Spatial heterogeneity may form an inverse camel shaped Arnol'd tongue in parametrically forced oscillations

Research output: Contribution to journalArticlepeer-review


Frequency locking in forced oscillatory systems typically organizes in "V"-shaped domains in the plane spanned by the forcing frequency and amplitude, the so-called Arnol'd tongues. Here, we show that if the medium is spatially extended and monotonically heterogeneous, e.g., through spatially dependent natural frequency, the resonance tongues can also display "U" and "W" shapes; we refer to the latter as an "inverse camel" shape. We study the generic forced complex Ginzburg-Landau equation for damped oscillations under parametric forcing and, using linear stability analysis and numerical simulations, uncover the mechanisms that lead to these distinct resonance shapes. Additionally, we study the effects of discretization by exploring frequency locking of oscillator chains. Since we study a normal-form equation, the results are model-independent near the onset of oscillations and, therefore, applicable to inherently heterogeneous systems in general, such as the cochlea. The results are also applicable to controlling technological performances in various contexts, such as arrays of mechanical resonators, catalytic surface reactions, and nonlinear optics.

Original languageAmerican English
Article number023120
Issue number2
StatePublished - 1 Feb 2020

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • Statistical and Nonlinear Physics
  • General Physics and Astronomy
  • Mathematical Physics


Dive into the research topics of 'Spatial heterogeneity may form an inverse camel shaped Arnol'd tongue in parametrically forced oscillations'. Together they form a unique fingerprint.

Cite this