Drive-response Synchronization Research Articles

Mittag‐Leffler stability and synchronization of discrete‐time quaternion valued delayed neural networks with fractional order and its application

This paper discusses the problem of Mittag‐Leffler stability and synchronization for discrete‐time fractional‐order delayed quaternion valued neural networks (DTFODQVNN). Firstly, a criterion is achieved to ensure the existence and uniqueness of the equilibrium point (EP) of DTFODQVNN through applying Brouwer's fixed‐point theory. Secondly, based on a Lyapunov function and a new discrete fractional inequality, the stability condition is established by employing a linear matrix inequality approach. In addition, by constructing a proper controller, drive–response synchronization is investigated by means of deploying Lyapunov direct method (LDM). Finally, two examples with simulations test the correctness of the acquired results. Moreover, image encryption is considered as an application based on the chaotic DTFODQVNN.

Adaptive Drive-Response Synchronization of Timescale-Type Neural Networks With Unbounded Time-Varying Delays.

In recent years, adaptive drive-response synchronization (DRS) of two continuous-time delayed neural networks (NNs) has been investigated extensively. For two timescale-type NNs (TNNs), how to develop adaptive synchronization control schemes and demonstrate rigorously is still an open problem. This article concentrates on adaptive control design for synchronization of TNNs with unbounded time-varying delays. First, timescale-type Barbalat lemma and novel timescale-type inequality techniques are first proposed, which provides us practical methods to investigate timescale-type nonlinear systems. Second, using timescale-type calculus, novel timescale-type inequality, and timescale-type Barbalat lemma, we demonstrate that global asymptotic synchronization can be achieved via adaptive control under algebraic and matrix inequality criteria even if the time-varying delays are unbounded and nondifferentiable. Adaptive DRS is discussed for TNNs, which implies our control schemes are suitable for continuous-time NNs, their discrete-time counterparts, and any combination of them. Finally, numerical examples on TNNs and timescale-type chaotic Ikeda-like oscillator with unbounded time-varying delays are carried out to verify the adaptive control schemes.

Synchronization of Takagi–Sugeno Fuzzy Time-Delayed Stochastic Bidirectional Associative Memory Neural Networks Driven by Brownian Motion in Pre-Assigned Settling Time

We are devoted, in this paper, to the study of the pre-assigned-time drive-response synchronization problem for a class of Takagi–Sugeno fuzzy logic-based stochastic bidirectional associative memory neural networks, driven by Brownian motion, with continuous-time delay and (finitely and infinitely) distributed time delay. To achieve the drive-response synchronization between the neural network systems, concerned in this paper, and the corresponding response neural network systems (identical to our concerned neural network systems), we bring forward, based on the structural properties, a class of control strategies. By meticulously coining an elaborate Lyapunov–Krasovskii functional, we prove a criterion guaranteeing the desired pre-assigned-time drive-response synchronizability: For any given positive time instant, some of our designed controls make sure that our concerned neural network systems and the corresponding response neural network systems achieve synchronization, with the settling times not exceeding the pre-assigned positive time instant. In addition, we equip our theoretical studies with a numerical example, to illustrate that the synchronization controls designed in this paper are indeed effective. Our concerned neural network systems incorporate several types of time delays simultaneously, in particular, they have a continuous-time delay in their leakage terms, are based on Takagi–Sugeno fuzzy logic, and can be synchronized before any pre-given finite-time instant by the suggested control; therefore, our theoretical results in this paper have wide potential applications in the real world. The conservatism is reduced by introducing parameters in our designed Lyapunov–Krasovskii functional and synchronization control.

Hybrid Impulsive Feedback Control for Drive–Response Synchronization of Fractional-Order Multi-Link Memristive Neural Networks with Multi-Delays

This article addresses the issue of drive–response synchronization in fractional-order multi-link memristive neural networks (FMMNN) with multiple delays, under hybrid impulsive feedback control. To address the impact of multiple delays on system synchronization, an extended fractional-order delayed comparison principle incorporating impulses is established. By leveraging Laplace transform, Mittag–Leffler functions, the generalized comparison principle, and hybrid impulsive feedback control schemes, several new sufficient conditions are derived to ensure synchronization in the addressed FMMNN. Unlike existing studies on fractional-order single-link memristor-based systems, our response network is a multi-link model that considers impulsive effects. Notably, the impulsive gains αi are not limited to a small interval, thus expanding the application range of our approach (αi∈(−2,0)∪(−∞,−2)∪(0,+∞)). This feature allows one to choose impulsive gains and corresponding impulsive intervals that are appropriate for the system environment and control requirements. The theoretical results obtained in this study contribute to expanding the relevant theoretical achievements of fractional-order neural networks incorporating memristive characteristics.

Drive-Response Synchronization for Second-Order Memristor-Based Delayed Neural Networks with Settling Time Estimation via Discontinuous Feedback Control

In this paper, the settling time estimation of synchronization issues for inertial memristive neural networks (IMNNs) with mixed time-varying delays is investigated. First, by using a new reduced order approach and introducing free-weighted coefficients η i and ξ i into variable transformation, the original second-order derivative system is transformed into a first-order differential system. Second, appropriate controllers are designed for IMNNs to guarantee the system synchronization in a settling time. In addition, the settling time is explicitly estimated and dependent on time delays and the initial values of the coupled system. Finally, two numerical examples are presented to demonstrate the effectiveness of the theoretical results.

The approach of hybrid adaptive coupling synchronization among N Lorenz systems and its application in secure communication for multi‐unmanned aerial vehicle formation

SummaryIn this paper, it is proposed that a hybrid global adaptive coupling synchronization scheme among Lorenz chaotic dynamical nodes to realize the secure communication system between base station and multi‐unmanned aerial vehicle (UAV) formation. The specific method is that the feedback drive–response synchronization is utilized for first two nodes of base station and the leader of multi‐UAV formation, and the nodes of all UAVs are coupled by unidirectional adaptive coupling synchronization according to a directed link in ad hoc network of multi‐UAV formation. It is demonstrated that the asymptotic stability of the proposed hybrid adaptive coupled synchronization by constructing the Lyapunov function. In this way, the encrypted information formed by plaintext information masked into the chaotic sequence generated by the chaotic dynamical node of base station; meanwhile, it is fed back into the base station node as the drive system. On the other hand, encrypted information is forwarded to the leader node as the response system for decryption. The feedback driver–response synchronization is used to realize secure communication between the base station and the leader of multi‐UAV formation. Meanwhile, secure communication among its leader and followers is achieved through the unidirectional adaptive coupling synchronization in the network. This strategy ensures the multi‐UAV formation decrypting encrypted information synchronously and effectively improves the security, consistency, and overall performance of their commands.

Global Existence and Fixed-Time Synchronization of a Hyperchaotic Financial System Governed by Semi-Linear Parabolic Partial Differential Equations Equipped with the Homogeneous Neumann Boundary Condition

Chaotic nonlinear dynamical systems, in which the generated time series exhibit high entropy values, have been extensively used and play essential roles in tracking accurately the complex fluctuations of the real-world financial markets. We are concerned with a system of semi-linear parabolic partial differential equations supplemented by the homogeneous Neumann boundary condition, which governs a financial system comprising the labor force, the stock, the money, and the production sub-blocks distributed in a certain line segment or planar region. The system derived by removing the terms involved with partial derivatives with respect to space variables from our concerned system was demonstrated to be hyperchaotic. We firstly prove, via Galerkin's method and establishing a priori inequalities, that the initial-boundary value problem for the concerned partial differential equations is globally well posed in Hadamard's sense. Secondly, we design controls for the response system to our concerned financial system, prove under some additional conditions that our concerned system and its controlled response system achieve drive-response fixed-time synchronization, and provide an estimate on the settling time. Several modified energy functionals (i.e., Lyapunov functionals) are constructed to demonstrate the global well-posedness and the fixed-time synchronizability. Finally, we perform several numerical simulations to validate our synchronization theoretical 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.

The design of a four-wing chaotic system and the application of synchronous control in weak signal detection

Simple fourth-order autonomous differential equations can exhibit chaotic properties. In this paper, a chaotic system with a four-wing attractor is proposed where the varying number of attractor wings depends not only on the system parameters but also on the initial state of the system. First, the phase diagram, Lyapunov exponential (LE) spectrum, bifurcation diagram, Poincaré section diagram and 0–1 test diagram can verify that the system has more complex dynamic characteristics. Meanwhile, not only is the randomness of the system is verified by complexity analysis, but the multistability of the system, namely, the coexistence attractor, is also simulated. Second, using Multisim to build an analog circuit diagram, the circuit simulation results and numerical simulation results coincide, proving the circuit feasibility of the system. Finally, a suitable controller is designed based on Lyapunov stability theory to realize the synchronization of the drive-response system. On the basis of synchronization, disturbance (measured signal) is added to the response system to transform the signal detection into the synchronization error analysis of the drive-response synchronization system. The frequency of synchronization error is obtained by frequency domain analysis, and the frequency value estimated by the multiple signal classification (MUSIC) algorithm. It is found that the proposed chaotic system has more complex dynamics. The method of synchronization control error combined with spectrum estimation can effectively estimate the frequency of weak signal and provide a large detection threshold for weak signal detection.

Design of a Single-Channel Chaotic Secure Communication System Implemented by DNA Strand Displacement.

DNA strand displacement (DSD) is regarded as a foundation for the construction of biological computing systems because of the predictability of DNA molecular behaviors. Some complex system dynamics can be approximated by cascading DSD reaction modules with different functions. In this paper, four DSD reaction modules are used to realize chaotic secure communication based on drive-response synchronization of four-dimensional chaotic systems. The system adopts the communication technology of chaos masking and uses a single-channel synchronization scheme to achieve high accuracy. The simulation results demonstrate that encryption and decryption of the signal are achieved by the design. Moreover, the system is robust to noise signals and interference during the DNA reactions. This work provides a method for the application of DNA molecular computation in the communication field.

Synchronization of Fractional Order Uncertain BAM Competitive Neural Networks

This article examines the drive-response synchronization of a class of fractional order uncertain BAM (Bidirectional Associative Memory) competitive neural networks. By using the differential inclusions theory, and constructing a proper Lyapunov-Krasovskii functional, novel sufficient conditions are obtained to achieve global asymptotic stability of fractional order uncertain BAM competitive neural networks. This novel approach is based on the linear matrix inequality (LMI) technique and the derived conditions are easy to verify via the LMI toolbox. Moreover, numerical examples are presented to show the feasibility and effectiveness of the theoretical results.

Quasi-FM Waveform Using Chaotic Oscillator for Joint Radar and Communication Systems

The authors propose a novel signal design for generating wideband quasi-Frequency Modulated (FM) waveforms using chaotic systems. The receiver is based on a self synchronizing chaotic system, making for fast synchronization that is robust to timing errors or Doppler shifts. The chaotic oscillator has fast and slow time scales, and the slow oscillating part of the chaotic system is used to sweep the fast oscillating part thereby generating a modulated waveform that changes its frequency as a function of time. The potentials of these waveforms are demonstrated for joint radar-communication (RadComm) systems. Using the same nonlinear system a chaos frequency shift keying (CFSK) approach is utilized to encode the digital information. To decode the information, a drive-response synchronization scheme is utilized. Results indicate that our proposed signal design closely matches the bit-error rate (BER) of theoretical noncoherent frequency shift keying (FSK) while having good radar imaging capabilities.

Sampled-data synchronization criteria for Markovian jumping neural networks with additive time-varying delays using new techniques

This paper investigates the sampled-data synchronization issue of Markovian jumping neural networks with additive time-varying delays. Firstly, a ternary quadratic function negative-determination condition and the bilateral sampled-interval-related Lyapunov functional (BSIRLF) approach are proposed. Based on the developed two novel approaches, some new criteria based on the linear matrix inequalities (LMIs) are established to guarantee the drive-response stochastic sampled-data synchronization of Markovian jumping neural networks with additive time-varying delays. Meanwhile, the corresponding sampled-data controller gains are designed under the larger sampling interval. In the end, the availability and merits of the developed approaches are displayed via two simulative examples.

Mode-dependent guaranteed cost event-triggered synchronization for singular semi-markov jump neural networks with time delays

This paper addresses the drive-response synchronization problem for singular semi-Markov jump neural networks with time delays. Furthermore, the mode-dependent event-triggered scheme is applied to improve data transmission efficiency. Sufficient criterion is derived by a designed mode-dependent Lyapunov–Krasovskii functional for synchronization error system. Then, synchronization controller gains matrix and event-triggered weight matrix are co-designed simultaneously assisted by linear matrix inequality, such that proposed guaranteed cost performance can be achieved in the mean-square sense. Finally, the usefulness of our synchronization design is verified by numerical simulations.

Synchronization of recurrent neural networks with unbounded delays and time-varying coefficients via generalized differential inequalities

In this paper, we revisit the drive-response synchronization of a class of recurrent neural networks with unbounded delays and time-varying coefficients, contrary to usual in the literature about time-varying neural networks, the signs of self-feedback coefficients are permitted to be indefinite or the time-varying coefficients can be unbounded. A generalized scalar delay differential inequality considering indefinite self-feedback coefficient and unbounded delay simultaneously is established, which covers the existing result with bounded delay, the applicabilities of the sufficient conditions are discussed. Some novel criteria for network synchronization are then derived by constructing different candidate functions. These results have been improved in some aspects compared with the existing ones. Differential inequality in vector form is also derived to obtain a more refined synchronization criterion which removes some strong assumptions. Three examples are presented to verify the effectiveness and show the superiorities of our theoretical results.

Neural network based asynchronous synchronization for fuzzy hidden Markov jump complex dynamical networks

This paper investigates the drive-response synchronization problem of Takagi–Sugeno fuzzy hidden Markov jump complex dynamical networks. More precisely, a novel asynchronous synchronization control strategy is developed for coping with mismatched hidden jumping modes. Furthermore, the neural network is adopted with online learning laws for unknown function approximation. By taking advantage of Lyapunov method, sufficient conditions are established to ensure mean-square synchronization performance with disturbances. Based on the synchronization criterion, asynchronous controller gains are designed in terms of linear matrix inequalities. An illustrative example is finally given to validate the effectiveness of the proposed synchronization techniques.

Synchronization of memristive neural networks with unknown parameters via event-triggered adaptive control

This paper considers the drive-response synchronization of memristive neural networks (MNNs) with unknown parameters, where the unbounded discrete and bounded distributed time-varying delays are involved. Aiming at the unknown parameters of MNNs, the updating law of weight in response system and the gain of adaptive controller are proposed to realize the synchronization of delayed MNNs. In view of the limited communication and bandwidth, the event-triggered mechanism is introduced to adaptive control, which not only decreases the times of controller update and the amount of data sending out but also enables synchronization when parameters of MNNs are unknown. In addition, a relative threshold strategy, which is relative to fixed threshold strategy, is proposed to increase the inter-execution intervals and to improve the control effect. When the parameters of MNNs are known, the algebraic criteria of synchronization are established via event-triggered state feedback control by exploiting inequality techniques and calculus theorems. Finally, one simulation is presented to validate the effectiveness of the proposed results.

Synchronization of drive-response networks with event-based pinning control

This work investigates the pinning synchronization problem of a drive-response network with nonlinear nodal dynamics under dynamic pinning strategy, where the control signal updates according to some well-designed triggering condition so as to reduce the control cost. By using a novel differential inequality, sufficient criteria are derived to guarantee synchronization, revealing the crucial role of the time average of the smallest eigenvalue of an augmented matrix in spite of the changeable pinning strength. Meanwhile, Zeno phenomenon is also successfully excluded. As applications, the main theorem is utilized to examine some specified dynamic pinning strategies, such as pinning control with periodic intermittency, switching pinned node set, and nonlinear pinning strength. An interesting finding is that drive-response synchronization is possible even when the underlying topology is disconnected. Finally, numerical examples on coupled Hopfield neural networks and networked nonlinear oscillators are given for demonstration purpose.

Dynamics, Control and Secure Transmission Electronic Circuit Implementation of a New 3D Chaotic System in Comparison With 50 Reported Systems

The very high demand for chaotic systems in the fields of sciences, particularly in secure communication, leads numerous researchers to build novel systems. This work announces a new easy to implement 3D chaotic system with five quadratic nonlinearities and three positive parameters, the proposed system is complex with larger bandwidth compared to at least 50 other systems that have been described. It contains eight terms and it can generate chaotic, periodic and quasi-periodic behaviors. The main dynamical properties of the proposed system are studied using Kaplan-Yorke dimension (KYD), Lyapunov exponents, bifurcation diagrams, multistability, equilibrium points stability and dissipativity. Then, the eight terms system feasibility is verified using Multisim software by designing its electronic circuit. In addition, active controllers are designed for leading the proposed system to achieve stability, tracking a desired dynamic and synchronizing with an identical model. Finally, using drive response synchronization, a novel secure communication electrical circuit design is built based on the suggested approach. The findings from numerical experiment demonstrated the new system’s success in completing the encryption/decryption process, as well as its secured transmission technique.

A Note on Sampled-Data Synchronization of Memristor Networks Subject to Actuator Failures and Two Different Activations

This brief is concerned with the drive-response synchronization problem of memristor networks subject to actuator failures and two different activations via sampled-data (SD) control strategy. By using δ-matrix measure method and Halanay inequality technique, the sufficient conditions for global exponential synchronization of driving-response memristor systems are obtained. Unlike the existing works, the common Lyapunov functionals are not employed, but two simple and general stability criteria are derived. Particularly, the established criteria are easier to demonstrate and execute in practice than the relevant results. And in order to verify the validity and superiority of the proposed theoretical results, a numerical simulation is finally provided.