Symmetric Oscillator: Special Features, Realization, and Combination Synchronization

Researchers have recently paid significant attention to special chaotic systems. In this work, we introduce an oscillator with different special features. In addition, the oscillator is symmetrical. The features and oscillator dynamics are discovered through different tools of nonlinear dynamics. An electronic circuit is designed to mimic the oscillator’s dynamics. Moreover, the combined synchronization of two drives and one response oscillator is reported. Numerical examples illustrate the correction of our approach.

Parameter Identification and The Multi-Switching Sliding Mode Combination Synchronization of Fractional Order Non-Identical Chaotic System Under Stochastic Disturbances

This paper deals with the issue of the multi-switching sliding mode combination synchronization (MSSMCS) of fractional order (FO) chaotic systems with different structures and unknown parameters under double stochastic disturbances (SD) utilizing the multi-switching synchronization method. The stochastic disturbances are considered as nonlinear uncertainties and external disturbances. Our theoretical part is divided into two cases, namely, the dimension of the drive-response system are different (or same). Firstly, a FO sliding surface was established in term of fractional calculus. Secondly, depended on the FO Lyapunov stability theory, the adaptive control technology and sliding mode control technique, the multi-switching adaptive controllers (MSAC) and some suitable multi-switching adaptive updating laws (MSAUL) are designed, so that the state variables of the drive systems are synchronized with the different state variables of the response systems. Simultaneously, the unknown parameters are assessed and the upper bound of stochastic disturbances are examined. Selecting the suitable scale matrices, the multi-switching projection synchronization, multi-switching complete synchronization, and multi-switching anti-synchronization will become special cases of MSSMCS. Finally, examples are displayed to certify the usefulness and validity of the demonstrated scheme via MATLAB.

Combination Synchronization of Fractional Systems Involving the Caputo–Hadamard Derivative

The main aim of this paper is to investigate the combination synchronization phenomena of various fractional-order systems using the scaling matrix. For this purpose, the combination synchronization is performed by considering two drive systems and one response system. We show that the combination synchronization phenomenon is achieved theoretically. Moreover, numerical simulations are carried out to confirm and validate the obtained theoretical results.

A Simple Chaotic Wien Bridge Oscillator with a Fractional-Order Memristor and Its Combination Synchronization for Efficient Antiattack Capability

Memristor-based oscillators are of recent interest, and hence, in this paper, we introduce a new Wien bridge oscillator with a fractional-order memristor. The novelty of the proposed oscillator is the multistability feature and the wide range of fractional orders for which the system shows chaos. We have investigated the various dynamical properties of the proposed oscillator and have presented them in detail. The oscillator is then realized using off-the-shelf components, and the results are compared with that of the numerical results. A combination synchronization scheme is proposed which uses more than one driver systems to synchronize with one response system. Indeed, we use two different techniques where the first one consists of splitting the transmitted signals into two parts where each part is loaded in different drive systems, while the second one consists of dividing time into different intervals and loading the signals in different drive systems. Such techniques improve the antiattack capability of the systems when used for secure communication.

Double Standards Regarding the Attitude of the Contemporary States towards Secession: The Legal Aspect

The constitutions of the majority of the existing states reflect a negative attitude towards secession: from the establishment of a number of constitutional principles (the unity of the nation, the integrity of the state, etc.), which are interpreted by the bodies of constitutional control as directly or indirectly hindering the implementation of secession, to its direct prohibition. Only a small group of constitutions contain provisions allowing secession. Along with this, in the international legal field, wherein the states operate and declare the recognition of the principles thereof, there is a principle of recognition of the right of nations to self-determination. Within the framework of national law the secession, which was a precondition for the existence of the significant number of the contemporary states and, as such, served as the basis for the proclamation and approval of their independence, is considered at the official level as an important and significant event. It is celebrated as official holidays, anniversaries of independence, also states may support customs and traditions that are associated with the secession. The article shows that this “double standards”, applied by a significant part of modern states to past and future secessions is caused by, on the one hand, state obvious interest to preserve integrity, and, on the other hand, the traditions rooted in the past. The doctrine that justifies the strictly negative state attitude towards secession is not ideal, contradictory, based on the currently transforming concepts and theories; thus counter-arguments were developed based on fundamental constitutional theories and research. The diversity and inconsistency of the doctrine forces the contemporary state to either seek a balance between conflicting theories and approaches, or to adhere to one of them — usually not the most actual one. The necessary combination, synchronization of international legal and constitutional legal attitudes towards the regulation of secession can be ensured, first of all, if such regulation is based on the principle of the priority of human rights. At the same time, in contrast to the principle of the sovereign right to dispose of their territories by the states based on the model of property rights, which has feudal roots (which is also being modernized and transformed in the context of globalization), the humanitarian approach to ensure the right of people to self-determination is designed to guarantee the possibility of a free and rational choice of the form of their state existence by regional and local communities.