We present a technique to engineer solitary states by means of delayed links in a network of neural oscillators and in coupled chaotic maps. Solitary states are intriguing partial synchronization patterns, where a synchronized cluster coexists with solitary nodes displaced from this cluster and distributed randomly over the network. We induce solitary states in the originally synchronized network of identical nodes by introducing delays in the links for a certain number of selected network elements. It is shown that the extent of displacement and the position of solitary elements can be completely controlled by the choice (values) and positions (locations) of the incorporated delays, reshaping the delay engineered solitary states in the network.
Chimera referring to a coexistence of coherent and incoherent states, is traditionally very difficult to control due to its peculiar nature. Here, we provide a recipe to construct chimera states in the multiplex networks with the aid of multiplexing-delays. The chimera state in multiplex networks is produced by introducing heterogeneous delays in a fraction of inter-layer links, referred as multiplexing-delay, in a sequence. Additionally, the emergence of the incoherence in the chimera state can be regulated by making appropriate choice of both inter-and intra-layer coupling strengths, whereas the extent and the position of the incoherence regime can be regulated by appropriate placing and strength of the multiplexing delays. The proposed technique to construct such engineered chimera equips us with multiplex network's structural parameters as tools in gaining both qualitative-and quantitative-control over the incoherent section of the chimera states and, in turn, the chimera. Our investigation can be of worth in controlling dynamics of multi-level delayed systems and attain desired chimeric patterns.
The dynamical behavior of networked systems is expected to reflect the properties of their coupling structure. Yet, symmetry-broken solutions often occur in symmetrically coupled networks. An example are so-called solitary states where the dynamics of one network node is different from the synchronized rest. Here, we investigate the structural constraints of networks for the appearance of solitary states. By performing a large number of numerical simulations, we find that such states occur with high probability in asymmetric networks, among them scale-free ones. We analyze the structural properties of the networks that support solitary states. We demonstrate that the minimum neighbor node degree of a solitary node is crucial for the appearance of solitary states. Finally, we perform bifurcation analysis of dimension-reduced systems, which confirm the importance of the connectivity of the neighboring nodes.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.