Modelling Damage Propagation in Complex Networks: Life Exists in Half-Chaos

Abstract

Human institutions and administrative units, technological processes, technical constructions, and living organisms can all be modelled as dynamical, discrete and finite complex networks. This is an important practical approach in modelling complex dynamical systems. Original Kauffman’s hypothesis life on the edge of chaos imposes considerable limitations on such modelling. The problem is exacerbated by the estimated network parameters usually far away from the range indicated by the hypothesis itself. This report describes experimental evidence and argues that the assumptions leading to Kauffman’s conclusion turn out to be too simplistic. In the Kauffman’s approach to predict statistical stability, random networks approximated by infinite and continuous systems are used. These networks can be either stable (i.e. ordered) or unstable (i.e. chaotic). By slightly adjusting the network parameters, a rapid jump between chaos and order appears. It is called a phase transition. Only for network parameters near this phase transition, the network changes have properties suitable for describing and capturing the stability of modelled real-world objects. Note however, that the modelled real systems are certainly neither infinite nor continuous. Their parameters are usually in the area of the random chaotic system, far from the narrow phase transition, yet, the objects do not exhibit chaotic behaviour and are not random. In this work, we demonstrate the third system state that we dubbed: half-chaos. The features of half-chaotic systems are tuned such that they can exhibit both, small and large reactions to small network disturbances. This third class of networks, half-chaotic, allow for expanding the current theories in order for improved modelling of complex dynamical systems. We argue, that half-chaotic systems better describe the modelled dynamical phenomena appearing in real world.