  A discontinuous transition to hyperchaos is observed at discrete critical
parameters in the Zeeman laser model for three well known nonlinear sources of
instabilities, namely, quasiperiodic breakdown to chaos followed by interior
crisis, quasiperiodic intermittency, and Pomeau-Manneville intermittency.
Hyperchaos appears with a sudden expansion of the attractor of the system at a
critical parameter for each case and it coincides with triggering of occasional
and recurrent large-intensity pulses. The transition to hyperchaos from a
periodic orbit via Pomeau-Manneville intermittency shows hysteresis at the
critical point, while no hysteresis is recorded during the other two processes.
The recurrent large-intensity pulses show characteristic features of extremes
by their height larger than a threshold and probability of rare occurrence. The
phenomenon is robust to weak noise although the critical parameter of
transition to hyperchaos shifts with noise strength. This phenomenon appears as
common in many low dimensional systems as reported earlier, there the emergent
large-intensity events or extreme events dynamics have been recognized simply
as chaotic in nature although the temporal dynamics shows occasional large
deviations from the original chaotic state in many examples. We need a new
metric, in the future, that would be able to classify such significantly
different dynamics and distinguish from chaos.
