We review a variety of control methods which are capable of enhancing the chaoticity and mixing properties of chaotic flows and also methods which work towards promoting the coherence properties of such flows. We discuss a parameter control method which can enhance the chaoticity and the rate of mixing of dissipative as well as conservative flows and outline methods which promote global mixing by the addition of noise and by preventing island formation. As the inverse side of this problem, we summarize methods which can create coherent structures in chaotic dynamical flows. We also discuss the utility of these methods from the point of view of applications as well as for understanding phenomena which occur in natural systems.

We present a brief report on the conference, a summary of the proceedings, and a discussion on the field of nonlinear science studies and its current frontiers.

We study message transfer in a 2-d communication network of regular nodes and randomly distributed hubs. We study both single message transfer and multiple message transfer on the lattice. The average travel time for single messages travelling between source and target pairs of fixed separations shows 𝑞-exponential behaviour as a function of hub density with a characteristic power-law tail, indicating a rapid drop in the average travel time as a function of hub density. This power-law tail arises as a consequence of the log-normal distribution of travel times seen at high hub densities. When many messages travel on the lattice, a congestion-decongestion transition can be seen. The waiting times of messages in the congested phase show a Gaussian distribution, whereas the decongested phase shows a log-normal distribution. Thus the waiting time distributions carry the signature of congested or decongested behaviour.

The strength and stability properties of hierarchical load-bearing networks and their strengthened variants have been discussed in a recent work. Here, we study the avalanche time distributions on these load-bearing networks. The avalanche time distributions of the V-lattice, a unique realization of the networks, show power-law behaviour when tested with certain fractions of its trunk weights. All other avalanche distributions show Gaussian peaked behaviour. Thus the V-lattice is the critical case of the network. We discuss the implications of this result.