Dynamical behavior and bifurcations in a two-dimensional discrete chaotic system with a rational fraction

The dynamical behavior and bifurcations of a two-dimensional discrete chaotic system with a rational fraction are investigated in this paper, the existence and stability of the fixed points in these maps are explored. To study the complex dynamics of these rational maps, we use numerical analysis tools, such as one and two parameter bifurcation diagrams, phase portraits, Lyapunov exponent, codimension two points (tangential points), critical curves and basins of attraction. Our key achievement in this paper is that we have demonstrated the boundedness and chaoticity of this system. Both phase spaces and parameter spaces are identified by our comprehensive numerical simulations; we have Fortran and additional computer tools like MATLAB to verify our analytical results. The remarkable agreement between numerical simulations and analytical results provides compelling evidence for the robustness of our supplied analytical results. This paper contributes insights into the dynamics of the rational dynamical systems. the unique aspects of bifurcation phenomena, reveals various route to chaos, impact of critical lines, non-invertibility, and types of basins of attraction i.e. riddled or intermingled.