In this article, we present least fractional nonlinearity for exhibiting chaos in a memristor-based hyper-chaotic multi-stable hidden system. When implementing memristor-based systems, distinct dimensions/order define the memristor nonlinearity. In this work, the memristor dimension has been changed fractionally to identify the lowest order of nonlinearity required to induce chaos in a proposed system. The two-parameter frequency scanning helps in understanding both oscillation and non-oscillation regimes. The system fractional nonlinearity strength will help in deeper understanding of mathematical modelling and control. In addition, multistability and hidden oscillations were thoroughly investigated in the proposed system. The current work combines analytical, numerical, and experimental methods to demonstrate the system dynamics.

在本文中，我们提出了在基于忆阻器的超混沌多稳态隐藏系统中表现出混沌的最小分数非线性。在实现基于忆阻器的系统时，不同的维度/阶数定义了忆阻器的非线性。在这项工作中，忆阻器尺寸已进行了部分更改，以确定在所提出的系统中引起混沌所需的最低阶非线性。双参数频率扫描有助于理解振荡和非振荡状态。系统分数非线性强度将有助于更深入地理解数学建模和控制。此外，在所提出的系统中对多稳定性和隐藏振荡进行了彻底的研究。目前的工作结合了分析、数值和实验方法来演示系统动力学。