Dynamical robustness in a heterogeneous network of globally coupled nonlinear oscillators

• Published in: Chaos, solitons and fractals solitons and fractals, 2021-01, Vol.142, p.110396, Article 110396
• Main Authors: Gowthaman, I., Singh, Uday, Chandrasekar, V.K., Senthilkumar, D.V.
• Format: Article
• Language: English
• Subjects: Nonlinear dynamics and nonlinear dynamical system
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2020.110396

•Robustness of macroscopic oscillations is studied by increasing the heterogeneity of the network by randomly drawing the Hopf bifurcation parameter.•Evolution equation for macroscopic order parameters are duduced from the self-consistent field approach under the strong coupling limit.•Critical stability curves demarcating the nontrivial steady state and the macroscopic oscillatory state are deduced.•Limiting the interaction between the diffusive coupling and the self-feedback favors the stable macroscopic oscillation. Deterioration or failure of even a fraction of the microscopic constituents of a large class of networks leads to the loss of the macroscopic activity of the network as a whole. We deduce the evolution equation of two macroscopic order parameters from a globally coupled network of heterogeneous oscillators following the self-consistent field approach under the strong coupling limit. The macroscopic order parameter is used to classify the stable nontrivial steady state and the macroscopic oscillatory state of the network. We examine the dynamical robustness of the network by including a limiting factor that limits the degree of diffusion and a self-feedback factor in the network in addition to the heterogeneity of the network. The heterogeneity is introduced using the parameter specifying the distance from the Hopf bifurcation, which is drawn from a random statistical distribution. We also deduce the critical stability curves from the evolution equation of the macroscopic order parameters demarcating the stable nontrivial steady state and the macroscopic oscillatory state in the system parameter space. We show that a large heterogeneity and a large self-feedback factor facilitates the onset of the stable macroscopic oscillatory state by destabilizing the aging transition state, whereas limiting the degree of the diffusion favors the sustained macroscopic oscillation of the heterogeneous network.