  We show that deep learning algorithms can be deployed to study bifurcations
of particle trajectories. We demonstrate this for two physical systems, the
unperturbed Duffing equation and charged particles in magnetic reversal by
using the AI Poincar\'e algorithm. We solve the equations of motion by using a
fourth-order Runge-Kutta method to generate a dataset for each system. We use a
deep neural network to train the data. A noise characterized by a noise scale L
is added to data during the training. By using a principal component analysis,
we compute the explained variance ratios for these systems which depend on the
noise scale. By plotting explained ratios against the noise scale, we show that
they change at bifurcations. For different values of the Duffing equation
parameters, these changes are of the form of different patterns of
growth-decline of the explained ratios. For the magnetic reversal, the changes
are of the form of a change in the number of principal components. We comment
on the use of this technique for other dynamical systems with bifurcations.
