On a measure of collective dynamics in particle swarm optimization

In this paper, we consider the self-organizing learning processes in collective dynamics of particle swarm optimization. The model system described here is a coupled map lattice which serves as a paradigm for the spatiotemporal behavior of coupled nonlinear systems. We find that there is a range of coupling strength for which synchronized nonlinear dynamics exists. Outside that range, synchronization breaks down and the system enters a regime of spatiotemporal nonlinear dynamics. The loss of synchronization is accompanied by spatially disordered behavior. Similar to the mutual information analysis of the synchronization of two coupled nonlinear dynamical systems, we propose a quantitative measure of self-organizing dynamics for the transition from spatiotemporal nonlinear dynamics to synchronized nonlinear dynamics in complex systems. We have presented a way to analyze the mechanism of collective dynamics on the basis of the spatial KS entropy for the measurement of the transition from spatially disordered to ordered behavior.