Persistence and coexistence of infinite attractors in a fractal Josephson junction resonator with unharmonic current phase relation considering feedback flux effect

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.