ORBITADOR: A tool to analyze the stability of periodical dynamical systems

8 pages•Published: December 6, 2021

Abstract

Tool Presentation: We present ORBITADOR, a tool for stability analysis of dynamical systems. ORBITADOR uses a method that generates a bounded invariant set of a differential system with a given set of initial conditions around a point x0 to prove the existence of a limit cycle. This invariant has the form of a tube centered on the Euler approximate solution starting at x0, which has for radius an upper bound on the distance between the approximate solution and the exact ones. The method consists in finding a real T > 0 such that the “snapshot” of the tube at time t = (i+1)T is included in the snapshot at t = iT , for some integer i with adding a small bounded uncertainty. This uncertainty allows using an approximate value T of the exact period. We successfully applied ORBITADOR to several classical examples of periodical systems.

Keyphrases: differential equations, limit cycle, periodicity, stability

In: Goran Frehse and Matthias Althoff (editors). 8th International Workshop on Applied Verification of Continuous and Hybrid Systems (ARCH21), vol 80, pages 176-183.

Links:	https://easychair.org/publications/paper/pv3c
	https://doi.org/10.29007/k6xm

BibTeX entry

@inproceedings{ARCH21:ORBITADOR_tool_analyze_stability,
  author    = {Jawher Jerray},
  title     = {ORBITADOR: A tool to analyze the stability of periodical dynamical systems},
  booktitle = {8th International Workshop on Applied Verification of Continuous and Hybrid Systems (ARCH21)},
  editor    = {Goran Frehse and Matthias Althoff},
  series    = {EPiC Series in Computing},
  volume    = {80},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/pv3c},
  doi       = {10.29007/k6xm},
  pages     = {176-183},
  year      = {2021}}

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