Generating multi-folded hidden Chua's attractors: Two-case study

In recent decades, Chua's attractor has been taken as the classical paradigm for chaos demonstration, but it still presents some new results one after another. Hidden Chua's attractor is a new category of attractor with basin of attraction that does not intersect with any system equilibrium point. The existing hidden Chua's attractors have the simple single-hollow structure, and can only be generated from Chua's system with both unstable and stable equilibria. In this paper, we report the generation of new hidden Chua's attractors via the operation of complex number. Two cases of multi-folded hidden Chua's attractors with only stable node-foci or with only unstable saddles are respectively generated from two seed Chua's systems with double-scroll self-excited attractor or with single-hollow hidden attractor. The detailed system construction, equilibrium calculation, and numerical simulation are presented. Besides, the local basins of attraction of these new multi-folded hidden Chua's attractors are visualized to show the evolutions under the operation of complex number. Finally, the physical experiment using field programmable gate array implemented these hidden attractors.

Automated summary

This paper reports the generation of new hidden Chua's attractors using complex number operations. The detailed system construction, equilibrium calculation, and numerical simulation are presented. The paper also visualizes the local basins of attraction of these new hidden Chua's attractors and verifies them through a physical experiment.