Convergence of chaotic attractors due to interaction based on closeness

Highlights: • Temporal connectivity pattern based on the closeness of their trajectories is considered. • Set of attractors converge into a single attractor depending on proximity of the trajectories. • Convergence of attractors is studied in terms of appearance of giant connected component. • Necessary condition for convergence is derived using master stability function approach. -- Abstract: Exploration of coherence phenomena in ensembles of interacting dynamical systems has been in the centre of research in social, physical, biological and technological systems for decades. But, in most of the studies, either completely percolated time- and space-static networks or temporal connectivities disregarding the systems' own dynamics have been dealt with. In this work, we examine the correlation between structural and dynamical evolution in networks of interacting dynamical systems. We specifically demonstrate the scenario of convergence of a set of chaotic attractors into a single attractor as a result of sufficient interaction based on the closeness of their own states. We characterize this occurrence through different measures, and map the collective states in network parameters' space. We further validate our proposition while exposing the whole scenario for different chaotic systems, namely Lorenz and Rössler oscillators.