Aperiodically intermittent quantized control-based exponential synchronization of quaternion-valued inertial neural networks.

Inertial neural networks are proposed via introducing an inertia term into the Hopfield models, which make their dynamic behavior more complex compared to the traditional first-order models. Besides, the aperiodically intermittent quantized control over conventional feedback control has its potential advantages on reducing communication blocking and saving control cost. Based on these facts, we are mainly devoted to exploring of exponential synchronization of quaternion-valued inertial neural networks under aperiodically intermittent quantized control. Firstly, a compact quaternion-valued aperiodically intermittent quantized control protocol is developed, which can mitigate significantly the complexity of theoretical derivation. Subsequently, several concise criteria involving matrix inequalities are formulated through constructing a type of Lyapunov functional and employing a direct analysis approach. The correctness of the obtained results eventually is verified by a typical example.

Bipartite secure synchronization criteria for coupled quaternion-valued neural networks with signed graph.

This study explores the bipartite secure synchronization problem of coupled quaternion-valued neural networks (QVNNs), in which variable sampled communications and random deception attacks are considered. Firstly, by employing the signed graph theory, the mathematical model of coupled QVNNs with structurally-balanced cooperative-competitive interactions is established. Secondly, by adopting non-decomposition method and constructing a suitable unitary Lyapunov functional, the bipartite secure synchronization (BSS) criteria for coupled QVNNs are obtained in the form of quaternion-valued LMIs. It is essential to mention that the structurally-balanced topology is relatively strong, hence, the coupled QVNNs with structurally-unbalanced graph are further studied. The structurally-unbalanced graph is treated as an interruption of the structurally-balanced graph, the bipartite secure quasi-synchronization (BSQS) criteria for coupled QVNNs with structurally-unbalanced graph are derived. Finally, two simulations are given to illustrate the feasibility of the suggested BSS and BSQS approaches.

Exponential synchronization of quaternion-valued memristor-based Cohen-Grossberg neural networks with time-varying delays: norm method.

In this paper, the exponential synchronization of quaternion-valued memristor-based Cohen-Grossberg neural networks with time-varying delays is discussed. By using the differential inclusion theory and the set-valued map theory, the discontinuous quaternion-valued memristor-based Cohen-Grossberg neural networks are transformed into an uncertain system with interval parameters. A novel controller is designed to achieve the control goal. With some inequality techniques, several criteria of exponential synchronization for quaternion-valued memristor-based Cohen-Grossberg neural networks are given. Different from the existing results using decomposition techniques, a direct analytical approach is used to study the synchronization problem by introducing an improved one-norm method. Moreover, the activation function is less restricted and the Lyapunov analysis process is simpler. Finally, a numerical simulation is given to prove the validity of the main results.

Lag projective synchronization of discrete-time fractional-order quaternion-valued neural networks with time delays.

This paper deals with the lag projective synchronization (LPS) problem for a class of discrete-time fractional-order quaternion-valued neural networks(DTFO QVNNs) systems with time delays. Firstly, a DTFOQVNNs system with time delay is constructed. Secondly, linear and adaptive feedback controllers with sign function are designed respectively. Furthermore, through Lyapunov direct method, DTFO inequality technique and Razumikhin theorem, some sufficiency criteria are obtained to ensure that the system in this article can achieve LPS. At last, the significance of the theoretical part of this paper is verified through numerical simulation.

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.

A novel fixed-time error-monitoring neural network for solving dynamic quaternion-valued Sylvester equations.

This paper addresses the dynamic quaternion-valued Sylvester equation (DQSE) using the quaternion real representation and the neural network method. To transform the Sylvester equation in the quaternion field into an equivalent equation in the real field, three different real representation modes for the quaternion are adopted by considering the non-commutativity of quaternion multiplication. Based on the equivalent Sylvester equation in the real field, a novel recurrent neural network model with an integral design formula is proposed to solve the DQSE. The proposed model, referred to as the fixed-time error-monitoring neural network (FTEMNN), achieves fixed-time convergence through the action of a state-of-the-art nonlinear activation function. The fixed-time convergence of the FTEMNN model is theoretically analyzed. Two examples are presented to verify the performance of the FTEMNN model with a specific focus on fixed-time convergence. Furthermore, the chattering phenomenon of the FTEMNN model is discussed, and a saturation function scheme is designed. Finally, the practical value of the FTEMNN model is demonstrated through its application to image fusion denoising.

Preassigned-time projective synchronization of delayed fully quaternion-valued discontinuous neural networks with parameter uncertainties.

This paper concerns with the preassigned-time projective synchronization issue for delayed fully quaternion-valued discontinuous neural networks involving parameter uncertainties through the non-separation method. Above all, based on the existing works, a new preassigned-time stability theorem is established. Subsequently, to realize the control goals, two types of novel and simple chattering-free quaternion controllers are designed, one without the power-law term and the other with a hyperbolic-tangent function. They are different from the existing common power-law controller and exponential controller. Thirdly, under the Filippov discontinuity theories and with the aid of quaternion inequality techniques, some novel succinct sufficient criteria are obtained to ensure the addressed systems to achieve the preassigned-time synchronization by using the preassigned-time stability theory. The preassigned settling time is free from any parameter and any initial value of the system, and can be preset according to the actual task demands. Particularly, unlike the existing results, the proposed control methods can effectively avoid the chattering phenomenon, and the time delay part is removed for simplicity. Additionally, the projection coefficient is generic quaternion-valued instead of real-valued or complex-valued, and some of the previous relevant results are extended. Lastly, numerical simulations are reported to substantiate the effectiveness of the control strategies, the merits of preassigned settling time, and the correctness of the acquired results.

Fixed-time synchronization for quaternion-valued memristor-based neural networks with mixed delays.

In this paper, the fixed-time synchronization (FXTSYN) of unilateral coefficients quaternion-valued memristor-based neural networks (UCQVMNNs) with mixed delays is investigated. A direct analytical approach is suggested to obtain FXTSYN of UCQVMNNs utilizing one-norm smoothness in place of decomposition. When dealing with drive-response system discontinuity issues, use the set-valued map and the differential inclusion theorem. To accomplish the control objective, innovative nonlinear controllers and the Lyapunov functions are designed. Furthermore, some criteria of FXTSYN for UCQVMNNs are given using inequality techniques and the novel FXTSYN theory. And the accurate settling time is obtained explicitly. Finally, in order to show that the obtained theoretical results are accurate, useful, and applicable, numerical simulations are presented at the conclusion.

Robust H∞ control of uncertain time-delay Markovian jump quaternion-valued neural networks subject to partially known transition probabilities: direct quaternion method.

This paper addresses the issue of robust stochastic stabilization and H∞ control of uncertain time-delay Markovian jump quaternion-valued neural networks (MJQVNNs) subject to partially known transition probabilities. First, the direct quaternion method is proposed to analyse the MJQVNNs, which is different from some conventional methods in that the former is without any decomposition for systems. After that, in order to estimate the upper bound of the derivative of the constructed Lyapunov-Krasovskii functional (LKF) more accurately, the real-valued convex inequality is extended to quaternion domain. Then, by designed the mode-dependent state feedback controllers, the robust stochastic stabilization conditions of MJQVNNs are given for the admissible uncertainties, and reduce the influence of input disturbance on the controlled output to a specified performance level. Lastly, two numerical examples are given to illustrate the effectiveness of the proposed method.

H ∞ state estimation of quaternion-valued inertial neural networks: non-reduced order method.

This paper concentrates on the problem of H ∞ state estimation for quaternion-valued inertial neural networks (QVINNs) with nonidentical time-varying delay. Without reducing the original second order system into two first order systems, a non-reduced order method is developed to investigate the addressed QVINNs, which is different from the majority of existing references. By constructing a new Lyapunov functional with tuning parameters, some easily checked algebraic criteria are established to ascertain the asymptotic stability of error-state system with the desired H ∞ performance. Moreover, an effective algorithm is provided to design the estimator parameters. Finally, a numerical example is given out to illustrate the feasibility of the designed state estimator.

Mittag-Leffler stability of fractional-order quaternion-valued memristive neural networks with generalized piecewise constant argument.

This paper studies the global Mittag-Leffler (M-L) stability problem for fractional-order quaternion-valued memristive neural networks (FQVMNNs) with generalized piecewise constant argument (GPCA). First, a novel lemma is established, which is used to investigate the dynamic behaviors of quaternion-valued memristive neural networks (QVMNNs). Second, by using the theories of differential inclusion, set-valued mapping, and Banach fixed point, several sufficient criteria are derived to ensure the existence and uniqueness (EU) of the solution and equilibrium point for the associated systems. Then, by constructing Lyapunov functions and employing some inequality techniques, a set of criteria are proposed to ensure the global M-L stability of the considered systems. The obtained results in this paper not only extends previous works, but also provides new algebraic criteria with a larger feasible range. Finally, two numerical examples are introduced to illustrate the effectiveness of the obtained results.

Quaternion attention multi-scale widening network for endoscopy image super-resolution.

Objective. In the field of endoscopic imaging, Super-Resolution (SR) plays an important role in Manufactured Diagnosis, physicians and machine Automatic Diagnosis. Although many recent studies have been performed, by using deep convolutional neural networks on endoscopic SR, most of the methods have large parameters, which limits their practical application. In addition, almost all of these methods treat each channel equally based on the real-valued domain, without considering the difference among the different channels. Our objective is to design a SR model named Quaternion Attention Multi-scale Widening Network (QAMWN) for endoscopy images to address the above problem.Approach. QAMWN contains a stacked Quaternion Attention Multi-Scale Widening Block, that composed of Multi-scale Feature Widening Aggregation Module (MFWAM) and Quaternion Residual Channel Attention (QRCA). The MFWAM adopts multi-scale architecture with step-wise widening on feature channels for better feature extraction; and in QRCA, quaternion is introduced to construct Residual Channel Attention Mechanism, which obtains adaptively scales features by considering compact cross-channel interactions in the hyper-complex domain.Main results. To verify the efficacy of our method, it is performed on two public endoscopic datasets, CVC ClinicDB and Kvasir dataset. The experimental results show that our proposed method can achieve a better trade-off in model size and performance. More importantly, the proposed QAMWN outperforms previous state-of-the-art methods in both metrics and visualization.Significance. We propose a lightweight SR network for endoscopy and achieves better performance with fewer parameters, which helps in clinical diagnosis of endoscopy.

Fixed-time and prescribed-time synchronization of quaternion-valued neural networks: A control strategy involving Lyapunov functions.

A control strategy containing Lyapunov functions is proposed in this paper. Based on this strategy, the fixed-time synchronization of a time-delay quaternion-valued neural network (QVNN) is analyzed. This strategy is extended to the prescribed-time synchronization of the QVNN. Furthermore, an improved two-step switching control strategy is also proposed based on this flexible control strategy. Compared with some existing methods, the main method of this paper is a non-decomposition one, does not contain a sign function in the controller, and has better synchronization accuracy. Two numerical examples verify the above advantages.

New exploration on bifurcation for fractional-order quaternion-valued neural networks involving leakage delays.

During the past decades, many works on Hopf bifurcation of fractional-order neural networks are mainly concerned with real-valued and complex-valued cases. However, few publications involve the quaternion-valued neural networks which is a generalization of real-valued and complex-valued neural networks. In this present study, we explorate the Hopf bifurcation problem for fractional-order quaternion-valued neural networks involving leakage delays. Taking advantage of the Hamilton rule of quaternion algebra, we decompose the addressed fractional-order quaternion-valued delayed neural networks into the equivalent eight real valued networks. Then the delay-inspired bifurcation condition of the eight real valued networks are derived by making use of the stability criterion and bifurcation theory of fractional-order differential dynamical systems. The impact of leakage delay on the bifurcation behavior of the involved fractional-order quaternion-valued delayed neural networks has been revealed. Software simulations are implemented to support the effectiveness of the derived fruits of this study. The research supplements the work of Huang et al. (Neural Netw 117:67-93, 2019).

Finite-time synchronization of quaternion-valued neural networks with delays: A switching control method without decomposition.

For a class of quaternion-valued neural networks (QVNNs) with discrete and distributed time delays, its finite-time synchronization (FTSYN) is addressed in this paper. Instead of decomposition, a direct analytical method named two-step analysis is proposed. That method can always be used to study FTSYN, under either 1-norm or 2-norm of quaternion. Compared with the decomposing method, the two-step method is also suitable for models that are not easily decomposed. Furthermore, a switching controller based on the two-step method is proposed. In addition, two criteria are given to realize the FTSYN of QVNNs. At last, three numerical examples illustrate the feasibility, effectiveness and practicability of our method.

Fixed/Preassigned-time synchronization of quaternion-valued neural networks via pure power-law control.

The fixed-time synchronization and preassigned-time synchronization of quaternion-valued neural networks are concerned in this article. By developing fixed-time stability and proposing a pure power-law control scheme, some simple conditions are obtained to realize fixed-time synchronization of quaternion-valued neural networks and the upper bound of the synchronized time is provided. Furthermore, the preassigned-time synchronization of quaternion-valued neural networks is investigated based on pure power-law control design, where the synchronization time is preassigned in advance and the control gains are finite. Note that the designed controllers in this paper are the pure power-law forms, which are simpler and more effective compared with the traditional design composed of the linear part and power-law part. Eventually, an example is given to illustrate the feasibility and validity of the results obtained.

Novel methods to global Mittag-Leffler stability of delayed fractional-order quaternion-valued neural networks.

In this paper, a type of fractional-order quaternion-valued neural networks (FOQVNNs) with leakage and time-varying delays is established to simulate real-world situations, and the global Mittag-Leffler stability of the system is investigated by using the non-decomposition method. First, to avoid decomposing the system into two complex-valued systems or four real-valued systems, a new sign function for quaternion numbers is introduced based on the ones for real and complex numbers. And two novel lemmas for quaternion-valued sign function and Caputo fractional derivative are established in quaternion domain, which are used to investigate the stability of FOQVNNs. Second, a concise and flexible quaternion-valued state feedback controller is directly designed and a novel 1-norm Lyapunov function composed of the absolute values of real and imaginary parts is established. Then, based on the designed quaternion-valued state feedback controller and the proposed lemmas, some sufficient conditions are given to ensure the global Mittag-Leffler stability of the system. Finally, a numerical simulation is given to verify the theoretical results.

Passive filter design for fractional-order quaternion-valued neural networks with neutral delays and external disturbance.

The problem on passive filter design for fractional-order quaternion-valued neural networks (FOQVNNs) with neutral delays and external disturbance is considered in this paper. Without separating the FOQVNNs into two complex-valued neural networks (CVNNs) or the FOQVNNs into four real-valued neural networks (RVNNs), by constructing Lyapunov-Krasovskii functional and using inequality technique, the delay-independent and delay-dependent sufficient conditions presented as linear matrix inequality (LMI) to confirm the augmented filtering dynamic system to be stable and passive with an expected dissipation are derived. One numerical example with simulations is furnished to pledge the feasibility for the obtained theory results.

Improved approach to the problem of the global Mittag-Leffler synchronization for fractional-order multidimension-valued BAM neural networks based on new inequalities.

This paper studies the problem of the global Mittag-Leffler synchronization for fractional-order multidimension-valued BAM neural networks (FOMVBAMNNs) with general activation functions (AFs). First, the unified model is established for the researched systems of FOMVBAMNNs which can be turned into the corresponding multidimension-valued systems as long as the state variables, the connection weights and the AFs of the neural networks are valued to be real, complex, or quaternion. Then, without any decomposition, the criteria in unified form are derived by constructing the new Lyapunov-Krasovskii functionals (LKFs) in vector form, combining two new inequalities and considering the easy controllers. It is worth mentioning that the obtained criteria have many advantages in higher flexibility, more diversity, smaller computation, and lower conservatism. Finally, a simulation example is provided to illustrate the availability and improvements of the acquired results.

Synchronization criteria for quaternion-valued coupled neural networks with impulses.

We consider the global exponential synchronization of a category of quaternion-valued coupled neural networks (QVCNNs) with impulses in this article. It makes up for the gap of coupled neural networks with impulses in quaternion. On account of the product of two quaternions cannot be exchanged under normal circumstances, for convenience, we isolate the QVCNN into four real-valued coupled neural networks (RVCNNs) which are converted into an augmented system by defining a new augmented vector. By leveraging a distinctive Lyapunov-Krasovskii function and some matrix inequalities, several sufficient conditions for the global exponential synchronization of the system are attained. Ultimately, two examples are used to prove the validity of the theories in this paper.