Skip to main content

Nonautonomous Bifurcation Theory

Article Category

Article available in the folowing languages:

Small changes can redefine entire systems

Dynamical systems are used to detail a wide variety of phenomena ranging from the simple movements of a pendulum through biological interactions to sociological patterns. A dynamical system is subject to various rules governing the motions of its application processes.


Real life situations can be described by applying the mathematical concept of dynamical systems, which depend on factors that reflect various conditions influencing the system. Examples of non-autonomous situations found in the applied sciences include climate modelling and studies of pollution-spreading processes. The dynamical bifurcation theory tackles the qualitative change in behaviour of a system whose parameters have been altered. The 'Nonautonomous bifurcation theory' (NBT) project sought to develop the bifurcation theory of non-autonomous systems beyond the traditional setting. The EU-funded project set a number of objectives to further work in this area. These included the characterisation of bifurcations of low-dimensional non-autonomous dynamical systems, studying higher-dimensional bifurcation scenarios, developing a bifurcation theory for random systems with bounded noise, and developing a concept of topological equivalence for non-autonomous dynamical systems. Researchers were successful in classifying bifurcations in one-dimensional non-autonomous differential equations and characterising discontinuous bifurcations in random systems with bounded noise. Team members developed a numerical scheme for detecting controlled heteroclinic orbits (a path that joins two different equilibrium points). This can be applied to a model for ship roll-motion. Other achievements include developing a concept of exponential attractivity and bifurcation for finite-time systems and a numerical scheme for approximating invariant sets in random systems with bounded noise. Advances in knowledge made during the NBT project contributed to how the concept of a non-autonomous dynamical system can be applied to model real world phenomena.

Discover other articles in the same domain of application