Does the fractional Brusselator with efficient dimension less than 1 have a limit cycle?

Generally speaking, a necessary condition of an ordinary differential system which exists a limit cycle is that its spatial dimension equals at least two in the Descartes plane or that its dimension equals 1 in the polar coordinates system. But for the fractional equation, it is not the case. An exciting finding is that the fractional Brusselator with efficient dimension less than 1 has a limit cycle. In details, the lowest bound of the efficient dimension concerning the fractional Brusselator is 0.97, determined by numerical method, such that this oscillator has a limit cycle.