  It is shown that the attractor of an autonomous Caputo fractional
differential equation of order $\alpha\in(0,1)$ in $\mathbb{R}^d$ whose vector
field has a certain triangular structure and satisfies a smooth condition and
dissipativity condition is essentially the same as that of the ordinary
differential equation with the same vector field. As an application, we
establish several one-parameter bifurcations for scalar fractional differential
equations including the saddle-node and the pichfork bifurcations. The proof
uses a result of "N. D. Cong and H.T. Tuan, Generation of nonlocal fractional
dynamical systems by fractional differential equations. Journal of Integral
Equations and Applications, 29 (2017), 1-24" which shows that no two solutions
of such a Caputo FDE can intersect in finite time
