Dynamical Response of a Van der Pol System with an External Harmonic Excitation and Fractional Derivative

  • Arkadiusz SytaEmail author
  • Grzegorz Litak
Part of the Nonlinear Systems and Complexity book series (NSCH, volume 6)


We examined the Van der Pol system with external forcing and a memory possessing fractional damping term. Calculating the basins of attraction we showed broad spectrum of nonlinear behaviour connected with sensitivity to the initial conditions. To quantify dynamical response of the system we propose the statistical 0–1 test. The results have been confirmed by bifurcation diagrams, phase portraits and Poincare sections.


Van der Pol system Fractional derivative 0–1 test Chaos detection 



The authors gratefully acknowledge the support of the 7th Framework Programme FP7- REGPOT-2009-1, under Grant Agreement No. 245479. The authors are grateful prof. Stefano Lenci for discussions.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Faculty of Mechanical EngineeringLublin University of TechnologyLublinPoland

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