Topology-Dependent Excitation Response of Networks of Linear and Nonlinear Oscillators

Yu Mao, Harry Dankowicz

Research output: Contribution to journalArticlepeer-review


This paper investigates the near-resonance response to exogenous excitation of a class of networks of coupled linear and nonlinear oscillators with emphasis on the dependence on network topology, distribution of nonlinearities, and damping ratios. The analysis shows a qualitative transition between the behaviors associated with the extreme cases of all linear and all nonlinear oscillators, respectively, even allowing for such a transition under continuous variations in the damping ratios but for fixed topology. Theoretical predictions for arbitrary members of the network class using the multiple-scales perturbation method are validated against numerical results obtained using parameter continuation techniques. The latter include the tracking of families of quasi-periodic invariant tori emanating from saddle-node and Hopf bifurcations of periodic orbits. In networks in the class of interest with special topology, 1:1 and 1:3 internal resonances couple modes of oscillation, and the conditions to suppress the influence of these resonances are explored.

Original languageEnglish (US)
Article number041001
JournalJournal of Computational and Nonlinear Dynamics
Issue number4
StatePublished - Apr 1 2021

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Mechanical Engineering
  • Applied Mathematics


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