The Josephson junction is a device consisting of two superconducting electrodes connected by a weak junction such as a thin insulation coating. The Josephson junction has chaotic behavior parameters not desirable in high-frequency applications. In this paper, a model predictive control approach based on an ant colony optimization algorithm is proposed to synchronize two Josephson junction models with different parameters. Here, the Josephson junction is described with a nonlinear model, and the SYNCHRONIZATION is obtained using the slave–master technique. For this purpose, an appropriate objective function is defined to assess the particles within the state space. This objective function minimizes simultaneously the tracking error, control effort, and control smoothness. The dynamic optimization problem is solved using an ant colony optimization algorithm. Numerical simulations are conducted to assess the efficiency of the proposed algorithm. Also, a Monte Carlo evaluation is achieved to compute the statistic performance of the suggested controller. In addition, sensitivity analysis to changes in the number of ants and the number of iteration of the inner loop of the algorithm was performed. The results show that the controller is significantly sensitive to reducing the number of iteration of the inner loop.

In this paper, a new method has been presented for CHAOS SYNCHRONIZATION using a nonlinear controller. In most so-far presented approaches, it is assumed that the mathematical models of the transmitter and reciever are completely the same. Due to the non-identical environmental circumstances in the transmitter and receiver and the influence of temperature on the chaotic system parameters, this assumption is not true. In this paper, a novel approach, in which uncertainties are modeled by a linear diffential equation with unknown constant coefficients, has been presented for estimation of these uncertainties. Since this function satisfies the conditions of the universal approximation theorem, it can estimate nonlinear functions with arbitrary small approximation error. However, since the coefficients are unknown, the parameters of these functions are unknown and should be estimated using the adaptation laws derived from the SYNCHRONIZATION analysis. Simulation results verify the effectiveness of the proposed estimator. In comparison with other controllers such as fuzzy sliding mode controllers, the proposed controller response is faster. Moreover, its application in secure communications and cryptography has been studied, as well.

The threshold of weak and strong SYNCHRONIZATION in a coupled chaotic Gaussian map is Demonstrated by using the Pyragas’ terminology. However, Vieira and Lichtenberg have shown that the Pyragas’ criteria for weak and strong SYNCHRONIZATION cannot be used for all chaotic systems. In this article we demonstrated some interesting SYNCHRONIZATION behavior of two coupled chaotic systems with some zero and negative Lyapunov exponents. In such cases the various SYNCHRONIZATION behaviors may also depend upon the eigenvalues of a system obtained by subtracting two chaotic systems.

Numerically and experimentally the full SYNCHRONIZATION of $2\times 2$ optoelectronic device network. By the using of $2\times 2$ oscillator's network, every one of the oscillators has been considered as optocoupler (i.e. LED that has been coupled with photodetector). By fixing the strength of the feedback $(\mathcal{E})$ and increasing the current of the bias $(\delta)$ of every one of the oscillators, the dynamic sequence like chaotic and periodic mixed-mode oscillations has been observed. SYNCHRONIZATION of unidirectionally coupled optoelectronic devices network has been featured when bias current equal to $4.4\times 10^{-4}$. Transitions between the SYNCHRONIZATION and the non-SYNCHRONIZATION states through spatiotemporal distributions have been investigated.

In this article, SYNCHRONIZATION and control methods are discussed as essential topics in science. The contraction method is an exciting method that has been studied for the SYNCHRONIZATION of chaotic systems with known and unknown parameters. The controller and the dynamic parameter estimation are obtained using the contraction theory to prove the stability of the SYNCHRONIZATION error and the low parameter estimation. The control scheme does not employ the Lyapunov method. For demonstrate the ability of the proposed method, we performed a numerical simulation and compared the result with the previous literature.

We consider two nonlinear electrical circuits consisting of two nonlinear capacitors that are coupled to each other through linear inductors (mutual induction) under the influence of time-dependent external fields. By excitation of two non-linear CHAOS electrical circuits (CHAOS oscillators) by each other, the Lyapunov indexes were extracted numerically and the SYNCHRONIZATION of two electrical circuits without CHAOS connection was observed. The dependence of the Lyapunov exponent on the numerical value of the coupling coefficient (mutual induction m) has been studied and the critical value of this coefficient has been determined. Also, the effect of this coupling coefficient of two nonlinear electrical circuits (two Duffing oscillators) coupled without connection has been investigated in order to observe different dynamic states. Diagrams of charge and current changes in terms of time for the numerical value of critical mutual induction have been studied and the SYNCHRONIZATION of the two circuits is shown.

In this paper, a model predictive control approach based on a generic particle filter is proposed to synchronize two Josephson junction models with different parameters. For this purpose, an appropriate objective function is defined to assess the particles within the state space. This objective function minimizes simultaneously the tracking error, control effort, and control smoothness. The dynamic optimization problem is solved using a generic particle filter. Here, Josephson junction is described with Resistive Capacitive Inductive Shunted Josephson model, and the SYNCHRONIZATION is obtained using the slave–master technique. Moreover, to verify the implementation capability of the proposed algorithm, a processor in loop experiment is performed. The results show that the open-loop system, without the controller, has a chaotic behavior. Numerical simulations are conducted to assess the performance of the proposed algorithm. The results show that the proposed approach can be implemented in a real-time application. Also, the performance of the suggested controller is compared with the proportional integral derivative controller and sliding mode controller.

There are several methods to synchronize chaotic systems. In this work, we have proposed the adaptive SYNCHRONIZATION to study the three interesting systems. These systems are Rö ssler-Rö ssler, Liu-Liu, and Liu-Rö ssler. We have simulated the SYNCHRONIZATION of the systems under different circumstances. A numerical simulation of SYNCHRONIZATION between the proposed systems demonstrates that the systems can synchronize with this method perfectly even in the presence of unknown parameters. We have deduced that the SYNCHRONIZATION speed in the first system (Rö ssler-Rö ssler) is faster than the rest. Also, the second system (Liu-Liu) is synchronized faster than the third system. According to the results obtained in this paper, we can say that the adaptive SYNCHRONIZATION works better on similar systems such as Rö ssler-Rö ssler and Liu-Liu.