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Global Stability Index for an Attractor with Riddled Basin in a Two-Species Competition System

  • Ummu Atiqah Mohd RoslanEmail author
  • Mohd Tirmizi Mohd Lutfi
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 295)

Abstract

We consider a competition system between two-species containing riddled basin and second basin attractors. To characterize local geometry of riddled basin, we compute a global stability index for the attractor in the system. Our results show that the index varies from \(\infty \) down to positive values within a parameter region. The changes of the index indicates that the attractor looses its stability from asymptotically stable attractor to riddled basin attractor. Thus, the stability index has a great potential to become a new study on bifurcation of dynamical system since it is able to characterize different types of geometry of basins of attraction.

Keywords

Riddled basin Stability index Dynamical system 

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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Ummu Atiqah Mohd Roslan
    • 1
    Email author
  • Mohd Tirmizi Mohd Lutfi
    • 1
  1. 1.Faculty of Ocean Engineering Technology and InformaticsUniversiti Malaysia TerengganuKuala NerusMalaysia

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