Skip to main content

Noise induced Phenomena and complex Systems

Final Activity Report Summary - NOISEINDPHENOM (Noise Induced Phenomena and Complex Systems)

The main objective of the project was the study of complex systems, particularly in relation to: pattern formation and propagation; noise induced phenomena; diffusive-reactive problems; modelling of social and / or economic systems; application of statistical physics to the modelling of climate systems.

Along the period of the project, I have obtained results in each one of these areas. It is worth to detach the following results.

Studies on the characterisation of the spatiotemporal chaos arising in inhomogeneous active media, and the analysis of the topological properties of the unstable periodic orbits in the arising slow chaotic dynamics. Studies on the effect of external noise on a typical (toy) climate model, with the aim of obtaining information about the interplay between chaos and noise in an extended system, and the role that this entanglement can play for climate prediction.

Studies related to pattern formation involving, among others, systems showing noise sustained patterns, and the analysis of the problem of stochastic resonance between the dissipative structures in such a noise sustained dynamics, where the same noise source sustaining the patterns induces the transitions among them. Analysis of activator-inhibitor models with local and nonlocal interactions (arising from the adiabatic elimination of a fast inhibitor), studying the problem of stochastic resonance between the dissipative structures in such systems within a bistable regime, and obtaining that the optimal range of the nonlocal interaction corresponds to a very localised interaction. Studies on the robustness of the enhancement found in the stochastic resonance response in extended FitzHugh-Nagumo system with a selective (local) coupling.

Regarding noise induced phenomena, I have studied the effect of non-Gaussian noises sources in several noise induced phenomena. In particular: for noise induced transitions it was determined the shift in the transition line associated with a departure from the Gaussian behaviour; as well as studies of the current and efficiency enhancement that arise in Brownian motors when driven by non-Gaussian noises. Also, studies of new forms of generation of f -1 noises, analysing the influence of a f -k noise spectrum on the stochastic resonance phenomenon.

In relation to diffusion in fluctuating media, we have obtained novel results for the resonant activation problem. Studying the problem of 'bulk mediated surface diffusion', we have analysed different situations: finite and infinite bulk cases; situations with non Markovian desorption dynamics with finite and infinite first moment, obtaining an excellent agreement between analytical and numerical results. Also, studies of optimal search strategies within Random-Walk schemes.

Studies on the effect of different aspects on opinion spreading models, particularly on the Sznajd model: effect of 'contrarians', system size stochastic resonance phenomena, etc. Studies on the application of van Kampen's approach in simple opinion spreading model including the presence of indecisive agents. Exploitation of the same kind of approach in models of language competition, and market behaviour.

It is worth remarking the following activities I have done:
- July 2005, as invited speaker at the European Physical Society meeting: EPS13: Beyond Einstein - Physics for the 21st Century, held at Bern, Switzerland. This meeting was part of the activities commemorating the Year of Physics. Title: System size stochastic resonance: General nonequilibrium potential framework.
- September 2005, I have organised a summer course on 'Complex systems: New trends and applications', as part of the 25th Summer Courses of the Universidad de Cantabria, that was held at Laredo, Cantabria, Spain. Participation of several Latin American students.

- May 2006, as invited speaker at the 19th Centennial Marian Smoluchovski Symposium on Statistical Physics, held in Krakow, Poland. This meeting commemorated the centenary of the famous M. Smoluchovski paper on Brownian motion. Title: Stochastic resonance in extended systems: General nonequilibrium potential framework.