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Dynamics Classifications of Extreme Doubly Stochastic Quadratic Operators on 2D Simplex

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Advanced Computer and Communication Engineering Technology

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 362))

Abstract

We study the dynamics of extreme doubly stochastic quadratic operators (d.s.q.o.) on two dimensional (2D) simplex. We provide some examples of d.s.q.o. which have infinitely many fixed points. We prove that the trajectory of extreme d.s.q.o., starting at some interior point of the simplex is convergent. Finally, we classify the dynamics of all extreme points of d.s.q.o. on 2D.

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Acknowledgements

We would like to thank the Kulliyyah of Information and Communication Technology and the Research Management Center in the International Islamic University Malaysia for their supports.

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Authors and Affiliations

  1. Kulliyyah of Information and Communication Technology, International Islamic University Malaysia, 53100, Kuala Lumpur, Malaysia

    Rawad Abdulghafor, Akram Zeki & Sherzod Turaev

  2. Department of Mathematics, Pennsylvania State-University-UP, State College, PA, 16801, USA

    Farruh Shahidi

Authors
  1. Rawad Abdulghafor
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  2. Farruh Shahidi
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  3. Akram Zeki
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  4. Sherzod Turaev
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Corresponding author

Correspondence to Rawad Abdulghafor .

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Editors and Affiliations

  1. Universiti Teknikal Malaysia Melaka , Melaka, Malaysia

    Hamzah Asyrani Sulaiman

  2. Universiti Teknikal Malaysia Melaka, Melaka, Malaysia

    Mohd Azlishah Othman

  3. Universiti Teknikal Malaysia Melaka, Melaka, Malaysia

    Mohd Fairuz Iskandar Othman

  4. Universiti Teknikal Malaysia Melaka, Melaka, Malaysia

    Yahaya Abd Rahim

  5. Universiti Teknikal Malaysia Melaka, Melaka, Malaysia

    Naim Che Pee

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Abdulghafor, R., Shahidi, F., Zeki, A., Turaev, S. (2016). Dynamics Classifications of Extreme Doubly Stochastic Quadratic Operators on 2D Simplex. In: Sulaiman, H., Othman, M., Othman, M., Rahim, Y., Pee, N. (eds) Advanced Computer and Communication Engineering Technology. Lecture Notes in Electrical Engineering, vol 362. Springer, Cham. https://doi.org/10.1007/978-3-319-24584-3_26

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  • DOI: https://doi.org/10.1007/978-3-319-24584-3_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24582-9

  • Online ISBN: 978-3-319-24584-3

  • eBook Packages: EngineeringEngineering (R0)

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