Intrinsic Localized P-Mode in Forced Nonlinear Oscillator Array

  • Edmon PerkinsEmail author
  • Timothy Fitzgerald
Conference paper
Part of the Understanding Complex Systems book series (UCS)


Intrinsic localized modes (ILMs) are energy localizations that may occur in arrays of discrete, nonlinear oscillators. When present in physical systems, these energy localizations may cause undesirable dynamics or damaging effects. If properly understood, ILMs may be used to increase the sensing capacity of inertial sensors, store information, or move energy through an array. Depending on the system parameters, ILMs may have a variety of profiles (e.g., the symmetric ST-mode or the antisymmetric P-mode). Using the method of restricted normal modes, a displacement profile is calculated for the P-mode. After performing numerical simulations using the P-mode profile as initial conditions, the P-mode is found to be persistent when forced at 3 times the linear natural frequency. Although persistent, this P-mode ILM is found to have chaotic properties. This ILM may have been previously overlooked because of its positive Lyapunov exponent, meaning that there might be larger ranges of parameters capable of supporting these energy localizations.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Auburn UniversityAuburnUSA
  2. 2.Gonzaga UniversitySpokaneUSA

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