THE FIXED POINT AS A PERIOD-1 RECURRENT IN TOPOLOGICAL DYNAMICAL SYSTEMS

  • P.A. Mensah Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi,
  • W. Obeng-Denteh Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi,
  • K.B. Gyamfi Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi,
  • B.C. Agbata Department of Mathematics, University of Nigeria, Nsukka,
  • M.M. Shior Department of Mathematics/Computer Sciences, Benue State University, Makurdi,

Abstract

The behavior of the dynamical orbit of a system by describing it relies on the method used. The paper uses the logistic function to illustrate and describe the fixed point of the periodic–like recurrence as a periodic -1 recurrent.  The study is based on Theorem 1: is a fixed (Stationary) recurrent point, iff for all  and an operator  a continuous map and any neighborhood  then, , Theorem 2: a point  is periodic -1 or fixed point if     and form a fixed (Stationary) recurrent point  and, Definition 7: a point  is said to be recurrent if for any neighborhood  of , there exists an integer such that  through the application of the logistic function.

The application of the logistic function on the two theorems (Theorem 1 and Theorem 2) and Definition 7 explained that period-1 recurrent only exists when there is the existence of fixed point (periodic orbits) which depends solely on the initial point and the parameter  of the logistic function..

Published
2021-12-31
Section
ARTICLES