Aging transition under weighted conjugate coupling

¹ Centre for Nonlinear Science & Engineering, School of Electrical & Electronics Engineering, SASTRA Deemed University - Thanjavur-613 401, Tamil Nadu, India
² School of Physics, Indian Institute of Science Education and Research - Thiruvananthapuram-695 551, Kerala, India

^(a) chandru25nld@gmail.com (corresponding author)
^(b) skumar@iisertvm.ac.in (corresponding author)

Received: 9 September 2019
Accepted: 20 December 2019

Abstract

We investigate the effect of symmetry breaking couplings on the macroscopic dynamical behavior of an ensemble of globally coupled active and inactive oscillators. Conjugate coupling among the ensemble and the weighted coupling within the active and inactive groups introduces the asymmetry. Large values of the global coupling strength facilitate the onset of the phenomenon of aging transition, thereby deteriorating the macroscopic oscillatory behavior. We find that the natural frequency of oscillation favors the onset of the aging transition even in the presence of a large proportion of the active oscillators because of the broken symmetry. Further the ratio of the intra-group (weighted) couplings plays a nontrivial role in determining the dynamical behaviors and their transitions. It is also observed that even a feeble change in the simple feedback factor in the coupling facilitates the counterintuitive effect of preserving the macroscopic oscillatory nature of the ensemble, comprising completely inactive oscillators, in the entire parameter space where the ensemble suffered the aging transition.