Dynamical behaviour of multi-particle large-scale systems

Abstract

Collective behaviours can be observed in both natural and man-made systems composed of a large number of elemental subsystems. Typically, each elemental subsystem has its own dynamics but, whenever interaction between individuals occurs, the individual behaviours tend to be relaxed, and collective behaviours emerge. In this paper, the collective behaviour of a large-scale system composed of several coupled elemental particles is analysed. The dynamics of the particles are governed by the same type of equations but having different parameter values and initial conditions. Coupling between particles is based on statistical feedback, which means that each particle is affected by the average behaviour of its neighbours. It is shown that the global system may unveil several types of collective behaviours, corresponding to partial synchronisation, characterised by the existence of several clusters of synchronised subsystems, and global synchronisation between particles, where all the elemental particles synchronise completely.

Analysis of Natural and Artificial Phenomena Using Signal Processing and Fractional Calculus

“…Examples of CS include living organisms and structures [16,53,6,21,31,46], geophysics [43,38,7,49,44,22], financial markets [18,34,15,25], transportation, telecommunication and social networks [1,42,51,23,39,41,35,5,2,24], music [26], economy [52,3,10,11], electrical and mechanical facilities [40,50,27], among others.…”

Power Law Behavior and Self-Similarity in Modern Industrial Accidents

“…Examples include financial markets [21], transportation infrastructures [3], telecommunication facilities [43], world and country economies [57], social networks [6], geophysics [50], living organisms [52], computational systems [18], electro-mechanical structures [29] and others [5,44].…”

The Persistence of Memory

“…Complexity is an underlining signature shared by many natural and man-made signals and systems. Examples include financial markets [21], transportation infrastructures [3], telecommunication facilities [43], world and country economies [57], social networks [6], geophysics [50], living organisms [52], computational systems [18], electro-mechanical structures [29] and others [5,44].…”