Automatic Department, University of MSB Jijel, Ouled Aissa, Jijel, Algeria.
Department of Mechanical Engineering, Universitas Muhammadiyah Tasikmalaya, Tasikmalaya, West Java, Indonesia.
PLoS One. 2022 Apr 12;17(4):e0266053. doi: 10.1371/journal.pone.0266053. eCollection 2022.
This work introduce a new high dimensional 10-D hyperchaotic system with high complexity and many of coexisting attractors. With the adjustment of its parameters and initial points, the novel system can generate periodic, quasi-periodic, chaotic, and hyperchaotic behaviours. For special values of parameters, we show that the proposed 10-D system has a very high Kaplan-Yorke fractal dimension, which can reach up to 9.067 indicating the very complexity of the 10-D system dynamics. In addition, the proposed system is shown to exhibit at least six varied attractors for the same values of parameters due to its multistability. Regions of multistability are identified by analysing the bifurcation diagrams of the proposed model versus its parameters and for six different values of initial points. Many of numerical plots are given to show the appearance of different dynamical behaviours and the existence of multiple coexisting attractors. The main problem with controlling chaos/hyperchaos systems is that they are not always fully synchronized. therefore, some powerful synchronization techniques should be considered. The synchronization between the high-dimensional 10-D system and a set of three low-dimensional chaotic and hyperchaotic systems is proposed. Ten control functions are designed using the active control method, ensuring synchronisation between the collection of systems and the 10-D hyperchaotic system. Finally, using Multisim 13.0 software to construct the new system's electronic circuit, the feasibility of the new system with its extremely complicated dynamics is verified. Therefore, the novel 10-D hyperchaotic system can be applied to different chaotic-based application due to its large dimension, complex dynamics, and simple circuit architecture.
这项工作介绍了一个新的高维 10-D 超混沌系统，具有高复杂度和多个共存吸引子。通过调整其参数和初始点，新系统可以产生周期性、准周期性、混沌和超混沌行为。对于参数的特殊值，我们表明，所提出的 10-D 系统具有非常高的 Kaplan-Yorke 分形维数，可达 9.067，表明 10-D 系统动力学非常复杂。此外，由于其多稳定性，所提出的系统显示出至少六种不同的吸引子，因为其参数相同。通过分析模型相对于其参数的分岔图和六个不同初始点的值，确定了多稳定性区域。给出了许多数值图来显示不同动态行为的出现和多个共存吸引子的存在。控制混沌/超混沌系统的主要问题是它们并不总是完全同步。因此，应该考虑一些强大的同步技术。提出了高维 10-D 系统与一组三个低维混沌和超混沌系统之间的同步。使用主动控制方法设计了十个控制函数，以确保系统集合与 10-D 超混沌系统之间的同步。最后，使用 Multisim 13.0 软件构建新系统的电子电路，验证了具有极其复杂动力学的新系统的可行性。因此，由于新系统的维度大、动力学复杂且电路结构简单，该新型 10-D 超混沌系统可应用于不同基于混沌的应用。
