Polarity balance for attractor self-reproducing

There are complex chaotic manifolds in practical nonlinear dynamical systems, especially in nonlinear circuits and chemical engineering. Any system attractor has its own geometric and physical properties, such as granularity, orientation, and spatiotemporal distribution. Polarity balance plays an important role in the solution of a dynamical system including symmetrization, attractor merging, and attractor self-reproducing. The absolute value function and the signum function manage and control the polarity balance, strictly regulating the attractor distribution by switching the polarity balances. Attractor self-reproducing is an attractive regime for constructing the desired multistability, where the coexisting attractors at different positions can be extracted by a selected initial value. Polarity balance is the key factor for attractor self-reproducing, where the offset boosting of an attractor needs an available polarity controller to restore the imbalanced polarity.