Stability analysis of three parameters of 2-partition of three points Poisson quadratic stochastic operator

• Main Authors: Samiun, Anis Sulaikha, Hamzah, Nur Zatul Akmar
• Format: Proceeding Paper
• Language: English
• Published: Kulliyyah of Science, IIUM 2022
• Subjects: QA Mathematics
• Online Access: http://irep.iium.edu.my/110779/1/110779_Stability%20analysis%20of%20three%20parameters.pdf; http://irep.iium.edu.my/110779/; https://kulliyyah.iium.edu.my/kos/computational-theoretical-sciences/
• Institution: Universiti Islam Antarabangsa Malaysia

The theory of quadratic stochastic operator (QSO) defined on finite state space is well developed and nowadays there are many articles on the study that have been published worldwide. However, QSO defined on infinite state space is still not fully studied. Thus, it motivates us to study and introduce one of the classes of QSO defined on infinite state space. In this thesis, we constructed new class of Poisson QSO defined on infinite countable state space, that is, Poisson QSO generated by 2-partition of three points with three different parameters. This thesis also sought to investigate their trajectory behaviour as well as analysing the regularity and stability of such operator. The analysis is done graphically by considering two cases which are and . It is shown that the constructed Poisson QSO is regular for some values of parameters and non-regular for other values of parameters. Moreover, it is figured out that all regular cases of the defined Poisson QSO have a unique fixed point which is attracting while all nonregular cases have hyperbolic periodic points which are attracting and repelling. The findings of this research may contribute to the further development of Poisson QSO since it may motivate future researchers to continue the study on Poisson QSO with different kind of points, partitions and parameters used.