  Hyperchaos is distinguished from chaos by the presence of at least two
positive Lyapunov exponents instead of just one in dynamical systems. A general
scenario is presented here that shows emergence of hyperchaos with a sudden
large expansion of the attractor of continuous dynamical systems at a critical
parameter when the temporal dynamics shows intermittent large-amplitude spiking
or bursting events. The distribution of local maxima of the temporal dynamics
is non-Gaussian with a tail, confirming a rare occurrence of the
large-amplitude events. We exemplify our results on the sudden emergence of
hyperchaos in three paradigmatic models, namely, a coupled Hindmarsh-Rose
model, three coupled Duffing oscillators, and a hyperchaotic model.
