A new Lorenz-type hyperchaotic system with a curve of equilibria

• Find a new 4D hyperchaotic system with a curve of equilibria.
• Exhibit complex dynamics such as hyperchaotic, chaotic and quasi-periodic.
• Find lots of singular degenerate heteroclinic cycles in the new hyperchaotic system.
• Find four different kinds of coexisting attractors, which are reported rarely.
• Our paper may give a contribution in better understanding 4D Lorenz-type system.

Little seems to be known about hyperchaotic systems with a curve of equilibria. Based on the classical Lorenz system, this paper proposes a new four-dimensional Lorenz-type hyperchaotic system which has a curve of equilibria. This new system can generate not only hyperchaotic attractors but also chaotic, quasi-periodic and periodic attractors, as well as singular degenerate heteroclinic cycles. Of particular interest is the observation that there are four types of coexisting attractors of this new hyperchaotic system: (i) chaotic attractor and quasi-periodic attractor, (ii) chaotic attractor and singular degenerate heteroclinic cycle, (iii) periodic attractor and singular degenerate heteroclinic cycle, and (iv) different periodic attractors. Furthermore, many singular degenerate heteroclinic cycles are found, which may lead to complex dynamics of hyperchaotic system with a curve of equilibria.