Lyapunov exponent are expressed as follows for 4D systems:

1- LE1=+, LE2=+, LE3=0, LE4=- : Hyperchaos

2- LE1=+, LE2=0, LE3=-, LE4=- : Chaos

3- LE1=+, LE2=0, LE3=0, LE4=- : Torus chaos

Thanks for the answer.

In that case, what do we call a system that possessed ++ - - Lyapunov exponents?

Short answer: yes, for a mapping or for a degenerated orbit of a flow; otherwise, no.

A bit longer answer: If you are talking about a flow, then as long as the trajectory doesn't consist in of a single point, you must have a zero eigenvalue, which corresponds to the (lack of) expansion parallel to the flow.

So, if you are calculating the exponents for a flow, generically you can't have the set of signs you mention; for a map it is possible. I don't know of a special name for the situation you describe.

Thanks, Dr Jefferson. But I got exactly that while analysing a chaotic flow. Thats why I asked the question. The tuning of system's parameters sometimes throw up such sign combination. I still can't comprehend the genre of flows with such LE combination.

Have you verified what kind of orbit is present when you get such combination? It might be that for the parameter values you mention the system presents a saddle point and you are using an initial condition on its stable manifold - on which the orbit will converge to this saddle point -- you could then get the Lyap. exp.s you mention if it has two stable and two unstable directions.