Spontaneous emergence of neuronal activity avalanches characterized by power-law distributions is known to occur in different types of nervous tissues suggesting that nervous systems may operate at a critical regime. Here, we explore the possible relation of this dynamical state with the underlying topology in a small-size network of interconnected Morris-Lecar neurons. Studying numerically different topological configurations, we find that, very close to the efficient small-world situation, the system self-organizes near to a critical branching process with observable distributions in the proximity of a power law with exponents similar to those reported in the experimental literature. Therefore, we conclude that the observed scaling is intimately related only with the small-world topology.

Methods are proposed for evaluation of complex dynamical systems, choice of their optimal operating modes, determination of optimal operating system out of given class of equivalent systems, system’s timeline behaviour analysis on the basis of versatile multicriteria, and multilevel analysis of behaviour of system's elements.

Information dissemination has become one of the most important services of communication networks. Modeling the diffusion of information through such networks is crucial for our modern information societies. In this work, novel models, segregating between useful and malicious types of information, are introduced, in order to better study Information Dissemination Dynamics (IDD) in wireless complex communication networks, and eventually allow taking into account special network features in IDD. According to the proposed models, and inspired from epidemiology, we investigate the IDD in various complex network types through the use of the Susceptible-Infected (SI) paradigm for useful information dissemination and the Susceptible-Infected-Susceptible (SIS) paradigm for malicious information spreading. We provide analysis and simulation results for both types of diffused information, in order to identify performance and robustness potentials for each dissemination process with respect to the characteristics of the underlying complex networking infrastructures. We demonstrate that the proposed approach can generically characterize IDD in wireless complex networks and reveal salient features of dissemination dynamics in each network type, which could eventually aid in the design of more advanced, robust, and efficient networks and services.