This paper investigates the stochastic stability problem of fractional-order quaternion-valued neural networks (FOQVNNs) on time scales with general probabilistic bounded Markovian switching and neutral delays. Owing to the noncommutative nature of quaternion algebra and the coexistence of fractional dynamics, time-scale calculus, Markovian switching, and neutral delays, stability analysis becomes highly challenging, especially when conventional decomposition methods are employed. To overcome these difficulties, the considered system is treated directly in the quaternion domain without decomposition, thereby preserving the intrinsic algebraic structure and avoiding unnecessary dimensional expansion. By constructing an appropriate Lyapunov–Krasovskii functional and combining the free-weighting matrix technique with matrix inequality approaches, a sufficient condition guaranteeing stochastic stability for the considered FOQVNNs is derived and expressed as quaternion-valued linear matrix inequalities. The obtained criteria are general and can be efficiently verified by using a numerical example.
This paper explores the asymptotic synchronization (AS) for a class of master-slave inertial neural networks (MSINNs). Without employing the existing study approaches such as matrix measure means (MMMs) and linear matrix inequality (LMI), by planning two classes of novel controllers of the trigonometric functions, two criteria to assure the AS for the considered MSINNs are achieved by utilizing the implicit zero point existence theorem of functions and differential inequality way (DIW). By applying the implicit point existence theorem of functions and constructing the controllers of the trigonometric functions, the more concise and more easily verified results on AS can be obtained for neural networks (NNs) than using LMI and MMMs. Our results reveal that the time delay plays a important part in the AS of the considered networks. Namely, when the time delay is less than a certain constant, the AS between the master system and the slave system can be achieved.
We propose a comparative study of chaotification techniques that enhance the complexity of one-dimensional maps for sustainable cryptographic applications. Specifically, we examine the use of modulo operation, remainder operation, and k-deep-zoom (k-DZ) transformation applied to the sine map. Each technique’s effectiveness is analyzed using bifurcation diagrams, Lyapunov exponents, and correlation results. Additionally, the statistical performance of the techniques is assessed using the NIST SP 800-22 battery of tests, and the computational efficiency is evaluated in terms of the number of operations. The study aims to identify the best chaotification method for generating robust pseudorandom bit generators (PRBGs) suitable for secure encryption and sustainable cryptography.
This paper develops an event-triggered distributed optimization algorithm (DOA) fordirected multi-agent systems. The algorithm is designed to solve fixed-time optimization problems with equality constraints, while also compensating for input time delays. Firstly, the time-delay system is transformed into an equivalent delay-free model by using the method of model order reduction. Secondly, to reduce the consumption of communication resources, an event-triggered communication scheme is utilized. Subsequently, based on Lyapunov stability theory, it is proved that the designed DOA can converge to the optimal solution within a fixed time. Finally, a numerical simulation shows the effectiveness and advantages of the event-triggered DOA for multi-agent systems.
This paper investigates the approximate controllability of a system of fractional control differential equations. The system involves Caputo fractional derivatives, Volterra–Fredholm integral equations, and impulsive effects. The analysis is carried out in the framework of Banach spaces under nonlocal conditions of order r ∈ (1, 2). The main objective is to establish sufficient conditions for the approximate controllability of the proposed control problem. Assuming that the associated linear system is approximately controllable, the analysis relies on tools from fractional calculus, Krasnoselskii’s fixed point theorem, and the theory of resolvent operators. The obtained results extend and improve several existing results in the related literature. Finally, two illustrative examples are presented to demonstrate the applicability of the theoretical findings.
We investigate the existence of positive solutions for a system of ψ-Riemann–Liouville fractional differential equations with positive parameters and sign-changing nonlinearities subject to nonlocal coupled boundary conditions containing Riemann–Stieltjes integrals and fractional derivatives of various orders. To prove our main result, we use the nonlinear alternative of Leray–Schauder type.
In this manuscript, we propose the notion of a strong extended s-suprametric space, a novel extension that outperforms both s-suprametric and extended suprametric spaces. It looks into the aspects of open and closed ball topologies within this structure. It also investigates the concepts of existence and uniqueness using basic contractions viz. Banach and Kannan contractions. Illustrative examples demonstrate how the strong extended s-suprametric space outperforms its extended equivalent. Our examples demonstrate the presence and distinctness of fixed points in this scenario. Furthermore, exploiting these newly launched results, the manuscript investigates the analysis of a boundary value problem, including diffusing chemical material constrained between parallel walls with related concentrations at the boundaries, taking into account supplied raw density and recognized absorbing coefficients. It also applies these insights to a nonlinear boundary value issue involving satellite web coupling in which a thin sheet joins two cylindrical spacecraft. This coupling causes nonlinearity, resulting in a separate boundary value issue influenced by radiation effects within the satellites.
In this paper, a direct method is presented for analyzing the adaptive synchronization of quaternion-valued inertial neural networks (QVINNs) with uncertain parameters and time delay. By this method, the forms of time delays and the Lyapunov function in this paper are flexible, and in stability analysis, the requirement for negative definiteness of Lyapunov functions will be weakened. In addition, a more generalized adaptive synchronization controller has been proposed for QVINNs, which no longer requires multiple calculations of the control gain. Since most of the previous adaptive control methods did not impose requirements on the convergence speed of the QVINNs, a class of improved adaptive controllers is designed to address the slow synchronization speed of QVINNs. Finally, numerical simulations are conducted to validate the synchronization conditions.
This paper studies the global asymptotic synchronization (GAS) and global exponential synchronization (GES) problems of a class of quaternion-valued bidirectional associative memory neural networks (QVBAMNNs) with time-varying delays. Based on the matrix measure approach and Halanay inequality, sufficient conditions for GAS of unbounded time-varying delay system and GES of bounded time-varying delay system were established. Different from existing methods, this approach does not require the construction of Lyapunov functions and obtains the criteria for system synchronization expressed in terms of norms and measures. Finally, the validity of the proposed theoretical results and the feasibility of the control strategy are verified through numerical simulations.
This paper presents a novel fixed-time adaptive control scheme with prescribed performance for nonlinear networked control systems (NCSs) under deception attacks. The Nussbaum function is first employed to tackle the challenge of unknown attack weights and their signs. A hybrid approach integrating a fixed-time performance function with a nonlinear shifting function is used to mitigate the influence of initial conditions on tracking errors. Furthermore, a sufficient condition is derived to guarantee the practical fixed-time stability of NCSs, even in the face of deception attacks. Finally, the effectiveness of the proposed methodology is demonstrated through a mass-spring-damper system simulation.
This paper investigates the controllability of a second-order impulsive damped integrodifferential nonautonomous system with state-dependent delay. The results are established using the properties of resolvent operators related to the second-order system behind them, and the analysis employs key mathematical tools such as Gronwall’s lemma and fixed-point theorems. Assuming the approximate controllability of the corresponding linearized system, we obtain a new set of sufficient conditions developed for the approximate controllability of the nonlinear second-order system. These findings contribute to our understanding of the approximate controllability in complex dynamical systems affected by both damping and state-dependent delay. Finally, we present an application that demonstrates and validates the theoretical findings of this study.
This paper considers the global asymptotic synchronization (GAS) for master-slave delayed inertial bidirectional associative memory (BAM) neural networks (NNs). Most existing studies on GAS rely on the LMI approach, integral inequality, matrix measure, and maximum-valued methods, usually with additional controllers. In contrast, this work achieves GAS without using the above methods or designing any controllers. Instead, two new sufficient conditions are derived via the fundamental solution matrix method for first-order differential systems. For the first time, the fundamental solution matrix method is introduced to deal with the GAS for the NNs.
It is well known that both media coverage and the presence of asymptomatic patients have a significant impact on the spread and control of infectious diseases. Therefore, this paper proposes a class of fractional epidemic models that incorporate media coverage and asymptomatic infection. Also, the time delay for individuals’ response to the current media coverage, as well as the time delay of media coverage, are incorporated in our proposed model to make it more practical. Based on fractional proportional-derivative (PD) control method, Hopf bifurcation is investigated by taking the sum of the two time delays and the order of the fractional derivatives as bifurcation parameters, respectively. Some sufficient delayed-induced and order-induced bifurcation conditions are given. The application and effectiveness of the presented theoretical results are illustrated through a simulation example. Furthermore, the impact of the feedback control gains and the media effect weight on the stability and Hopf bifurcation of the considered epidemic model is explored.
This paper investigates the existence of positive solutions for a resonant system of nonlinear differential equations subject to coupled integral boundary conditions involving Riemann–Stieltjes integral. Our analysis is based on Leggett–Williams norm-type theorem for coincidence equations due to O’Regan and Zima. By employing a general abstract framework, we obtain new existence criteria that complement and extend recent results in the literature.
Volatility is a key measure of financial risk, and GARCH models are widely used to describe its dynamics. However, they do not account for the influence of news sentiment, which can significantly shape market volatility. Recently proposed News-Augmented GARCH model addresses it by incorporating sentiment signals in a nonlinear, asymmetric, and multiplicative form. This paper examines its theoretical properties and performs a simulation-based hyperparameter study. The analysis establishes the existence of a unique and causal solution, derives a stability condition, and evaluates model sensitivity and parameter recovery under controlled scenarios. Results demonstrate robust performance across various settings and provide guidance for informed hyperparameter selection and evaluation, enhancing model’s reliability for empirical applications.
The autonomous Duffing–Holmes oscillator ẋ = y, ẏ = x – x3 + by – kz, ż = w(y – z), depending on the three parameters b, k, and w, has been studied previously by several authors who showed that for certain parameter values, it exhibits chaotic motion, or that numerically it has two periodic orbits coming from a Hopf bifurcation, or that it can have three equilibria for some given values of the parameters. Here we provide new results on the integrability and the global dynamics of the autonomous Duffing–Holmes oscillator using its first integrals and Darboux invariants when these exist for some given values of its parameters.
In this paper, we introduce two new algorithms for solving variational inequalities in Banach spaces. Our aim is finding a common element of the solution set of variational inequalities (for two inverse-strongly monotone operators) and an equilibrium problem and the set of fixed points of two relatively nonexpansive mappings and a family of resolvent operators. Then the strong convergence of the sequences generated by these algorithms to this element will be proved under suitable conditions. Finally, we provide a numerical example to illustrate our main results.
We investigate a triple system of fractional Sturm-Liouville-Langevin equations with cyclic antiperiodic boundary conditions. The fixed point theorem serves as a tool to establish the existence and uniqueness criteria for solutions. By applying the Banach contraction principle, we also obtain the Ulam-Hyers stability of the proposed system. Finally, examples are provided to illustrate main results.
This article aims to study the problem of fixed-time consensus for nonlinear leader- follower multi-agent systems (MASs) with time delay. Firstly, a new fixed-time stability lemma is derived, where the condition of inequality contains a time-delayed term. Furthermore, a more precise estimated value of settling time (ST) including delayed parameter is obtained, which is different from those existing fixed-time stability lemmas. Thereby, it provides some options for designers in many practical scenarios when considering the delayed systems. Secondly, for the purpose of explaining its applicability, fixed-time consensus of leader-follower nonlinear MASs is investigated by designing a nonlinear control protocol including constant time delay. The designed protocol not only guarantees fixed-time consensus but also effectively improves the convergence rate. With the new proposed lemma, a novel consensus criterion is designed. This is the first time to obtain the time-delayed dependent fixed-time stability criterion for MASs. Finally, the validity and superiority of the established theoretical results are confirmed by one numerical simulation.
This paper addresses the distributed optimization problem in linear multiagent systems (MASs) under external disturbances. Firstly, an observation system is designed by utilizing the output values of agents, which can eliminate external disturbances of system. Secondly, an event-triggered control algorithm is proposed through the gradient information of local cost functions, and its convergence is rigorously established using the Lyapunov stability and looped functional theory. This novel event-triggered protocol incorporates dwell time within the threshold function, effectively eliminating Zeno behavior. By leveraging the looped functional technique, more relaxed conditions are derived for solving the distributed optimization problem. Finally, the validity and feasibility of the proposed protocol are substantiated through numerical simulation.
