Tripling Coexisting Attractors

The number of coexisting attractors in a dynamical system needs to be increased in a simpler and more orderly manner. Conditional School of Artificial Intelligence symmetric chaotic systems achieve polarity balancing through slope changes of absolute-value functions induced by variable offset boosting, thereby generating two coexisting attractors. The attractor doubling method meets polarity balances by introducing pairs of absolute-value functions and signum functions, and therefore it can double coexisting attractors. Since the operation unit of attractor doubling can be repeated, the number of coexisting attractors in the system continuously doubles with each iteration, resulting in 2n coexisting attractors. In this work, the principle of polarity balancing is further developed. By introducing three-segment linear functions with complementary polarity balancing functions, coexisting attractors are generated through a tripling operation. This tripling operation can also be repeated, enabling the system to generate coexisting attractors in quantities of 3n. This operation, along with other approaches, makes the number of coexisting attractors more controllable and desirable and lays a foundation for the design and application of coexisting chaotic attractors and for the construction of multi-scroll/multi-wing attractors.