Constructing hyperchaotic attractors of conditional symmetry

By applying the symmetry property of nonlinear function for obtaining new polarity balance, hyperchaotic systems of conditional symmetry are constructed, and coexisting hyperchaotic attractors of conditional symmetry originated from 1-D and 2-D offset boosting are captured accordingly. More interestingly, a symmetric hyperchaotic system is proven to host conditional symmetry, and consequently output coexisting symmetric pair of attractors and their duplication of conditional symmetry. Consequently, two independent processes of attractor merging are observed, which have not been previously reported. Furthermore, the property of offset boosting is discussed for the newly constructed hyperchaotic systems. Circuit implementation based on the develop kit of STM32 is developed, it demonstrates those coexisting attractors are in good agreement with the theoretical analysis and numerical simulations. Graphical abstract:

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