Synchronization Of Competitive Neural Networks Research Articles

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.

Saturation function-based continuous control on fixed-time synchronization of competitive neural networks

Currently, through proposing discontinuous control strategies with the signum function and discussing separately short-term memory (STM) and long-term memory (LTM) of competitive artificial neural networks (ANNs), the fixed-time (FXT) synchronization of competitive ANNs has been explored. Note that the method of separate analysis usually leads to complicated theoretical derivation and synchronization conditions, and the signum function inevitably causes the chattering to reduce the performance of the control schemes. To try to solve these challenging problems, the FXT synchronization issue is concerned in this paper for competitive ANNs by establishing a theorem of FXT stability with switching type and developing continuous control schemes based on a kind of saturation functions. Firstly, different from the traditional method of studying separately STM and LTM of competitive ANNs, the models of STM and LTM are compressed into a high-dimensional system so as to reduce the complexity of theoretical analysis. Additionally, as an important theoretical preliminary, a FXT stability theorem with switching differential conditions is established and some high-precision estimates for the convergence time are explicitly presented by means of several special functions. To achieve FXT synchronization of the addressed competitive ANNs, a type of continuous pure power-law control scheme is developed via introducing the saturation function instead of the signum function, and some synchronization criteria are further derived by the established FXT stability theorem. These theoretical results are further illustrated lastly via a numerical example and are applied to image encryption.

Predefined-time synchronization for competitive neural networks with different time scales and external disturbances

This paper presents a study on the predefined-time (PdT) and practical PdT synchronization of competitive neural networks (CNN) in the presence of different time scales and external disturbances. Two types of external disturbances, which satisfy Lipschitz or bounded conditions, are investigated respectively. The new PdT and practical PdT stability theorems are derived in singularly perturbed systems, where the final residual set is given in detail. By employing the newly derived stability theorems, novel autonomous controllers are designed without relying on a continuous linear term and time scale parameters, while enabling PdT or practical PdT synchronization for drive-response CNNs. Additionally, upper bounds for the settling time are estimated, allowing for adjusting the predefined synchronization times regardless of the initial conditions. Finally, numerical simulations are conducted to demonstrate the effectiveness of the main results.

Predefined-time synchronization of competitive neural networks with deterministic disturbances and stochastic noises

This paper presents the drive-response synchronization problem for competitive neural networks in predefined time. The response system is considered in the presence of deterministic disturbances satisfying Lipschitz conditions and in the presence of both stochastic white noises and deterministic disturbances satisfying Lipschitz conditions. The effect of deterministic disturbances and stochastic noises is suppressed by designing a linear time-varying continuous control input driving the synchronization errors at the origin for an a priori predefined time, independently of initial conditions, deterministic disturbances, and stochastic noises. Finally, numerical simulations are conducted to demonstrate validity of the obtained theoretical results. The conducted comparisons with other predefined-time convergent synchronization algorithms reveal better performance of the proposed synchronization technique.

Fixed-Time Synchronization of Competitive Neural Networks With Multiple Time Scales.

In this brief, we investigate the fixed-time synchronization of competitive neural networks with multiple time scales. These neural networks play an important role in visual processing, pattern recognition, neural computing, and so on. Our main contribution is the design of a novel synchronizing controller, which does not depend on the ratio between the fast and slow time scales. This feature makes the controller easy to implement since it is designed through well-posed algebraic conditions (i.e., even when the ratio between the time scales goes to 0, the controller gain is well defined and does not go to infinity). Last but not least, the closed-loop dynamics is characterized by a high convergence speed with a settling time which is upper bounded, and the bound is independent of the initial conditions. A numerical simulation illustrates our results and emphasizes their effectiveness.

Predefined-time synchronization of competitive neural networks

In this paper, the predefined-time synchronization of competitive neural networks (CNNs) is researched based on two different predefined-time stability theorems. In view of the bilayer structure of CNNs, we design two bilayer predefined-time controllers. The first controller utilizes sign function, while the second controller utilizes exponential function and Lyapunov function. In these two controllers, the predefined time is set as a controller parameter, and it can be an arbitrary positive constant. Under these two controllers, the considered CNNs can achieve synchronization within the predefined time regardless of the initial values. A specific example is presented to validate the theoretical results.

Fixed-time synchronization for competitive neural networks with Gaussian-wavelet-type activation functions and discrete delays

In this article, the fixed-time synchronization for competitive neural networks (CNNs) with Gaussian-wavelet-type activation functions and discrete delays is investigated. Firstly, in terms of Lyapunov stability theory and inequality technique, simple synchronization conditions are obtained by designing some feedback controllers. Secondly, the activation functions adopted in CNNs are Gaussian-wavelet-type activation functions for the first time, which have great preponderance in network optimization and storage capacity. Furthermore, the settling time with upper bound of the system to achieve fixed-time synchronization can be explicitly evaluated, which is irrelevant to the initial value of the system. Finally, the theoretical results which we derived are attested to be indeed feasible in terms of two numerical simulations.

Fixed-time synchronization of competitive neural networks with proportional delays and impulsive effect

This paper investigates the fixed-time synchronization problems for competitive neural networks with proportional delays and impulsive effect. The concerned network involves two coupling terms, i.e., long-term memory and short-term memory, which leads to the difficulty to the dynamics analysis. Based on Lyapunov functionals, the differential inequalities and for the objective of making the settling time independent of initial condition, a novel criterion guaranteeing the fixed-time synchronization of addressed system is derived. Finally, two examples and their simulations are given to demonstrate the effectiveness of the obtained results.

General Decay Lag Synchronization for Competitive Neural Networks with Constant Delays

This paper is concerned with the general decay lag synchronization problem for a class of competitive neural networks with constant delays via designing a novel nonlinear feedback controller. Based on the useful lemma, which guarantee the general decay synchronization of chaotic systems, some simple sufficient criteria ensuring the general decay lag synchronization of addressed competitive neural networks are obtained via constructing a novel Lyapunov–Krasovskii functional and using some inequality techniques. Finally, one numerical example is provide to demonstrate the feasibility of the established theoretical results. The results of this paper are general since the classical polynomial synchronization and exponential synchronization can be seen the special cases of general decay synchronization.

Improved synchronization analysis of competitive neural networks with time-varying delays

Synchronization and control are two very important aspects of any dynamical systems. Among various kinds of nonlinear systems, competitive neural network holds a very important place due to its application in diverse fields. The model is general enough to include, as subclass, the most famous neural network models such as competitive neural networks, cellular neural networks and Hopfield neural networks. In this paper, the problem of feedback controller design to guarantee synchronization for competitive neural networks with time-varying delays is investigated. The goal of this work is to derive an existent criterion of the controller for the exponential synchronization between drive and response neutral-type competitive neural networks with time-varying delays. The method used in this brief is based on feedback control gain matrix by using the Lyapunov stability theory. The synchronization conditions are given in terms of LMIs. To the best of our knowledge, the results presented here are novel and generalize some previous results. Some numerical simulations are also represented graphically to validate the effectiveness and advantages of our theoretical results.

Finite-time synchronization of competitive neural networks with mixed delays

In this paper, finite-time synchronization of competitive neural networks (CNNs) with bounded time-varying discrete and distributed delays (mixed delays) is investigated. A simple controller is added to response (slave) system such that it can be synchronized with the driving (master) CNN in a setting time. By introducing a suitable Lyapunov-Krasovskii's functional and utilizing some inequalities, several sufficient conditions are obtained to ensure the control object. Moreover, the setting time is explicitly given. Different from previous results, the setting is related to both the initial value of error system and the time delays. Finally, numerical examples are given to show the effectiveness of the theoretical results.

Finite-time synchronization for competitive neural networks with mixed delays and non-identical perturbations

This paper considers the drive-response synchronization in finite time of competitive neural networks (CNNs) with different time scales, time-varying and infinite-time distributed delays (mixed delays), as well as uncertain non-linear perturbations. The drive and response systems are disturbed by different uncertain non-linear perturbations. The effects of the non-identical uncertain non-linear perturbations are suppressed by designing some simple controllers. Moreover, by designing new Lyapunov–Krasovskii functionals, sufficient conditions are obtained to guarantee that the CNNs can be synchronized in a setting time without using existing finite-time stability theorem. Furthermore, the setting time is explicitly estimated for CNNs with bounded distributed delay and without delay. It is shown that the setting time is dependent on the time delays and the initial values of the coupled CNNs. Some results on synchronization of CNNs are essentially extended. Finally, numerical examples are provided to illustrate the effectiveness of the presented synchronization scheme.

Synchronization of competitive neural networks with different time scales and time-varying delay based on delay partitioning approach

In this paper, the synchronization problem for a class of competitive neural networks with different time scales and time-varying delay is investigated. A novel delay partitioning approach is developed to derive a delay-dependent condition guaranteeing the response system can be synchronized with the drive system. The design of the gain matrix of the linear feedback controller can be achieved by solving a linear matrix inequality. By constructing a novel Lyapunov–Krasovskii functional, which can guarantee the new synchronization conditions to be less conservative than those in the literature. This paper also presents an illustrative example and uses simulated results of this example to show the feasibility and effectiveness of the proposed scheme.

Adaptive Lag Synchronization for Competitive Neural Networks With Mixed Delays and Uncertain Hybrid Perturbations

This paper investigates the problem of adaptive lag synchronization for a kind of competitive neural network with discrete and distributed delays (mixed delays), as well as uncertain nonlinear external and stochastic perturbations (hybrid perturbations). A simple but robust adaptive controller is designed such that the response system can lag-synchronize with a drive system. Based on the Lyapunov stability theory and some suitable Lyapunov-Krasovskii functionals, several sufficient conditions ensuring the lag synchronization are developed. Our synchronization criteria are easily verified and do not need to solve any linear matrix inequality. Some existing results are improved and extended. Moreover, the designed adaptive controller has better anti-interference capacity and is more practical than the usual adaptive controller. Numerical simulations are exploited to show the effectiveness of the theoretical results.

Adaptive synchronization for competitive neural networks with different time scales and stochastic perturbation

In this paper, an adaptive feedback controller is designed to achieve complete synchronization of coupled delayed competitive neural networks with different time scales and stochastic perturbation. LaSalle-type invariance principle for stochastic differential delay equations is employed to investigate the globally almost surely asymptotical stability of the error dynamical system. An example with numerical simulation is given to demonstrate the effectiveness of the theory results.

Synchronization of competitive neural networks with different time scales

In this paper, the exponential synchronization problem for a class of competitive neural networks is investigated. Moreover, without assuming the active functions to be differentiable and bounded, some exponential synchronization criteria are devised by Lyapunov functionals, linear matrix inequality (LMI) approach, the Leibniz–Newton formula. The conditions are less conservative than existing ones reported in the literature for delayed neural networks. The applicability of the conditions are validated by an illustrative example.