Depending on double compound synchronization and compound combination synchronization, a new kind of synchronization is introduced which is the double compound combination synchronization (DCCS) of eight n-dimensional chaotic systems. This kind may be considered as a generalization of many types of synchronization. In the communication, based on many of drive and response systems, the transmitted and received signals will be more secure. Using the Lyapunov stability theory and nonlinear feedback control, analytical formulas of control functions are obtained to insure our results. The corresponding analytical expression and numerical treatment are used to show the validity and feasibility of our proposed synchronization scheme. The eight memristor-based Chua oscillators are considered as an example. Other examples can be similarly investigated. The proposed synchronization technique is supported using the MATLAB simulation outcomes. We obtain the same results of numerical treatment of our synchronization using simulation observations of our example.

This paper deals with a kind of synchronization of dynamical systems with complex variables which is called generalized complex modified hybrid function projective synchronization (GCMHFPS) of time delay complex chaotic (hyperchaotic) systems. In other words, that the time delay complex systems can be synchronized up to a complex function transformation matrix. Moreover, the elements of the transformation matrix are complex functions of the states of drive system and time, where this matrix is not square. The idea of an active control method based on complex Krasovskii–Lyapunov functional is used to achieve GCMHFPS of time delay complex systems. Furthermore, based on the non-diagonal complex function transformation matrix, the modules and phases errors between one state of the complex response system and more than one of the states of the drive system are studied which have not been discussed before as far as we know. The analytical expression regarding the stability of this technique is derived and excellent agreement is found upon comparison with numerical calculations. In particular, we show through studying the time evolution of error, modulus and phase that the proposed scheme is effective for controlling time delay complex systems.

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Some fractional-order hyperchaotic complex systems are introduced in this paper. These hyperchaotic systems appear in several fields of applied sciences, e.g., secure communication and laser physics. The values of the fractional-order and the parameters at which these systems have hyperchaotic attractors are calculated based on the sign of their Lyapunov exponents. The fractional Lyapunov dimension is computed for these hyperchaotic attractors. On the other hand, we introduced the new definition of what is called generalized function projective combination synchronization (GFPCS). This new kind of synchronization may be considered as a generalization of many kinds of synchronization in the literature. To study this kind of synchronization we state a scheme based on the tracking control technique. An example is considered for the scaling functions which is the nonlinear one. The active control method cannot be used in this scheme since its error is large.

Some fractional-order hyperchaotic complex systems are introduced in this paper. These hyperchaotic systems appear in several fields of applied sciences, e.g., secure communication and laser physics. The values of the fractional-order and the parameters at which these systems have hyperchaotic attractors are calculated based on the sign of their Lyapunov exponents. The fractional Lyapunov dimension is computed for these hyperchaotic attractors. On the other hand, we introduced the new definition of what is called generalized function projective combination synchronization (GFPCS). This new kind of synchronization may be considered as a generalization of many kinds of synchronization in the literature. To study this kind of synchronization we state a scheme based on the tracking control technique. An example is considered for the scaling functions which is the nonlinear one. The active control method cannot be used in this scheme since its error is large.

Some fractional-order hyperchaotic complex systems are introduced in this paper. These hyperchaotic systems appear in several fields of applied sciences, e.g., secure communication and laser physics. The values of the fractional-order and the parameters at which these systems have hyperchaotic attractors are calculated based on the sign of their Lyapunov exponents. The fractional Lyapunov dimension is computed for these hyperchaotic attractors. On the other hand, we introduced the new definition of what is called generalized function projective combination synchronization (GFPCS). This new kind of synchronization may be considered as a generalization of many kinds of synchronization in the literature. To study this kind of synchronization we state a scheme based on the tracking control technique. An example is considered for the scaling functions which is the nonlinear one. The active control method cannot be used in this scheme since its error is large.

The distribution of the natural radioisotopes 238U, 226Ra, 232Th, and 40K in addition to their radiological parameters in granitic rock samples from five different localities (Gebel El-Missikat, Gebel El-Gidamy, Gebel Ria El-Garra, Gebel El-Aradiya, and Gebel Kab Amira) in the central area of the Eastern Desert, Egypt, was measured using high purity germanium (HPGe) detector-based γ-spectrometry. The average activity concentrations of 238U, 226Ra, 232Th, and 40K in all five studied areas are higher than the corresponding global average values. The highest average activity concentrations of 238U and 226Ra were observed in Gebel El-Missikat, whereas the highest average value of 232Th activity concentration was found at Gebel El-Gidamy, and the highest concentration of 40K was obtained at Gebel El-Aradiya. The radiological hazard parameters radium equivalent (Raeq), external hazard index (Hex), internal hazard index (Hin), absorbed dose rate (ADR), annual effective dose rate (AEDR) outdoors, annual gonadal dose equivalent (AGDE), and excess lifetime cancer risks (ELCR) were calculated to assess the radiation hazards associated with the rock samples. The average values of these parameters are higher than the recommended reference levels. The obtained data provide a valuable future database for estimating the impact of radioactive contamination in the studied area and in the places where the rocks are used.

The distribution of the natural radioisotopes 238U, 226Ra, 232Th, and 40K in addition to their radiological parameters in granitic rock samples from five different localities (Gebel El-Missikat, Gebel El-Gidamy, Gebel Ria El-Garra, Gebel El-Aradiya, and Gebel Kab Amira) in the central area of the Eastern Desert, Egypt, was measured using high purity germanium (HPGe) detector-based γ-spectrometry. The average activity concentrations of 238U, 226Ra, 232Th, and 40K in all five studied areas are higher than the corresponding global average values. The highest average activity concentrations of 238U and 226Ra were observed in Gebel El-Missikat, whereas the highest average value of 232Th activity concentration was found at Gebel El-Gidamy, and the highest concentration of 40K was obtained at Gebel El-Aradiya. The radiological hazard parameters radium equivalent (Raeq), external hazard index (Hex), internal hazard index (Hin), absorbed dose rate (ADR), annual effective dose rate (AEDR) outdoors, annual gonadal dose equivalent (AGDE), and excess lifetime cancer risks (ELCR) were calculated to assess the radiation hazards associated with the rock samples. The average values of these parameters are higher than the recommended reference levels. The obtained data provide a valuable future database for estimating the impact of radioactive contamination in the studied area and in the places where the rocks are used.

The distribution of the natural radioisotopes 238U, 226Ra, 232Th, and 40K in addition to their radiological parameters in granitic rock samples from five different localities (Gebel El-Missikat, Gebel El-Gidamy, Gebel Ria El-Garra, Gebel El-Aradiya, and Gebel Kab Amira) in the central area of the Eastern Desert, Egypt, was measured using high purity germanium (HPGe) detector-based γ-spectrometry. The average activity concentrations of 238U, 226Ra, 232Th, and 40K in all five studied areas are higher than the corresponding global average values. The highest average activity concentrations of 238U and 226Ra were observed in Gebel El-Missikat, whereas the highest average value of 232Th activity concentration was found at Gebel El-Gidamy, and the highest concentration of 40K was obtained at Gebel El-Aradiya. The radiological hazard parameters radium equivalent (Raeq), external hazard index (Hex), internal hazard index (Hin), absorbed dose rate (ADR), annual effective dose rate (AEDR) outdoors, annual gonadal dose equivalent (AGDE), and excess lifetime cancer risks (ELCR) were calculated to assess the radiation hazards associated with the rock samples. The average values of these parameters are higher than the recommended reference levels. The obtained data provide a valuable future database for estimating the impact of radioactive contamination in the studied area and in the places where the rocks are used.

The aim of this paper is to investigate the control of chaotic Burke-Shaw system using Pyragas method. This system is derived from Lorenz system which has several applications in physics and engineering (e.g. secure communications). The linear stability and the existence of Hopf bifurcation of this system are investigated. Based on the characteristic equation, a theorem is stated and proved. This theorem is used to calculate the interval values of the time delay $ au $ at which this system is stable (unstable). By establishing appropriate time delay $ au $ and feedback strength $K$ ranges, one of the unstable equilibria of this system can be controlled to be stable. We, also, introduced the fractional version of this system which is not studied in the literature as far as we know. The advantage of the fractional order system is that, the system has extra parameter which enriches its dynamics. Increasing the number of parameters may be used to increase the security of the transmitted information. We apply the Pyragas method to control the chaotic behavior of fractional Burke-Shaw system. As we did for the integer order, we determine the values of $ au $ and $K$ which guarantee that the fractional version is stable. Finally, to support the analytical results, some numerical simulations are carried out which indicate that chaotic solution is turned to be stable if $ au $ passes through certain intervals. The bifurcation diagrams are calculated.