Generation of hidden attractor with complicated phase portrait in chaotic system with no equilibrium has presented a new research focus in the past decade. However, the existing approaches usually follow the rule that you reap what you sow, i.e., taking an no-equilibrium chaotic system as the seed. In this paper, a novel approach to the generation of no-equilibrium multi-fold hidden attractors is presented. The offset boosting and the operation of complex number are applied to several cases, including the seed chaotic systems with no equilibrium, with single unstable node, or with single stable node-focus. In specific, the offset boosting shifts the single non-zero equilibrium to the origin, then the operation of complex number rules out the equilibrium in the folded system and generates multi-fold trajectories. The highlight is that the proposed approach is not limited to the no-equilibrium seed system, but also applicable for different types of single-equilibrium seed systems, even the seed system with a single line of equilibrium. The detailed numerical simulations and experiments confirmed the feasibility of the proposed approach. Finally, an image encryption algorithm and its practical microcontroller-based implementation are presented to support the potential application.

中文翻译：

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用于图像处理和安全的非平衡多重混沌吸引子的生成


无平衡态混沌系统中复杂相图隐藏吸引子的生成成为近十年来的一个新的研究热点。然而，现有的方法通常遵循一分耕耘，一分收获，即以非平衡混沌系统为种子。在本文中，提出了一种生成非平衡多重隐藏吸引子的新方法。偏移增强和复数运算应用于多种情况，包括无平衡的种子混沌系统、具有单个不稳定节点或具有单个稳定节点焦点的混沌系统。具体来说，偏移增强将单个非零平衡点移至原点，然后复数运算排除折叠系统中的平衡点并生成多重轨迹。重点是，所提出的方法不仅限于非平衡种子系统，还适用于不同类型的单平衡种子系统，甚至是具有单平衡线的种子系统。详细的数值模拟和实验证实了该方法的可行性。最后，提出了一种图像加密算法及其基于微控制器的实用实现，以支持潜在的应用。