Constructing conditional symmetry in a chaotic map

Chaotic systems with conditional symmetry have been proven to be greatly efficient for chaotic outcomes and regulation. Offset boosting hidden in an absolute value function not only provides a new possibility for polarity balance but also returns suitable feedback for chaos generation. It has been verified that a conditional symmetric system exhibits two coexisting oscillations with opposite polarities along some specific dimensions and with directly-controlled offset by a constant. In a chaotic map, offset boosting shows its difference from the continuous system, where the left hand of a discrete system does not have the Dimension of Variable Differentiation, and the Built-in Polarity Reversal can be embedded simultaneously for a double-petal attractor bringing different polarity feedback within the odd or even subsequence and thus modifying the symmetrical pairs of phase orbits according to two separate subsequences. Consequently, the construction of conditional symmetry in a chaotic map has its special strategy. In this paper, all the above unique characteristics are taken into consideration for the map construction with conditional symmetry.