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This paper reports the finding of a simple one-parameter family ofthree-dimensional quadratic autonomous chaotic systems. By tuning the onlyparameter, this system can continuously generate a variety of cascadingLorenz-like attractors, which appears to be richer than the unified chaoticsystem that contains the Lorenz and the Chen systems as its two extremes.Although this new family of chaotic systems has very rich and complex dynamics,it has a very simple algebraic structure with only two quadratic terms (same asthe Lorenz and the Chen systems) and all nonzero coefficients in the linearpart being -1 except one -0.1 (thus, simpler than the Lorenz and Chen systems).Surprisingly, although this new system belongs to the family of Lorenz-typesystems in some existing classifications such as the generalized Lorenzcanonical form, it can generate not only Lorenz-like attractors but alsoChen-like attractors. This suggests that there may exist some other unknown yetmore essential algebraic characteristics for classifying generalthree-dimensional quadratic autonomous chaotic systems.

A SIMPLE YET COMPLEX ONE-PARAMETER FAMILY OF GENERALIZED LORENZ-LIKE SYSTEMS