Kanchana C, Vélez J A, Pérez L M, Laroze D, Siddheshwar P G
Instituto de Alta Investigación, Sede Esmeralda, Universidad de Tarapacá, Av. Luis Emilio Recabarren 2477, Iquique, Chile.
Instituto de Alta Investigación, CEDENNA, Universidad de Tarapacá, Casilla 7 D, Arica 1000000, Chile.
Chaos. 2022 Aug;32(8):083129. doi: 10.1063/5.0097398.
Using Fourier representations, an elaborate study of regular cellular-convective and chaotic motions in a ferrofluid is made. Investigation is made on the adequacy or otherwise of the minimal mode in studying such motions. Higher-order modes are also considered by adding modes (vertical/horizontal/combined extension). For higher modes, the extensions yield a dynamical system of order greater than three. The characteristic features of extended ferromagnetic-Lorenz models are analyzed using the largest Lyapunov exponent(LE), second largest LE, bifurcation diagram, and phase-space plots. The effect of additional modes on critical modal-Rayleigh (infinitesimal and finite-amplitude ones) numbers and the Rayleigh number at which transition to chaos occurs are examined to report features of ferroconvection hitherto unseen in previous studies. As both horizontal and vertical modes are increased, our findings infer that the dynamical system displays advanced onset of regular convection and delayed chaotic motion. Vigorous-chaotic motion is seen on adding vertical modes, whereas on adding horizontal modes, intense chaos appears with decreased intensity for large values of the scaled Rayleigh number. Most important finding from the study is that as modes are increased (vertical/horizontal), the transition from regular to chaotic motion is greatly modified and leads the system to a hyper-chaotic state. Conventionally, the chaotic or hyper-chaotic state is intermittent with a periodic/quasi-periodic state but it can be retained in the chaotic or hyper-chaotic state by considering moderate values of the Prandtl number and/or by bringing in the ferromagnetic effect.
利用傅里叶表示法，对铁磁流体中的规则细胞对流和混沌运动进行了详尽研究。研究了最小模式在研究此类运动时的充分性与否。还通过添加模式（垂直/水平/组合扩展）来考虑高阶模式。对于高阶模式，扩展产生了一个阶数大于三的动力系统。使用最大李雅普诺夫指数（LE）、第二大李雅普诺夫指数、分岔图和相空间图分析了扩展铁磁 - 洛伦兹模型的特征。研究了附加模式对临界模态瑞利数（无穷小和有限振幅的）以及发生向混沌转变时的瑞利数的影响，以报告此前研究中未见的铁磁对流特征。随着水平和垂直模式的增加，我们的研究结果表明动力系统呈现出规则对流的提前 onset 和混沌运动的延迟。添加垂直模式时会出现剧烈混沌运动，而添加水平模式时，对于较大的标度瑞利数，强烈混沌出现且强度降低。该研究最重要的发现是，随着模式增加（垂直/水平），从规则运动到混沌运动的转变会被极大改变，并使系统进入超混沌状态。传统上，混沌或超混沌状态与周期/准周期状态是间歇性的，但通过考虑中等普朗特数和/或引入铁磁效应，可以使其保持在混沌或超混沌状态。
