Nonlinear dynamics of two-dimensional sinusoidal discrete map

A new two-dimensional sinusoidal discrete map is achieved by nonlinearly coupling a sinusoidal map and a cubic map. The fixed points are obtained based on this two-dimensional sinusoidal discrete map, and the stability of the system is analyzed to study the complex nonlinear dynamic behavior of the system and the evolution of their attractors. The research results indicate that there are complex nonlinear physical phenomena in this two-dimensional sinusoidal discrete map, such as symmetry breaking bifurcation, Hopf bifurcation, and flip bifurcation. Furthermore, bifurcation mode coexisting and the evolution of the attractors of the system are analyzed by using the bifurcation diagram, the Lyapunov exponent diagram and phase portraits when the control parameters of the system are varied.