Discontinuous Activations Research Articles

Biomass-based three-dimensional network porous carbon anodes derived from discontinuous activation for high performance Li-ion batteries

An approach of discontinuous activation and frozon-dry pretreatment toward a three-dimensional network porous carbon was proposed by using apple as the carbon source. The porous carbon, characterized by its high surface area and abundant porosity, was optimized through the manipulation of temperature and activator quantities during the activation process. The sample obtained by first calcining at 500 °C and then at 800 °C shows ultra-high rate electrochemical performance of over 900 mA h g−1 after 100 cycles and over 500 mA h g−1 after 500 cycles under the condition of charging and discharging current density of 0.2 A g−1 due to the high porosity. It is ascribed to the unique porous structure that can make the electrolyte and lithium ion transport and path short on the surface and inside the electrode material, further enhance its fast transport ability. The described approach represents an innovative and potentially impactful method for producing porous carbon electrodes with excellent electrochemical performance, particularly in the context of high-rate capability lithium-ion batteries.

Quasi-synchronization of fractional-order complex-value BAM neural networks with time delays and discontinuous activations

Quasi-synchronization of fractional-order complex-value BAM neural networks with time delays and discontinuous activations

Fixed-Time Synchronization and Energy Consumption Prediction of Interconnected Memristive Neural Networks with Discontinuous Activation Functions

Fixed-Time Synchronization and Energy Consumption Prediction of Interconnected Memristive Neural Networks with Discontinuous Activation Functions

Improved fixed-time stability analysis and applications to synchronization of discontinuous complex-valued fuzzy cellular neural networks

This article mainly centers on proposing new fixed-time (FXT) stability lemmas of discontinuous systems, in which novel optimization approaches are utilized and more relaxed conditions are required. The conventional discussions about Vt>1 and 0<Vt⩽1 are no longer required. For the purpose of verifying the new lemmas, complex-valued fuzzy cellular neural networks (CVFCNNs) with discontinuous activation functions are studied with a nontraditional non-separation method, which could reduce the conservatism of the obtained results greatly. Besides, FXT synchronization is discussed simultaneously. When contrasted with the results of other similar prominent pioneering works nowadays, the accuracy of settling times (STs) is quite enhanced. At last, numerical simulations are conducted to demonstrate the validity and superiority of our established theoretical results.

Fixed-time control and estimation of discontinuous fuzzy leakage-delayed networks: Indefinite and economical conditions of Filippov systems

This paper considers the fixed-time stability of Filippov systems and discontinuous networks described by the Filippov systems. Firstly, the more generalized and economical inequality condition on Lyapunov function is proposed, which can not only improve the previous negative definite conditions, but also the indefinite conditions. Based on the definition of the Lyapunov stability and finite-time convergence, new fixed-time stability lemmas are proposed and the settling-time is also estimated. In order to apply the new fixed-time stability lemmas to the neural networks, fixed-time stabilization of a class of fuzzy leakage-delayed neural networks with discontinuous activations is considered which is rarely studied since the delay is leakage and activations are discontinuous and they are not easy to deal with simultaneously. By means of the Filippov regularization and differential inclusions theory, new criteria on the stabilization of the considered networks are derived via the new modified non-chattering controller, which can improve the previous ones with parameter and symbolic function. Finally, example and numerical simulations further examine the correctness of the main results.

Projective synchronization in fixed/predefined-time for quaternion-valued BAM neural networks under event-triggered aperiodic intermittent control

This study aims to solve the fixed/predefined-time projective synchronization (FTPS/PTPS) of quaternion-valued BAM neural networks (BAMNNs) through event-triggered aperiodic intermittent control (ETAIC). Firstly, a novel quaternion-valued BAMNN model is established by integrating discontinuous activations, parameter uncertainties and time-varying delays. Subsequently, under the framework of the non-separation method several concise ETAIC schemes are designed by utilizing an exponential term instead of a sign function and two power-law terms. Different from the previous time-triggered intermittent controllers, the control and rest intervals of the ETAIC strategies are determined according to the dynamics of the network rather than being pre-specified. Furthermore, several adequate conditions are acquired to guarantee the FTPS and PTPS of the considered networks by constructing auxiliary functions and applying Taylor expansion Ultimately, three simulation examples are presented to confirm the validity and usefulness of the theoretical findings.

Capacity bounds for hyperbolic neural network representations of latent tree structures

We study the representation capacity of deep hyperbolic neural networks (HNNs) with a ReLU activation function. We establish the first proof that HNNs can ɛ-isometrically embed any finite weighted tree into a hyperbolic space of dimension d at least equal to 2 with prescribed sectional curvature κ<0, for any ɛ>1 (where ɛ=1 being optimal). We establish rigorous upper bounds for the network complexity on an HNN implementing the embedding. We find that the network complexity of HNN implementing the graph representation is independent of the representation fidelity/distortion. We contrast this result against our lower bounds on distortion which any ReLU multi-layer perceptron (MLP) must exert when embedding a tree with L>2d leaves into a d-dimensional Euclidean space, which we show at least Ω(L1/d); independently of the depth, width, and (possibly discontinuous) activation function defining the MLP.

Quasi-synchronization of neural networks via non-fragile impulsive control: Multi-layer and memristor-based

In this paper, the quasi-synchronization for memristor-based multi-layer neural networks is solved, where each layer possesses a unique topology. The focus is on the incorporation of proportional delay, which represents an exceptional unbounded delay. To enhance the network’s robustness against external interferences and minimize control expenses, the non-fragile impulsive control is devised. By utilizing the impulsive comparison principle and interval matrix method, sufficient conditions for achieving quasi-synchronization are derived under discontinuous activation function. Moreover, the error bounds are estimated for synchronizing and desynchronizing impulses. The correctness of the theoretical results is finally testified by numerical examples.

Fixed-time synchronization of fractional-order complex-valued delayed neural networks with discontinuous activation functions

Fixed-time synchronization of fractional-order complex-valued delayed neural networks with discontinuous activation functions

Quasi-Synchronization of Fractional Multiweighted Coupled Neural Networks via Aperiodic Intermittent Control.

This article investigates the quasi-synchronization for fractional multiweighted coupled neural networks (FMCNNs) with discontinuous activation functions and mismatched parameters. First, under the generalized Caputo fractional-order derivative operator, a novel piecewise fractional differential inequality is established to study the convergence of fractional systems, which significantly extends some related published results. Subsequently, by exploiting the new inequality and Lyapunov stability theory, some sufficient quasi-synchronization conditions of FMCNNs are presented by aperiodic intermittent control. Meanwhile, the exponential convergence rate and synchronization error's bound are given explicitly. Finally, the validity of theoretical analysis is confirmed by numerical examples and simulations.

Fixed-Time Aperiodic Intermittent Control for Quasi-Bipartite Synchronization of Competitive Neural Networks.

This paper concerns a class of coupled competitive neural networks, subject to disturbance and discontinuous activation functions. To realize the fixed-time quasi-bipartite synchronization, an aperiodic intermittent controller is initially designed. Subsequently, by combining the fixed-time stability theory and nonsmooth analysis, several criteria are established to ensure the bipartite synchronization in fixed time. Moreover, synchronization error bounds and settling time estimates are provided. Finally, numerical simulations are presented to verify the main results.

μ-stability and instability of multiple equilibrium points in delayed neural networks with general discontinuous activation functions

This paper proposes a general type of discontinuous activation functions (AFs) and studies the μ-stability of multiple equilibrium points (EPs) in delayed neural networks (DNNs). By judging 4n algebraic inequalities and the nonsingularity of an M-matrix, DNNs with the general discontinuous AFs can be shown to have 5n EPs, therein 3n EPs are locally μ-stable. Moreover, these 3n EPs are located at the points of continuity of the AF. Compared with the existing general continuous AF, DNNs with the general discontinuous AF can have more total/stable EPs. Hence, DNNs with the general discontinuous AF could store a much larger number of memory patterns if they are applied to associative memory. In addition, the attraction basin (AB) of each stable EP in DNNs is estimated. Two numerical examples are shown to testify the validity of the obtained results.

Quantized dynamic event-triggered control for fixed/preset-time bipartite synchronization of memristor-based discontinuous multi-layer signed networks

This study addresses the fixed/preset-time bipartite synchronization (FTBS/PTBS) of memristor-based discontinuous multi-layer signed networks via quantized dynamic event-triggered control (ETC). Firstly, a memristor-based neural network model incorporating multi-layer coupling structures, signed networks and discontinuous activations is built. Subsequently, by designing two quantized dynamic ETC strategies without the linear feedback term, the FTBS and PTBS of the considered networks are discussed, and it is proved that Zeno behavior can be ruled out. In contrast to the previous static ETC mechanism, the introduced internal dynamic variable can significantly decrease the triggering times and further save communication resources. Lastly, three numerical examples are offered to verify the correctness and practicability of the theoretical analysis.

Finite-time synchronization of discontinuous network systems via two control schemes

This article considers network systems (NSs) which can realize random switch among different NSs based on Bernoulli random variables. As a result, the systems will be the networks with linear coupling, nonlinear coupling or partial communication failure. Discontinuous activation function is introduced, which is overcome by the theories of differential inclusions. Finite-time (FET) synchronization is established under the designed intermittent adaptive control and the reason why it cannot get the results of prespecified-time (PDT) synchronization is analysed, where PDT synchronization is a special case of FET synchronization. Moreover, PDT synchronization is realized via a feedback controller which switches based on the state information of systems. In addition, simulation experiments are provided to verify the control methods and synchronization results.

Prefixed-Time Local Intermittent Sampling Synchronization of Stochastic Multicoupling Delay Reaction-Diffusion Dynamic Networks.

This article focuses on the problem of prefixed-time synchronization for stochastic multicoupled delay dynamic networks with reaction-diffusion terms and discontinuous activation by means of local intermittent sampling control. Notably, unlike the existing common fixed-time synchronization, this article puts forward a new synchronization concept, prefixed-time synchronization, based on the fact that stochastic noise and discontinuous activation can be seen everywhere in practical engineering, which can effectively perfect and improve the existing works. Specifically, a local intermittent in the time domain and point sampling control strategy in the spatial domain is proposed instead of a simple single intermittent control approach, which greatly reduces the control cost. In addition, by some effective means, including the famous Young's inequality, Jensen's inequality, and Hölder's inequality, we obtain two different synchronization criteria of the networks without delay and with multicoupling delays and deeply reveal the quantitative relationship among control period, point sampling length, and network scale. Finally, a numerical example is given to verify the effectiveness of the developed method and the practicability by Chua's circuit model.

Event-Triggered Finite-Time Stabilization of Fuzzy Neural Networks With Infinite Time Delays and Discontinuous Activations

This paper unifies the stability criteria of asymptotic, exponential and finite-time control within a single framework for fuzzy neural networks (FNNs) with infinite time delays. First, the boundedness and differentiability for time delays are removed. Then, Lipschitz condition for activation function is relaxed, which is allowed to have jumping discontinuous points. To stabilize FNNs, the analytical method is established by comparison principle, contradiction method and inequality techniques. Moreover, different from the traditional Lyapunov method and finite-time stability theorem, several sufficient conditions are deduced and the suppression functions are designed to guarantee asymptotic, exponential and finite-time stabilization for FNNs by adjusting the parameters of the same controller. There is not necessary to construct the complex integral-type Lyapunov functional to deal with infinite time delays and to design power function in controller for finite-time stabilization. In addition, the designed event-triggered mechanism (ETM) has the inherent advantages of saving communication resources and indirectly eliminates the chattering caused by signum function. Finally, simulations are presented to illustrate the feasibility and effectiveness of the theoretical results.

Fixed/Preassigned-Time Synchronization of Fully Quaternion-Valued Cohen–Grossberg Neural Networks with Generalized Time Delay

This article is concerned with fixed-time synchronization and preassigned-time synchronization of Cohen–Grossberg quaternion-valued neural networks with discontinuous activation functions and generalized time-varying delays. Firstly, a dynamic model of Cohen–Grossberg neural networks is introduced in the quaternion field, where the time delay successfully integrates discrete-time delay and proportional delay. Secondly, two types of discontinuous controllers employing the quaternion-valued signum function are designed. Without utilizing the conventional separation technique, by developing a direct analytical approach and using the theory of non-smooth analysis, several adequate criteria are derived to achieve fixed-time synchronization of Cohen–Grossberg neural networks and some more precise convergence times are estimated. To cater to practical requirements, preassigned-time synchronization is also addressed, which shows that the drive-slave networks reach synchronization within a specified time. Finally, two numerical simulations are presented to validate the effectiveness of the designed controllers and criteria.

A Simplified Controller Design for Fixed/Preassigned-Time Synchronization of Stochastic Discontinuous Neural Networks

This paper addresses the synchronization problem of delayed stochastic neural networks with discontinuous activation functions (DSNNsDF), specifically focusing on fixed/preassigned-time synchronization. The objective is to develop a class of simplified controllers capable of effectively addressing the challenges posed by time delays, discontinuous activation functions, and stochastic perturbations during the synchronization process. In this regard, we propose several controllers with simpler structures to achieve the desired preassigned-time synchronization (PTS) result. To enhance the accuracy of time estimation, stochastic fixed-time control theory is employed. Rigorous numerical simulations are conducted to validate the effectiveness of our approach. The utilization of our proposed results significantly improves the performance of the synchronization controller for DSNNsDF, thereby enabling advancements and diverse applications in the field.

Quasi-synchronization of fractional-order complex-value neural networks with discontinuous activations

In this paper, under the framework of Filippov solutions, quasi-synchronization issue of fractional-order complex-valued neural networks (FCNNs) with discontinuous activations and uncertainties is investigated. Firstly, using Laplace transform and the property of Mittag-Leffler function, a novel fractional differential inequality is derived. Then combining the newly constructed inequality with delay feedback control scheme, several quasi-synchronization conditions are obtained for the considered FCNNs by means of non-decomposable method. Eventually, a numerical example is provided to substantiate validation of the proposed results.

Anti-synchronisation in fixed-/preassigned-time of delayed memristive neural networks with discontinuous activation functions

In this paper, the fixed-/preassigned-time anti-synchronisation problem is studied for delayed memristive neural networks (DMNNs) with discontinuous activation functions and external disturbance. First of all, several simple controllers are structured for the fixed-time anti-synchronisation (FTAS) of DMNNs with discontinuous activation functions. Moreover, an effective and convenient control scheme for preassigned-time anti-synchronisation (PTAS) is presented by modifying the controller parameters. The proposed control scheme is also available for DMNNs with continuous activation functions or without time delays. In addition, sufficient conditions for FTAS and PTAS of DMNNs are derived and the accurate estimation for settling-time is given. Finally, simulation examples are presented to verify the validity of the main results.