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

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.