#### Alladi Ramakrishnan Hall

#### Transition to synchronization in complex networks: Role of frustration

#### Prosenjit Kundu

##### Department of Mathematics, National Institute of Technology (NIT) Durgapur, India

*We present the results of our analytical as well as numerical investigation on transition to synchronization in Sakaguchi-Kuramoto (SK) model on complex networks. On one hand, we analytically derive self-consistent equations involving the order parameter and the group angular velocity for fully as well as partially degree-frequency correlated SK model using annealed approximation and mean field approach. We then numerically compute the critical coupling strength for the onset of synchronization from the self-consistent equations. On the other hand, for the validation of the results obtained from the self-consistent equations, we simulate the complex networks numerically for Barab\'{a}si-Albert (BA) scale-free networks and Erd\"{o}s-R\'{e}nyi (ER) random network. We also present here a mathematical framework for achieving optimal as well as perfect synchronization states in SK model on complex networks having single layer and two layers (multiplex). This is a challenging task, as the phase-frustration in Kuramoto dynamics usually inhibits synchronization. For single layer case, we also check the sensitivity of the achieved synchronization state by perturbing the constructed frequency set and by changing the network structure. Where as for the multiplex set up, we derive a multiplex synchrony alignment function (MSAF) for the purpose of achieving optimal synchronization.*

Done