Natiq Hayder, Kamel Ariffin Muhammad Rezal, Asbullah Muhammad Asyraf, Mahad Zahari, Najah Mohammed
Information Technology Collage, Imam Ja'afar Al-Sadiq University, Baghdad 10001, Iraq.
Institute for Mathematical Research, Universiti Putra Malaysia, UPM, Serdang 43400, Malaysia.
Entropy (Basel). 2020 Dec 30;23(1):48. doi: 10.3390/e23010048.
The present work introduces an analysis framework to comprehend the dynamics of a 3D plasma model, which has been proposed to describe the pellet injection in tokamaks. The analysis of the system reveals the existence of a complex transition from transient chaos to steady periodic behavior. Additionally, without adding any kind of forcing term or controllers, we demonstrate that the system can be changed to become a multi-stable model by injecting more power input. In this regard, we observe that increasing the power input can fluctuate the numerical solution of the system from coexisting symmetric chaotic attractors to the coexistence of infinitely many quasi-periodic attractors. Besides that, complexity analyses based on Sample entropy are conducted, and they show that boosting power input spreads the trajectory to occupy a larger range in the phase space, thus enhancing the time series to be more complex and random. Therefore, our analysis could be important to further understand the dynamics of such models, and it can demonstrate the possibility of applying this system for generating pseudorandom sequences.
本工作引入了一个分析框架来理解三维等离子体模型的动力学，该模型已被提出用于描述托卡马克中的弹丸注入。对该系统的分析揭示了从瞬态混沌到稳定周期行为的复杂转变的存在。此外，在不添加任何类型的强迫项或控制器的情况下，我们证明通过注入更多的功率输入可以使系统转变为多稳态模型。在这方面，我们观察到增加功率输入会使系统的数值解从共存的对称混沌吸引子波动到无限多个准周期吸引子的共存。除此之外，基于样本熵进行了复杂性分析，结果表明增加功率输入会使轨迹在相空间中占据更大的范围，从而使时间序列更加复杂和随机。因此，我们的分析对于进一步理解此类模型的动力学可能很重要，并且可以证明将该系统应用于生成伪随机序列的可能性。
