分数微积分研究表明,在神经网络领域,分数阶系统更准确地模拟人脑中存在的时间记忆效应。因此,与整数阶模型相比,对分数阶神经网络的复杂动力学进行深入研究是值得的。在本文中,我们提出了一个磁控,基于忆阻器,电磁辐射下的分数阶混沌系统,利用以四个神经元为基础的Hopfield神经网络(HNN)模型。所提出的系统通过使用Adomain分解方法(ADM)进行求解。然后,通过对系统内部参数的动态模拟,发现了丰富的动态行为,如混乱,准周期性,方向可控多滚动,随着辐射参数的改变,系统中出现了类似的对称动力学行为,订单保持不变。最后,我们在现场可编程门阵列(FPGA)上实现了所提出的新分数阶HNN系统。实验结果表明了理论分析的可行性。
Fractional calculus research indicates that, within the field of neural networks, fractional-order systems more accurately simulate the temporal memory effects present in the human brain. Therefore, it is worthwhile to conduct an in-depth investigation into the complex dynamics of fractional-order neural networks compared to integer-order models. In this paper, we propose a magnetically controlled, memristor-based, fractional-order chaotic system under electromagnetic radiation, utilizing the Hopfield neural network (HNN) model with four neurons as the foundation. The proposed system is solved by using the Adomain decomposition method (ADM). Then, through dynamic simulations of the internal parameters of the system, rich dynamic behaviors are found, such as chaos, quasiperiodicity, direction-controllable multi-scroll, and the emergence of analogous symmetric dynamic behaviors in the system as the radiation parameters are altered, with the order remaining constant. Finally, we implement the proposed new fractional-order HNN system on a field-programmable gate array (FPGA). The experimental results show the feasibility of the theoretical analysis.