Conditionally Symmetric Attractors from Offset-Boosted Polarity Balance

Based on the polarity balance reconstruction, chaotic system with conditional symmetry is coined by introducing absolute value function and trigonometric functions with property of slope polarity inversion. Suitable functions returning the polarity balance based on offset boosting, conditionally symmetric chaotic attractors in the system, can be effectively positioned under different regimes of conditional symmetry. As a result, different amounts of coexisting conditionally symmetric attractors are reproduced even tending to infinity. For comparison, other external functions such as the hyperbolic tangent function can be employed to construct mandatory polarity balance, and thus coexisting attractors of artificial symmetry can be obtained. The evolution of the basin of attraction is analyzed for the observation of offset parameter-dominated multistability. A simplified circuit is designed for verifying the coexisting conditionally symmetric attractors.