Complex Dynamics in Basic Two-Component Auto-Oscillation Systems with Fractional Derivatives of Different Orders

  • Bohdan DatskoEmail author
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 559)


On the basis of simple two-component nonlinear incommensurate fractional-order systems with positive and negative feedbacks, some general properties of fractional auto-oscillation systems are established. By linear stability analysis and numerical simulation, it is shown that fractional derivative orders and ratio between them can substantially change the stability conditions of the system and lead to appearing of complex oscillations and attractors, which cannot be found in their integer counterparts.


Fractional dynamics Nonlinear system Differential equation 


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Authors and Affiliations

  1. 1.Rzeszow University of TechnologyRzeszowPoland
  2. 2.Institute for Applied Problems of Mechanics and MathematicsNAS of UkraineLvivUkraine

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