## Phase transitions and diversification in complex systems: The role of heterogeneites, adaptation a other essencial aspects of real systems

##### Metadatos

Mostrar el registro completo del ítem##### Autor

Villa Martín, Paula##### Editorial

Universidad de Granada

##### Director

Muñoz Martínez, Miguel Ángel##### Departamento

Universidad de Granada. Departamento de Electromagnetismo y Física de la Materia##### Materia

Física estadística Transformaciones de fase (Física estadística) Probabilidades Conjuntos difusos Análisis de sistemas Dinámica de sistemas Termodinámica Mecánica estadística Procesos estocásticos Heterogeneidad ecológica

##### Materia UDC

53 517/519.1 (043.2) 1209

##### Fecha

2017##### Fecha lectura

2017-02-24##### Referencia bibliográfica

Villa Martín, P. Phase transitions and diversification in complex systems: Tthe role of heterogeneites, adaptation a other essencial aspects of real systems. Granada: Universidad de Granada, 2017. [http://hdl.handle.net/10481/45496]

##### Patrocinador

Tesis Univ. Granada. Programa Oficial de Doctorado en: Física y Matemáticas##### Resumen

Let us summarize the main issues treated in the different chapters of this thesis.
In chapter 1 basic concepts needed in this thesis are summarized. Firstly, main
features of continuous and discontinuous phase transitions are presented in order to a
correct distinction between them (section 1.1). Then, prototypical models presenting
these types of transition are described and analyzed in section 1.2.
In chapter 2, we study the importance of demographic stochasticity and diffusion
in a generic system subjected to a discontinuous transition in the mean-field approach. We investigate how the order of the transition would surprisingly depend
on such mechanisms. Beside this, we also study the the unavoidable presence of
spatial heterogeneity in real systems. In this case, a rounding phenomenon for low dimensional
systems appears. The ideas presented here can help to further understand
discontinuous transitions, and contribute to the discussion about the possibility of
preventing these shifts in order to minimize their disruptive ecological, economic, and
societal consequences.
For a deeper understanding of some of the previous results, in chapter 3 we
present a more technical and detailed study of the effect of spatial heterogeneity on
a prototypical model exhibiting a discontinuous transition. Here we try to explain
how, in analogy with what happens in problems of thermodynamic equilibrium, the
existence of some form of spatial disorder implies that potentially discontinuous transitions
are rounded-off, thus making the system critical (at low dimensions).
In this context, in chapter 4 we wonder whether a structurally (and so spatially)
disordered system would also present the same smoothing effect. An extensive
analysis of all possible systems presenting this structural heterogeneity may constitute
a thesis itself. As a consequence, we focus on the brain cortex, a system that is
well described by models exhibiting discontinuous transitions at mean-field and which
presents a complex and known network structure. Interestingly, criticality appears for
small topological dimensions and so, a compatibility of integrative models of neural
activity (exhibiting discontinuous transitions in mean-field), and the critical features
experimentally measured in the cortex, is accomplished.
The above chapters do not consider any type of mutation or variation of its individuals
due to the fact that, in those cases, evolution usually takes place in longer
times than the considered ones. However, apart from the previous inherent properties,
adaptation is an essential feature of real systems. What would it happen if
individuals rapidly evolve affecting community dynamics? In chapter 5 we propose a relatively simple computational eco-evolutionary model
specifically devised to describe rapid phenotypic diversification in a particular experiment
of species-rich communities [236]. Despite this, the model is easily generalizable
to analyze different eco-evolutionary problems within a relatively simple and unified
computational framework. We show that it captures the main phenomenology observed
experimentally, and it also makes non-trivial predictions. Although, unlike it
was awaited, no phase transition from poor to rich communities appear, in future we
will investigate the needed mechanisms for which this phase transition occurs.
Finally, thesis conclusions are presented in chapter chapter 6.