Controlling a complex system near its critical point via temporal correlations
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Abstract:
Abstract Many complex systems exhibit large fluctuations both across space and over time. These fluctuations have often been linked to the presence of some kind of critical phenomena, where it is well known that the emerging correlation functions in space and time are closely related to each other. Here we test whether the time correlation properties allow systems exhibiting a phase transition to self-tune to their critical point. We describe results in three models: the 2D Ising ferromagnetic model, the 3D Vicsek flocking model and a small-world neuronal network model. We demonstrate that feedback from the autocorrelation function of the order parameter fluctuations shifts the system towards its critical point. Our results rely on universal properties of critical systems and are expected to be relevant to a variety of other settings.Keywords:
Flocking (texture)
Critical point (mathematics)
Complex system
Abstract Prompted by the ubiquity of empirical observations of critical phenomena, often in non-equilibrium macrostates, we developed a modelling approach in which several critical phenomena coexist. Instead of a single critical point, many coexisting critical points in the system are identified, forming a one-dimensional critical manifold. Identified within our game-of-life-like heterogeneous agent-based simulation model, where agents can be created and annihilated in the presence of a catalyst, each critical point belonging to the critical manifold is associated with a multi-spectrum of critical exponents. We find this situation in non-equilibrium mixed percolation-like macrostates obeying continuous phase transitions. These macrostates are quasi-stationary, where some system characteristics are time-independent while others are not. This novel look at universality signals the existance of complexity of critical phenomena richer than described to date.
Critical point (mathematics)
Directed percolation
Critical mass (sociodynamics)
Stable manifold
Percolation (cognitive psychology)
Manifold (fluid mechanics)
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