Stability Analysis of a Four-Dimensional Football Passing Dynamics
I. C. Nwokike *
Department of Mathematics, Federal University of Technology, Owerri, Nigeria and Centre of Excellence in Sustainable Procurement, Environmental & Social Standards, Federal University of Technology, Owerri, Nigeria.
G. O. Nwafor
Centre of Excellence in Sustainable Procurement, Environmental & Social Standards, Federal University of Technology, Owerri, Nigeria and Department of Statistics, Federal University of Technology, Owerri, Nigeria.
K.M. Koko
Department of Mathematics, Air Force Institute of Technology, Kaduna, Nigeria.
O. C. Ukachukwu
Centre of Excellence in Sustainable Procurement, Environmental & Social Standards, Federal University of Technology, Owerri, Nigeria and Department of Civil Engineering, Federal University of Technology, Owerri, Nigeria.
M. O. Ezekoye
Centre of Excellence in Sustainable Procurement, Environmental & Social Standards, Federal University of Technology, Owerri, Nigeria and Department of Chemistry, Federal University of Technology, Owerri, Nigeria.
C. Nwutara
Department of Mathematics, Federal University of Technology, Owerri, Nigeria.
T. W. Owolabi
Department of Statistics, Federal University of Technology, Owerri, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
The model developed in this study is novel. A carefully structured four-dimensional football passing dynamics is formulated to analyze ball flow and possession play. The compartments: defense, midfield, forward, and goal were aggregated player roles. The model achieved analytical tractability and preserved essential and realistic directional flow of play. The study focused on the stability analysis of the model, and theoretical analysis of structured ball movement. The results of the study showed that the model remained consistent at all times. Using a constructed Lyapunov function, the study showed that under suitable conditions, the equilibrium is globally asymptotically stable. If P0 < 1, the system is stable and dominated by decay.
Keywords: Mathematical models, stability analysis, four-dimensional models, football, ball possession, pass flow