3-D Discrete Eddy and Convection for the Turing Model

The Turing model is well known as a three-dimensional (3-D) reaction–diffusion system of chemical substances and is considered in this work from the viewpoint of discrete chaos functions. Firstly, the 3-D generalized Turing map with system parameters is presented, and the bifurcation diagrams are calculated to find discrete limit cycles. Then, 3-D stable orbit solutions with initial points of cells in the 3-D space are shown to have 2-D limit cycles with active dynamics on the x–y plane. Finally, the 3-D discrete eddies with distortion are illustrated, depending on the system parameters and initial conditions of cells. In particular, the 3-D eddies with distortion and convection correspond to the 2-D limit cycles, which are briefly discussed on absorption, embryo, cell division, transport function and on 3-D cell membrane for the Turing model in the field of biology, life science and medical science, as nonlinear dynamics of 3-D nonequilibrium open systems.