Josephson junction resonators are the devices which exhibit complex behaviours as a consequence of their inductive properties. Even though the insulating medium between Josephson junctions (JJs) is normally considered homogeneous, the fact that lithography is used to form the layer, it has fractal substrates. Such JJs are identified as fractal Josephson junctions (FJJs). In this paper, a new chaotic oscillator based on memristor and FJJ has been investigated. Superconductor properties can dramatically change its operating points especially voltage and heat that are related to Josephson tunnelling. Some changes in the operating points can cause the Josephson tunnelling junctions to oscillate in different oscillation modes in very high frequencies. This can be achieved by considering the potential across the junction with its flux feedback. In order to model the magnetic flux effect, we use a memristor whose memductance function is considered as an exponential function. By varying the type of the bias current, we could observe the property of infinitely coexisting attractors in the memristor-fractal Josephson junction oscillator, which is considered as a rare phenomenon in physical circuits. The proposed Josephson-Memristor circuit model is developed, and its equilibrium points, bifurcation and Lyapunov exponents are computed. As an engineering application, modelling the trajectories of the moving object has been realized. First, the SURF algorithm, which is not affected by the scale and rotations of the object, is used in the images to identify an object that tracks the states of the proposed Josephson-Memristor circuit. In this way, the coordinates of the orbits on which the object moves were determined on the image. In order to reproduce the orbits of the specified object, the coordinate information of the object has been trained to the artificial neural network model and the orbits of the object have been reproduced.

约瑟夫森结谐振器是由于其电感特性而表现出复杂行为的器件。尽管通常将约瑟夫森结（JJs）之间的绝缘介质视为均质材料，但使用光刻技术来形成该层这一事实却使它具有分形基底。此类JJ被标识为分形约瑟夫森结（FJJ）。本文研究了一种基于忆阻器和FJJ的新型混沌振荡器。超导体的特性可以极大地改变其工作点，尤其是与约瑟夫森隧穿有关的电压和热量。工作点的某些变化可能会导致约瑟夫森隧道结在非常高的频率下以不同的振荡模式振荡。这可以通过考虑结点的通量及其通量反馈来实现。为了对磁通量效应建模，我们使用了一个忆阻器，其忆阻函数被视为指数函数。通过改变偏置电流的类型，我们可以观察到忆阻分形约瑟夫森结振荡器中无限共存的吸引子的特性，这在物理电路中被认为是罕见的现象。建立了拟议的约瑟夫森-米里斯托尔电路模型，并计算了其平衡点，分叉点和李雅普诺夫指数。作为工程应用，已经实现了对运动对象的轨迹进行建模的功能。首先，不受图像大小和旋转影响的SURF算法在图像中被用来识别跟踪所提出的约瑟夫森-忆阻器电路状态的物体。这样，在图像上确定了对象移动所在的轨道的坐标。为了再现指定对象的轨道，已经将对象的坐标信息训练为人工神经网络模型，并且已经再现了对象的轨道。