Seminarium Gamma

Dynamical systems are sets of differential equations that govern the evolution of parameters of mathematical models with respect to time. Dynamical systems appear in a large number of fields, such as Physics, Chemistry, Biology, Engeneering, etc. The analysis of dynamical systems can be done, in some cases, by direct integration of the equation of the model. This, however, is not possible in general. Instead, qualitative analysis may provide useful information about the system, such as equilibrium points, limit cycles, chaotic behavior, etc.In this talk, I will present a brief introduction to the theory of dynamical systems, as well as its application to a particular example. The Brusselator is a 2-variable model of a cyclic chemical reaction with interesting properties from the point of view of dynamical systems. I will present the main properties of the Brusselator system and describe a coupling among two and three Brusselators. This coupling provides the system with a rich variety of properties, such as chaotic behaviour, which my group has studied during the last years [1,2]. Lastly, I will describe how the analysis of coupled Brusselators allows us to study the synchronization properties of the model.[1] F. Drubi et al., "Connecting chaotic regions in the Coupled Brusselator System". Chaos, Solitons & Fractals 169, 113240 (2023).[2] A. Mayora-Cebollero et al., "Almost synchronization phenomena in the two and three coupled Brusselator systems", Physica D 472, 134457 (2025).