Asymptotic Synchronization Research Articles

Comparative analysis of two novel chaotic systems, and validation of hybrid function projective and complete synchronization using active-adaptive control

Abstract This study investigates the nonlinear characteristics of two novel 3D-chaotic models using phase portraits, bifurcation diagrams, Lyapunov exponents, time series analysis, and Poincaré maps. Here, we have examined hybrid-function projective and complete synchronization schemes via adaptive and active control methods. Moreover, the performance of hybrid-function projective synchronization, utilizing sine, cosine, and exponential terms, is compared to complete synchronization through two control strategies. Our designed controllers ensure asymptotic global chaotic synchronization based on Lyapunov stability principles. We have also compared our results with other competitive schemes and validated the theoretical findings through simulations on the MATLAB platform.

Asymptotic synchronisation for coupled heterogeneous complex networks via L' Hoptial' rule

This paper considers the global asymptotic synchronisation (GAS) for the drive-response coupled heterogeneous complex networks (DRCHCNS). By using the different inequality techniques (DIT), L' Hoptial' rule and limit algorithms, three criteria to assure the GAS for the DRCHCNS are derived. Up to now, the results on GAS for DRCHCNS have been obtained usually by applying linear matrix inequality (LMI) and matrix measure approach (MMA). But, in this paper, without applying above approaches, we establish the GAS criteria for the DRCHCNS by using L' Hoptial' rule and limit algorithms. So, our study approach for the complex networks (CNS) extends the study fields of synchronisation of the CNS.

Estimations of global Mittag–Leffler bounds and synchronization for fractional-order permanent magnet synchronous motor systems

This article investigates the global Mittag-Leffler bounds (GM-LBs) and synchronization of fractional-order permanent magnet synchronous motors (FOPMSMs). To begin with, by using some appropriate generalized Lyapunov functions, the extremum principle of function and fractional differential inequalities, a few new bounds for the three-dimensional cylindrical and ellipsoidal domains and a rotatory parabolic body of FOPMSMs are estimated by utilizing the parameters in the systems, which improves the earlier studies and may conclude some new estimates. Moreover, linear feedback control strategies owning one or two inputs and fractional adaptive control owning both single input and single state are accepted to come true the global Mittag-Leffler synchronization (GM-LS) and global asymptotic synchronization (GAS) of two FOPMSMs. Some new criteria for the synchronization are acquired by utilizing some inequality approaches. Finally, the feasibility of the proposed control schemes is verified by numerical simulations.

Asymptotic Synchronization for Caputo Fractional-Order Time-Delayed Cellar Neural Networks with Multiple Fuzzy Operators and Partial Uncertainties via Mixed Impulsive Feedback Control

To construct Caputo fractional-order time-delayed cellar neural networks (FOTDCNNs) that characterize real environments, this article introduces partial uncertainties, fuzzy operators, and nonlinear activation functions into the network models. Specifically, both the fuzzy AND operator and the fuzzy OR operator are contemplated in the master–slave systems. In response to the properties of the considered cellar neural networks (NNs), this article designs a new class of mixed control protocols that utilize both the error feedback information of systems and the sampling information of impulse moments to achieve network synchronization tasks. This approach overcomes the interference of time delays and uncertainties on network stability. By integrating the fractional-order comparison principle, fractional-order stability theory, and hybrid control schemes, readily verifiable asymptotic synchronization conditions for the studied fuzzy cellar NNs are established, and the range of system parameters is determined. Unlike previous results, the impulse gain spectrum considered in this study is no longer confined to a local interval (−2,0) and can be extended to almost the entire real number domain. This spectrum extension relaxes the synchronization conditions, ensuring a broader applicability of the proposed control schemes.

Networks of reinforced stochastic processes: A complete description of the first-order asymptotics

We consider a finite collection of reinforced stochastic processes with a general network-based interaction among them. We provide sufficient and necessary conditions for the emergence of some form of almost sure asymptotic synchronization. Specifically, we identify three regimes: the first involves complete synchronization, where all processes converge towards the same random variable; the second exhibits almost sure convergence of the system, but no form of synchronization subsists; and the third reveals a scenario where there is almost sure asymptotic synchronization within the cyclic classes of the interaction matrix, together with an asymptotic periodic behavior among these classes.

Sampled‐data‐based synchronization of complex networks under scaling attacks

In this study, our main objective is to address the issue of sampled‐data‐based synchronization of complex networks subjected to stochastic scaling attacks using a looped‐functional approach. To begin with, the design of a Lyapunov functional, which involves tuning parameters and slack variables, considers the error state information of and . Then, the scaling attack is a type of deception attack that is formulated using an interval matrix approach. In addition, the complex networks considered in this study incorporate uncertain inner coupling strengths, which are more general than the existing ones, owing to the presence of uncertainties in the coupling strengths. Using a looped‐functional approach to construct an appropriate Lyapunov–Krasovskii functional, we derive a set of sufficient conditions to achieve mean‐square asymptotic synchronization for considered complex networks under scaling attacks. In the end, the proposed results are illustrated using three examples, including a practical example that highlights their effectiveness and superiority.

Synchronization analysis of fuzzy inertial neural networks with time‐varying delays via non‐reduced order method

SummaryIn this article, the asymptotic synchronization of a class of fuzzy inertial neural networks (FINNs) with time‐varying delays is investigated. First, the direct analysis approach is applied to replace the accustomed variable transformation and the reduced‐order method for addressing the inertial term. Second, a suitable Lyapunov function and control scheme are devised to obtain several new sufficient conditions to guarantee the asymptotic synchronization of the class of FINNs with time‐varying delays. It turns out that the obtained criteria are simpler and more effective. Meanwhile, some numerical examples demonstrate the effectiveness of the proposed strategies and verify the theoretical results.

Synchronization of Fractional Delayed Memristive Neural Networks with Jump Mismatches via Event-Based Hybrid Impulsive Controller

This study investigates the asymptotic synchronization in fractional memristive neural networks of the Riemann–Liouville type, considering mixed time delays and jump mismatches. Addressing the challenges associated with discrepancies in the circuit switching speed and the accuracy of the memristor, this paper introduces an enhanced model that effectively navigates these complexities. We propose two novel event-based hybrid impulsive controllers, each characterized by unique triggering conditions. Utilizing advanced techniques in inequality and hybrid impulsive control, we establish the conditions necessary for achieving synchronization through innovative Lyapunov functions. Importantly, the developed controllers are theoretically optimized to minimize control costs, an essential consideration for their practical deployment. Finally, the effectiveness of our proposed approach is demonstrated through two illustrative simulation examples.

Drive–response asymptotic shape synchronization for a class of two-dimensional chaotic systems and its application in image encryption

This paper proposes the concept of drive–response asymptotic shape synchronization for two-dimensional chaotic systems and its application in image encryption. It overcomes the limitations of traditional shape synchronization, eliminates the restrictions on the drive system’s continuous differentiability, and the response system’s specific format, while simplifying the controller design, thereby demonstrating enhanced applicability and ease of implementation. Moreover, based on the characteristics of asymptotic shape synchronization, we propose a novel image encryption scheme. In this scheme, the drive and response systems, initialized with distinct values, achieve identical chaotic attractors through rotation and translation parameters in rigid transformation, which are utilized for encryption and decryption processes, respectively. Our encryption algorithm employs DNA coding to construct a DNA plane and incorporates the concept of Rubik’s cube rotations for scrambling and diffusion. Experimental simulations and performance analysis verify the effectiveness of the proposed encryption scheme in withstanding various attacks, ensuring a high level of security.

Global asymptotic synchronization for coupled heterogeneous complex networks via Laplace transform approach

Global asymptotic synchronization for coupled heterogeneous complex networks via Laplace transform approach

Finite-Time Adaptive Synchronization and Fixed-Time Synchronization of Fractional-Order Memristive Cellular Neural Networks with Time-Varying Delays

Asymptotic synchronization requires continuous external control of the system, which is unrealistic considering the cost of control. Adaptive control methods have strong robustness to uncertainties such as disturbances and unknowns. On the other hand, for finite-time synchronization, if the initial value of the system is unknown, the synchronization time of the finite-time synchronization cannot be estimated. This paper explores the finite-time adaptive synchronization (FTAS) and fixed-time synchronization (FDTS) of fractional-order memristive cellular neural networks (FMCNNs) with time-varying delays (TVD). Utilizing the properties and principles of fractional order, we introduce a novel lemma. Based on this lemma and various analysis techniques, we establish new criteria to guarantee FTAS and FDTS of FMCNNs with TVD through the implementation of a delay-dependent feedback controller and fractional-order adaptive controller. Additionally, we estimate the upper bound of the synchronization setting time. Finally, numerical simulations are conducted to confirm the validity of the finite-time and fixed-time stability theorems.

Synchronization Analysis for Quaternion-Valued Delayed Neural Networks with Impulse and Inertia via a Direct Technique

The asymptotic synchronization of quaternion-valued delayed neural networks with impulses and inertia is studied in this article. Firstly, a convergence result on piecewise differentiable functions is developed, which is a generalization of the Barbalat lemma and provides a powerful tool for the convergence analysis of discontinuous systems. To achieve synchronization, a constant gain-based control scheme and an adaptive gain-based control strategy are directly proposed for response quaternion-valued models. In the convergence analysis, a direct analysis method is developed to discuss the synchronization without using the separation technique or reduced-order transformation. In particular, some Lyapunov functionals, composed of the state variables and their derivatives, are directly constructed and some synchronization criteria represented by matrix inequalities are obtained based on quaternion theory. Some numerical results are shown to further confirm the theoretical analysis.

Security synchronization problem for stochastic complex networks via event-triggered impulsive control with actuation delays

This study focused on the security synchronization problem for stochastic complex networks (SCNs) via event-triggered impulsive control (ETIC) with actuation delays. Firstly, incorporating the network topology and the Lyapunov function theory, a novel event-triggered mechanism (ETM) is devised, which accounts for actuation delays; Secondly, an ETM-based quantizer is introduced to optimize network resources, meantime, building upon this foundation, the Lipschitz–Razumikhin method is integrated with graph theory to establish a positive lower bound on the minimum event interval time, thereby preventing Zeno behavior; Additionally, some sufficient conditions are obtained to achieve global asymptotic synchronization of SCNs under quantization and deception attacks; Finally, a Chua’s circuit numerical simulation is employed to demonstrate the effectiveness of our theoretical findings.

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.

Collective dynamics of fluctuating–damping coupled oscillators in network structures: Stability, synchronism, and resonant behaviors

The investigation of collective behaviors and synergies in coupled systems holds great significance in many fields. In this paper, we propose the coupled system of overdamped fluctuating–damping oscillators in a general network framework. Our initial theoretical analysis focuses on the system’s synchronization and stability, revealing that both the first and second moments of the mean field are asymptotic stability, and the system exhibits a property of stochastic asymptotic synchronization with the mean field, irrespective of coupled structures. Furthermore, we explore the system’s collective behaviors by analyzing the output amplitude amplification (OAA), where we observe the emergence of generalized stochastic resonance (GSR) phenomena. Finally, we numerically verify the influence of system parameters on stability and synchronization in different coupled structures by introducing the mean first stability time and mean first synchronization time in the simulations. Our findings indicate that the structure does not significantly influence the system stability, whereas it does play a synergistic role in influencing the synchronization. Moreover, we further extend the investigation in complex networks, and observe the non-monotonous phenomena of mean first synchronization time varying with the heterogeneity.

Passivity-based control and asymptotic synchronization for multi-variable discrete stochastic genetic regulatory networks with complex network dynamics

Passivity-based control and asymptotic synchronization for multi-variable discrete stochastic genetic regulatory networks with complex network dynamics

A delay-product-type Lyapunov functional approach for enhanced synchronization of chaotic Lur'e systems using a quantized controller

<abstract><p>The asymptotic synchronization problem of chaotic Lur'e systems in the master-slave framework was explored in this paper. A time-varying delay feedback controller with quantization considerations and a delay-product-type Lyapunov-Krasovskii functional technique were employed to tackle this problem. Consider an error system based on master and slave systems, for which sufficient asymptotic stability requirements are developed to assure that the addressed system achieves proper synchronization. Following that, the desired control gain was determined by finding a feasible solution to these stability requirements. The results of this paper were validated using a numerical example with simulations, which revealed that they were superior to previously published ones.</p></abstract>

Synchronization analysis of delayed quaternion-valued memristor-based neural networks by a direct analytical approach

<abstract><p>This issue discusses the asymptotic synchronization and the exponential synchronization for memristor-based quaternion-valued neural networks under the time-varying delays. Some criteria for synchronization of the memristor-based quaternion-valued neural networks are given by exploiting the set-valued theory, the differential inclusion theory, some analytic techniques, as well as constructing novel controllers, It is worth noting that the synchronization problem about the memristor-based quaternion-valued neural networks were studied by the direct analysis method in this paper. Finally, the main theoretical results were verified by numerical simulations.</p></abstract>

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.

A novel financial system with one stable and two unstable equilibrium points: Dynamics, coexisting attractors, complexity analysis and synchronization using integral sliding mode control

In the world of economics, financial risk is a significant issue that concerns countries and all economic agents. It refers to the potential for experiencing losses due to unpredictable fluctuations in financial or investment activities caused by endogenous factors. Chaos theory provides an explanation for the complexity observed in economic time series, as it supports an endogenous view. This article proposed an enhanced chaos-based financial risk system with one stable and two unstable equilibrium points. The existence of stable and unstable equilibrium points shows that the proposed system has both hidden and self-excited chaotic attractors. By analyzing its dynamic behavior, the study unveils the transition from stability to chaos in the improved financial risk system, while also describing how the complex dynamics of the system affect changes in financial market risk. In addition, this study explores the fundamental dynamic behavior of the financial risk system, including stability analysis, Lyapunov exponent, bifurcation analysis, coexisting attractors, 0–1 test, algorithm and spectral entropy (SE). Finally, with the help of integral sliding mode control (ISMC), we discover the outcomes for the asymptotic synchronization of two chaotic financial systems that are constructed as master and slave systems. Simulations are provided to accompany and support the findings from this research.