Multiset of Agents in a Network for Simulation of Complex Systems

A Complex System (CS) exhibits the four salient properties: (i) Collective, coordinated and efficient interaction among its components (ii) Self-organization and emergence (iii) Power law scaling under emergence (iv) Adaptation, fault tolerance and resilience against damage of its components. We describe briefly, three interrelated mathematical models that enable us to understand these properties: Fractal and percolation model, Stochastic / Chaotic (nonlinear) dynamical model and Topological (network) or graph model. These models have been very well studied in recent years and are closely related to the properties such as: self-similarity, scale-free, resilience, self-organization and emergence. We explain how these properties of CS can be simulated using the multi-set of agents-based paradigm (MAP) through random enabling, inhibiting, preferential attachment and growth of the multiagent network. We discuss these aspects from the point of view of geometric parameters-Lyapunov exponents, strange attractors, metric entropy, and topological indices-Cluster coefficient, Average degree distribution and the correlation length of the interacting network.