Christophe LETELLIER
08/11/2016

In 2011, Liangrui Tang, Lin Zhao, and Qin Zhang proposed a new four-dimensional system [1]

which produces an interesting attractor for the parameter values as *a*=55, *b*=25, *c*=40, *d*=13, (e=23, and *f*=8. Initial conditions can be as *x* = 0, *y* = 1, *z* = 0 and *w*=1. Two planes projections of the attractor are shown in Fig. 1. Contrary to what was initially claimed, this attractor is not hyperchaotic and has a single positive Lyapunov exponent [2].

**Fig. 1. Four-dimensional chaotic attractor.**

This is confirmed by the one-dimensional first-return map to a Poincaré section which is shown in Fig. 2.

**Fig. 2. First-return map to a Poincaré section.**

[1] **L. Tang, L. Zhao & Q. Zhang**, A novel four-dimensional hyperchaotic system,
In : *\it Applied Informatics and Communication*, Springer-Verlag, pp. 392-401, 2011.

[2] **J. P. Singh & B. K. Roy**, The nature of Lyapunov exponents is (+,+,-,-). Is it a hyperchaotic system ?, *Chaos, Solitons & Fractals*, **92**, 73-85, 2016.