading to the emergence of global patterns in space and time, which can not be guessed from the independent study of the elements alone. The simulation of complex networks and lattice models, such as cellular automata or agent based models, allows to describe the otherwise indescipherable evolution of these sophisticated multicomponent systems.
Helping you find the right path in a chaotic world.
Life is made of choices, whose consequences can not be predicted in the long run. Therefore, mathematical and computational techniques that allow to estimate the possible consequences and the amount of uncertainty in our choices are deserved. Also the chances to adapt to changing scenarios are of fundamental importance. A set of specialized tools can be acquired in the present master, which are at the same time general enough to be applied to a broad class of physical systems, and also to biological and other complex systems found in nature an society.
Searching to increase your skills?
Master studies constitute a nice opportunity to complete and extend the knowledge acquired in your degree studies. In particular, we put an emphasis on practical applications, which can be of great advantage both for your personal development in the society and for business success, as well.
Computation and mathematics have become the cornerstone of any rigorous investigation and can empower you to develop more informed choices in your life. In our master you will learn to create a great number of computational tools in different programming languages, such as MATLAB, JULIA or C++. These programming skills will endow you with the capacity to study dynamical systems and solving complicated problems.
In particular, discrete systems and systems based on differential equations, both deterministic and stochastic, are thoroughly studied. The development and characterization of complex networks are addressed too. Finally, groundbreaking modeling techniques, such as agent based modeling and cellular automata will allow to you deal with complex dynamical spatio-temporal systems.
Dig into the course structure link for a detailed description of the course!