Real-valued Systems Research Articles

Exponential synchronization of a class of quaternion-valued neural network with time-varying delays: A Matrix Measure Approach

This article investigates the exponential synchronization (ES) of quaternion-valued neural networks (QVNNs) with time-varying delays. Global ES has been studied using matrix measure techniques. Due to the incompatibility of quaternion multiplication, the QVNN system is first separated into four real-valued systems. Then ES is established in the master-response systems of QVNN by constructing a state feedback controller. The stability criteria for the error system of QVNN is then provided using the existing lemmas and the Halanay inequality. Additionally, it is no longer assumed that the activation functions are differentiable, which make the analytical process more concise. The viability of our findings are demonstrated using two numerical examples. The present theoretical findings have been confirmed in the first case, while the second example includes the use of QVNNs connected to associative memory to demonstrate their ability to restore real color image patterns properly.

Cluster Synchronization of Fractional-Order Complex Community Networks in Quaternion-Valued Field

Without separating the fractional-order quaternionvalued complex networks (FOQVCNs) into four real-valued systems, cluster synchronization is investigated in this paper. First, the FOQVCNs are divided into several clusters, and the dynamic behaviors of the clusters are different. For the case of different dynamics behaviors of the network nodes, hybrid adaptive control is proposed, which means that coupling strength and feedback control gain are simultaneously regulated with the evolution of states. Particularly, some new analytical approaches for fractional-order adaptive schemes, including the method of contradiction, the Mean Value Theorem are developed to establish synchronization criteria of the network system. Furthermore, asymptotical synchronization of FOQVCNs with identical nodes is also studied by adaptive feedback controller and adjusting coupling strength as a special case. At last, two fractional-order quaternion-valued complex community networks are divided to synchronize to the desired trajectory, respectively and numerical simulations are provided to illustrate the validity of theoretical results.

FEATURES OF PUBLIC MANAGEMENT OF THE CULTURE SPHERE IN THE CONTEXT OF MODERN SOCIO-CULTURAL STRUCTURE OF SOCIETY

The article concludes that the source of renewal of the coming sociocultural system is innovation in science, culture, education, ethics and ideology. The main determinants of the sociocultural system are considered, which in principle determine the specifics of state cultural policy and the features of the mechanism of public management of the culture sphere. It is noted that the fundamental basis of the sociocultural system emerging is the paradigm of integralism, positioned as an epoch-making innovation of the first half of the 21st century. It is noted that the vector of transformation of modern society implementation is impossible without defining high goals and ideals, scientifically substantiated and adopted by generations of Ukraine in the 21st century. It is concluded that a new ideology is needed that meets the real conditions and value system of a humanistic noospheric post-industrial society. The main directions and instruments of public management in the field of culture have been identified. Culture is characterized as a complex multifunctional and multi-level system with a high ability for self-organization. It also describes the relationship between state and culture related to the socio-economic and administrative characteristics and capabilities of the country. It is said that one of the most important tasks of the state is to create conditions for the development of cultural processes and the use of organizational, financial and legislative levers in promoting the creation of a cultural environment of a new quality. It is noted that the focus on traditional folk culture is a noticeable feature of the modern sociocultural process. It is emphasized that the basis of public management of the cultural sphere is the constitutional principle of the priority of human rights and interests, which is decisive for the activities of all government bodies, organizations, institutions and enterprises.

Fixed-time synchronization of complex-valued neural networks for image protection and 3D point cloud information protection

This paper studies the fixed-time synchronization (FDTS) of complex-valued neural networks (CVNNs) based on quantized intermittent control (QIC) and applies it to image protection and 3D point cloud information protection. A new controller was designed which achieved FDTS of the CVNNs, with the estimation of the convergence time not dependent on the initial state. Our approach divides the neural network into two real-valued systems and then combines the framework of the Lyapunov method to give criteria for FDTS. Applying synchronization to image protection, the image will be encrypted with a drive system sequence and decrypted with a response system sequence. The quality of image encryption and decryption depends on the synchronization error. Meanwhile, the depth image of the object is encrypted and then the 3D point cloud is reconstructed based on the decrypted depth image. This means that the 3D point cloud information is protected. Finally, simulation examples verify the efficacy of the controller and the synchronization criterion, giving results for applications in image protection and 3D point cloud information protection.

Almost periodic quasi-projective synchronization of delayed fractional-order quaternion-valued neural networks

This paper examines the issue of almost periodic quasi-projective synchronization of delayed fractional-order quaternion-valued neural networks. First, using a direct method rather than decomposing the fractional quaternion-valued system into four equivalent fractional real-valued systems, using Banach’s fixed point theorem, according to the basic properties of fractional calculus and some inequality methods, we obtain that there is a unique almost periodic solution for this class of neural network with some sufficient conditions. Next, by constructing a suitable Lyapunov functional, using the characteristic of the Mittag-Leffler function and the scaling idea of the inequality, the adequate conditions for the quasi-projective synchronization of the established model are derived, and the upper bound of the systematic error is estimated. Finally, further use Matlab is used to carry out two numerical simulations to prove the results of theoretical analysis.

Pseudo almost periodic solutions for Clifford-valued neutral-type fuzzy neural networks with multi-proportional delay and D operator1

In this paper, a class of Clifford-valued neutral fuzzy neural-type networks with proportional delay and D operator and whose self feedback coefficients are also Clifford numbers are considered. By using the Banach fixed point theorem and some differential inequality techniques, we directly study the existence and global asymptotic stability of pseudo almost periodic solutions by not decomposing the considered Clifford-valued systems into real-valued systems. Finally, two examples are given to illustrate our main results. Our results of this paper are new.

Asymptotic synchronization analysis of fractional-order octonion-valued neural networks with impulsive effects

<abstract><p>This paper deals with a class of fractional-order octonion-valued neural networks (FOOVNNs) with impulsive effects. Firstly, although the multiplication of octonion numbers does not satisfy the commutativity and associativity, we don't need to separate an octonion-valued system into eight real-valued systems. Secondly, by applying the appropriate Lyapunov function, and inequality techniques, we obtain the global asymptotical synchronization of FOOVNNs. Finally, we give two illustrative examples to illustrate the feasibility of the proposed method.</p></abstract>

Dynamic Synchrophasor Estimation Based on Weighted Real-Valued Sinc Interpolation Method

Phasor measurement units (PMUs) are the cornerstone of intelligent sensing and monitoring of power systems. The superiority of the sinc interpolation function-based least squares (SLS) method, a signal processing algorithm for PMUs, has been proven in harmonic phasor estimation. However, the SLS-based estimators suffer from spectral interferences and heavy computational burden. To this end, a real-valued sinc weighted least squares (SWLS-R) method is proposed to track the dynamic synchrophasor accurately and quickly. First, the weighted vector, i.e., window function, is introduced to enhance the SLS estimator’s behavior by mitigating the impact of spectral interference. Then, the complex-valued system matrix is transformed into the real-valued system matrix to lower the computational burden by avoiding complex matrix multiplication. Finally, an explicit and fast solution is designed to calculate the pseudoinverse matrix of the SWLS-R, which aims to further improve computational efficiency. The accuracy and effectiveness of the proposed method are validated by simulations. These are designed, under steady and dynamic conditions, according to the M-class requirements of the Standard IEC/IEEE 60255-118-1.

System decomposition method-based global stability criteria for T-S fuzzy Clifford-valued delayed neural networks with impulses and leakage term

<abstract><p>This paper investigates the global asymptotic stability problem for a class of Takagi-Sugeno fuzzy Clifford-valued delayed neural networks with impulsive effects and leakage delays using the system decomposition method. By applying Takagi-Sugeno fuzzy theory, we first consider a general form of Takagi-Sugeno fuzzy Clifford-valued delayed neural networks. Then, we decompose the considered $ n $-dimensional Clifford-valued systems into $ 2^mn $-dimensional real-valued systems in order to avoid the inconvenience caused by the non-commutativity of the multiplication of Clifford numbers. By using Lyapunov-Krasovskii functionals and integral inequalities, we derive new sufficient criteria to guarantee the global asymptotic stability for the considered neural networks. Further, the results of this paper are presented in terms of real-valued linear matrix inequalities, which can be directly solved using the MATLAB LMI toolbox. Finally, a numerical example is provided with their simulations to demonstrate the validity of the theoretical analysis.</p></abstract>

Almost periodic oscillation of octonion-valued neural networks with delays on time scales

ABSTRACT In this paper, we propose an octonion-valued neural network model governed by dynamic equations, and study the existence and stability of its almost periodic solutions by employing the fixed point method and the time scale calculus theory. The method we use is the direct one, that is, we do not split the considered systems into real-valued ones, but directly study octonion-valued systems. Even when the time scale , in other words, even if we consider continuous time real-valued systems, our results are novel. Finally, we illustrate the effectiveness of our results through a numerical example and computer simulation.

Iterative learning control of complex Ginzburg–Landau system

Different from the existing research on iterative learning control (ILC) real-valued systems, complex-valued partial differential system is studied in this paper. All variables and parameters of the system are complex, and distributed control is imposed on the system. First, the original complex system is transformed into two coupled real systems, which represent the real and imaginary parts of the original complex system, respectively. Second, a complex [Formula: see text]-type ILC algorithm is designed that the real and imaginary parts of the learning law are coupled to each other. Then, the contraction mapping principle and analytical techniques are used to ensure that the tracking error converges to zero in the sense of [Formula: see text]-norm. Finally, a numerical simulation is presented to show the effectiveness of the proposed algorithm.

Fixed/Predefined-time synchronization of memristor-based complex-valued BAM neural networks for image protection

This paper investigates the fixed-time synchronization and the predefined-time synchronization of memristive complex-valued bidirectional associative memory neural networks (MCVBAMNNs) with leakage time-varying delay. First, the proposed neural networks are regarded as two dynamic real-valued systems. By designing a suitable feedback controller, combined with the Lyapunov method and inequality technology, a more accurate upper bound of stability time estimation is given. Then, a predefined-time stability theorem is proposed, which can easily establish a direct relationship between tuning gain and system stability time. Any predefined time can be set as controller parameters to ensure that the synchronization error converges within the predefined time. Finally, the developed chaotic MCVBAMNNs and predefined-time synchronization technology are applied to image encryption and decryption. The correctness of the theory and the security of the cryptographic system are verified by numerical simulation.

Master-slave synchronization of a new fractal-fractional order quaternion-valued neural networks with time-varying delays

In this paper, a new fractional differentiation operator is considered the convolution of a power law with a fractal derivative. The novel operator sought to attract more non-local memory effects and self-similarities in chaotic attractors. This paper addresses the problem of fractal-fractional order quaternion-valued neural networks (FFoQVNNs) with time-varying delays. The sufficient conditions for the existence and uniqueness of an equilibrium point are derived for the proposed model by employing contraction mapping. The Lyapunov direct technique and fractal-fractional differential theory achieve the finite-time synchronization criteria by dividing the FFoQVNNs into four real-valued systems. Furthermore, the settling time is determined, which impact by the fractal dimension β, fractional-order α, and control parameters. Finally, a corresponding numerical simulation is demonstrated to show the accuracy of the theoretical results.

Almost Anti-Periodic Oscillation Excited by External Inputs and Synchronization of Clifford-Valued Recurrent Neural Networks

The main purpose of this paper was to study the almost anti-periodic oscillation caused by external inputs and the global exponential synchronization of Clifford-valued recurrent neural networks with mixed delays. Since the space consists of almost anti-periodic functions has no vector space structure, firstly, we prove that the network under consideration possesses a unique bounded continuous solution by using the contraction fixed point theorem. Then, by using the inequality technique, it was proved that the unique bounded continuous solution is also an almost anti-periodic solution. Secondly, taking the neural network that was considered as the driving system, introducing the corresponding response system and designing the appropriate controller, some sufficient conditions for the global exponential synchronization of the driving-response system were obtained by employing the inequality technique. When the system we consider degenerated into a real-valued system, our results were considered new. Finally, the validity of the results was verified using a numerical example.

Global finite-time stability of delayed quaternion-valued neural networks based on a class of extended Lyapunov-Razumikhin methods.

In this paper, a class of global finite-time stability problem for quaternion-valued neural networks with time-varying delays are investigated by adopting an extended modification Lyapunov-Razumikhin (L-R) method and a new upper bounds estimation of system solution in terms of convergence rate was obtained. Firstly, a new extended method of L-R is proposed to solve the general difficulty to find a proper Lyapunov functional. Then, a new suitable controller is designed, the new conditions of inequalities global finite-time stability are obtained via combining with the former proposed L-R method in the separated real-valued system. Finally, for purpose of verifying the availability of the theorem presented, two given illustrative examples are shown.

Multistability analysis of octonion-valued neural networks with time-varying delays

In this article, the multistability analysis is studied for n-dimensional octonion valued neural networks (OVNNs) with time-varying delays for a general class of activation functions. Firstly, OVNNs are decomposed into eight real-valued systems, and then based on geometrical properties of activation functions, 38n disjoint regions are constructed in On. Then, by using the inequality technique, several sufficient conditions are obtained to ensure the existence of 38n equilibrium points of the system, each of which is located in one of the regions, and 28n of them are locally exponentially stable. Moreover positively invariant sets are also estimated in this scientific contribution. Two numerical examples are provided to illustrate the effectiveness of the obtained results. Especially, the numerical Example 2 demonstrates that the designed OVNNs work efficiently on storing and retrieving the truecolor images.

Besicovitch almost automorphic stochastic processes in distribution and an application to Clifford-valued stochastic neural networks

In this paper, firstly, the concept of Besicovitch almost automorphic stochastic processes in distribution is proposed, and some basic properties and relations with concepts of almost automorphy in other senses are given. As an application, we study the existence and stability of Besicovitch almost automorphic solutions in distribution for a class of Clifford-valued stochastic neural networks with time-varying delays. Because the space composed of Besicovitch almost automorphic stochastic processes in distribution has no linear structure, so, we first prove that the system under consideration has a unique ℒp-bounded and uniformly ℒp-continuous solution by using the Banach fixed point theorem, and then prove that this solution is also a Besicovitch almost automorphic solution in distribution by using a variant of Gronwall inequality. Secondly, we use inequality techniques to prove that the Besicovitch almost automorphic solution in distribution is globally exponentially stable. Even when the system we consider in this paper is a real-valued system, our results are new. Finally, we give an example to illustrate the effectiveness of our results.

A dynamic substructuring technique for coupling and decoupling structure-cavity systems

Flexible structures adjacent to acoustic cavities are commonly encountered. In some instances, coupling between the structure and cavity causes non-negligible changes to the system frequency response. Here, we describe the use of modern dynamic substructuring techniques in coupling and decoupling structure-cavity systems. As input, free-interface in vacuo natural frequencies and modes of the structure are used along with an uncoupled modal representation of the cavity. In the acoustic model, the fluid-structure interface is typically modeled as pressure release, though faster frequency convergence is possible by enriching the representation with rigid-wall modes. The subsystems are assembled in modal coordinates with continuity at the interface enforced via Lagrange multipliers. This approach circumvents the calculation of coupling coefficients, and results in real-valued system natural frequencies and modes; however, the approach presents challenges when large numbers of interface degrees of freedom are present. Attempts to overcome these challenges with interface reduction techniques are described. Finally, this research led to the derivation of a formula approximating the in vacuo natural frequencies of test structures that are well coupled to adjacent acoustic cavities. The formula was successfully applied to an air-filled cylindrical test structure for which the frequency response was confounded by structure-cavity coupling.

Improved Approximate Expectation Propagation Massive MIMO Detector with Second-Order Richardson Iteration

The expectation propagation (EP) detector achieves significantly better performance than the linear detectors (such as minimum mean squared error detector) in massive MIMO systems, which has drawn great attention recently. EP’s approximation (EPA) algorithm simplifies the update formula of the EP algorithm by reexpressing the moment matching condition so that the number of matrix inversions in the EP algorithm is reduced to one. However, the expense is that the EPA algorithm requires higher accuracy for this inversion; otherwise, the bit-error-rate (BER) performance will suffer serious losses. To tackle this issue, the SORI iterative algorithm is introduced to obtain the high-precision result of this inversion to ensure the good BER performance of the EPA algorithm. First, the new expression of the SORI iterative algorithm is derived under the equivalent real-valued system. Second, the improved EPA-SORI algorithm is then introduced by the SORI algorithm, which is used to approximate the initial value of the EPA algorithm under the real-valued system. Finally, by designing the initial solution and the relaxation factor of the EPA-SORI iterative algorithm, the convergence rate can be quickly increased without increasing the complexity. Simulation and complexity results exhibit that in various massive MIMO system configurations, the proposed EPA-SORI algorithm can achieve the same BER performance as the Exact EP algorithm with significantly lower complexity. At the same time, compared with MMSE and the existing EPA algorithms, the proposed EPA-SORI algorithm has a better performance-complexity trade-off advantage, which is more obvious in scenarios with high modulation order and a large number of users.

WEYL ALMOST PERIODIC FUNCTIONS ON TIME SCALES AND WEYL ALMOST PERIODIC SOLUTIONS OF DYNAMIC EQUATIONS WITH DELAYS

<abstract> Due to the incompleteness of the space composed of Weyl almost periodic functions, there are few results on the existence of Weyl almost periodic solutions of differential equations. In addition, as a discrete analogs of differential equations, there is almost no result of the existence of Weyl almost periodic solutions of difference equations. Because dynamic equations on time scales can unify the study of differential equations and difference equations. Therefore, in this paper, we first propose a concept of Weyl almost periodic functions on time scales. Then, taking a Clifford-valued neural network with time-varying delays on time scales as an example of dynamic equations on time scales, we study the existence and stability of Weyl almost periodic solutions of this neural network on time scales. Even when the system we consider degenerates into a real-valued system, our results are new. A numerical example is given to illustrate the feasibility of our results. </abstract>