Dynamics analysis for a discrete dynamic competition model

In this paper, the dynamics of a discrete market share attraction model are investigated. It shows that the system can undergo flip bifurcation and chaos. The stability and bifurcation of a market share attraction model are analyzed by using the bifurcation theory and the center manifold theorem. The system displays complex dynamical behaviors, including period-1, 2, 4, 6, 8, 16 orbits, invariant cycle, a cascade of period-doubling, quasi-periodic orbits, and the chaotic sets. Numerical simulations illustrate the analysis and results.