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In this paper, we develop a nonconservative kinetic framework to be applied to the study of immune system dysregulation. From the modeling viewpoint, the model regards a system composed of stochastically interacting agents, under the action of an eternal force field. According to the application perspectives of this paper, the external force field has a specific analytical shape. In this case, some analytical results are proved, i.e. existence, uniqueness, positivity, and boundedness of solution of the related Cauchy problem, at least locally in time. Then, the model is refined to be implemented for the study of treatment strategies in case of autoimmune response. Specifically, we distinguish the autonomous case from the nonautonomous one, representing the absence or delivery of drugs, respectively. The former allows us to gain some stability results. Whereas, the latter is qualitatively studied. Numerical simulations are provided for both schemes. • A nonconservative kinetic model with external force field. • Solution existence, uniqueness, positivity, boundedness for nonautonomous system. • Kinetic system applied to autoimmune treatment strategy. [ABSTRACT FROM AUTHOR]

Anti-disturbance state estimation for reaction–diffusion neural networks (RDNNs) subject to persistent dwell-time (PDT) switching constraints is investigated in this paper. First, PDT switching that can be utilized to characterize both the fast and slow switching processes is used in this paper to accurately model the RDNNs. Moreover, by designing the time-sampling and space-splitting measurement algorithms, the proposed state estimator can significantly reduce the measurement cost while tolerating the frequent asynchrony of the system modes and estimator ones caused by the sensor update lag. Furthermore, a state estimator is constructed to obtain the state of RDNNs affected by matched disturbances. To suppress the impact of the disturbance on the system's state estimation, a disturbance observer and a disturbance-related controller are designed to estimate the disturbance information and ensure state estimation performance. Then, sufficient conditions for the proposed state estimator making the estimation error bounded are derived. Finally, numerical simulations for switched RDNNs with two-dimensional spatial diffusion are presented to illustrate the effectiveness and superiority of the proposed method. • Different from existing 1D spatial switched RDNNs, this paper focuses on switched RDNNs with high-dimensional diffusion and PDT switching rule, which are more in line with the system characteristics. • A combined time-sampling and space-splitting measurement method is proposed to reduce the measurement cost. To address the frequent asynchrony of system modes and estimator ones, stability analysis and estimator design are performed using iterative and recursive methods. • To obtain the system's state and to minimize the effect of disturbances on state estimation, an anti-disturbance state estimation scheme is proposed for PDT-switched RDNNs based on the disturbance observer. [ABSTRACT FROM AUTHOR]

This paper focuses on the p th moment exponentially stability for Markov switching and multi-impulse jumps stochastic time-varying delay system, where the switching behavior among subsystems of the target system is determined by Markov chains, and the occurrence of impulsive jumps is decided according to event-triggered impulsive mechanism when certain well-designed conditions are satisfied. By applying the Itô formula, Gronwall inequality and Razumikhin theorem, some novel sufficient criteria are provided to assure the system stability and get rid of Zeno phenomenon. It is worth pointing out that the multi-impulse jumps are our research aim and the range of delays considered is relatively wide, i.e., the daily bounded delay τ (t) ∈ [ 0 , 1) and the unupper bound delay τ (t) ∈ [ 1 , ∞). Subsequently, two diverse event trigger mechanism about impulsive jumps are proposed for such two types of delays, namely the defined event-triggered impulsive mechanism with delay. Finally, the validity and feasibility of the developed theoretical results are verified by two numerical simulations. • Different from the bounded delay system in Wang et al. (2023), Peng et al. (2021),Li and Zhu (2023),Peng et al. (2010), Zhu (2014), Zhua and Cao (2012),Yang and Zhu (2014), Xu and Zhu (2022), we discuss the daily bounded delay τ (t) ∈ [ 0 , 1) and the unupper bound delay τ (t) ∈ [ 1 , ∞). Two categories of event trigger impulsive method named event-triggered impulsive mechanism with delay (ETIMD) are proposed for two types delay, respectively. And in event-triggered condition, it fully consider the impact of delays. Moreover, the upper bound of the delay τ (t) ∈ [ 0 , 1) is required to avoid Zeno phenomenon. While for τ (t) ∈ [ 1 , ∞) , only the lower bound is required to escape Zeno phenomenon, in which is independent of the delayed upper bound. • Compared with Wang et al. (2022), Li et al. (2020), Peng et al. (2021), Zhu (2014), Xu and Zhu (2022), the Markov switching and multi-impulse jumps stochastic time-varying delay system as a benchmark is considered in this paper, where the switching behavior between subsystems is driven by Markov chains, and the occurrence of impulsive jump is decided according to ETIMD strategy. It should be emphasized that the multi-impulse jumps are the research goal. Thus, the system in [27,28,36,43] could be regarded as a special case of the stochastic delay system when the Markov switching is not considered in this study. • By applying the Itô formula, Gronwall inequality and Razumikhin theorem, some novel sufficient criteria of Lyapunov-Razumikhin type for p-ES are provided for unstable subsystems with stable impulses. [ABSTRACT FROM AUTHOR]

This paper aims to investigate a thermal frictional contact model with damage and long memory effects. We consider a deformable body made of viscoelastic material and assume the process to be dynamic. The material is expected to adhere to the Kelvin–Voigt constitutive law, with damage and thermal effects incorporated. The variational formulation of the model results in a coupled system comprising a history-dependent hemivariational inequality governing the displacement field, a parabolic variational inequality describing the damage field and an evolution equation for the temperature field. In the analysis of this system, we initially introduce a fully discrete scheme, and then concentrate on deriving error estimates of numerical solutions. An optimal order error estimate is attained under some appropriate solution regularity assumptions. At the tail of this manuscript, numerical simulations are provided for the contact problem to validate the theoretical results. • We have studied a complex thermoviscoelastic contact model with damage and long memory. • The variational formulation gives rise to a differential hemivariational inequality. • We focus on optimal error estimates of numerical solutions. • Theoretical analysis and numerical simulation have faced considerable challenges. [ABSTRACT FROM AUTHOR]

In this paper, a stochastic multi-weighted complex network with regime-switching diffusions (SMCNRSD) is considered. Here, the jump and the diffusion processes are interdependent, which generalizes the most existing network model. In the study of stochastic multi-weighted complex networks, stability analysis is an important topic. But so far, some work on stability requires stochastic multi-weighted complex networks to satisfy the global linear growth condition, which cannot be applied to some high-order or nonlinear networks. Therefore, one of the research contents of this study is to obtain the global existence and uniqueness of SMCNRSD under local conditions. Besides, the SMCNRSD usually does not stabilize spontaneously for reasons such as stochastic disturbance, multiple weights and nonlinear coupling. To stabilize SMCNRSD, periodic intermittent control is introduced to obtain the stability criterion. In application, stochastic multi-weighted Chua's circuits with regime-switching diffusions are taken into account. The corresponding existence and uniqueness as well as stability criteria are given under local conditions. To further illustrate the validity of theoretical results, numerical simulations are given. • The well-posedness of SMCNRSD is first proposed under the local conditions. • Regime-switching diffusions are introduced such that network model is more general. • Graph-theoretic method is a novel strategy to obtain the well-posedness of SMCNRSD. [ABSTRACT FROM AUTHOR]

The issue of group consensus for heterogeneous fractional-order multi-agent systems under the cooperation-competition networks with time delays is investigated in this paper. Novel group consensus control protocols with input and communication delays are designed based on cooperative-competitive interaction. The considered multi-agent systems consists of fractional order dynamics with the single integrator and the double integrator, and the speed of agents is not known. The matrix theory, frequency domain approach and graph theory are used to figure out the sufficient conditions for group consensus under the switching and fixed topology, respectively. Finally, numerical simulation examples are given to verify the correctness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we construct and analyze a reaction–diffusion hybrid model incorporating impulsive control and periodic evolution domain in Wolbachia -infected and wild mosquito populations to investigate the joint impact of spatial diffusion, impulsive control and the evolution of a domain on the control of mosquitoes. The explicit formulas of the two ecological reproduction indexes R U and R I are introduced, which relate to the evolution rate of domain and the impulsive function. Then we establish the threshold-type dynamics for the impulsive problem in terms of R U and R I by the method of upper and lower solutions, which present the extinction of mosquitoes, and competition and the coexistence of Wolbachia -infected and wild mosquitoes under impulsive control and periodic evolution domain. Numerically, we perform simulations to certify the analytical results, determine the importance of parameters on the persistence and extinction of mosquito populations, and expound how impulsive control, the evolution domain and fitness effect caused by Wolbachia affect the mosquito population evolution. • A model including impulsive control, Wolbachia and evolving domain is developed. • The formulas of the two ecological reproduction indexes (R U and R I) are derived. • The threshold dynamics in terms of R U and R I are fully solved. • Numerical simulations expound the effect of key parameters on the mosquitoes. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new numerical simulation iterative algorithm to solve the split feasibility problem and the fixed point problem with demicontractive mappings. Our algorithm mainly involves primal-dual iterative, relaxed projection, inertial technique and self-adaptive step size. Under reasonable conditions, the strong convergence of our algorithm is established. Moreover, we provide some numerical simulation examples to demonstrate the efficiency of our iterative algorithm compared to existing algorithms in the other literature. [ABSTRACT FROM AUTHOR]

In this paper, the global exponential stability and stabilization problems are investigated for memristive neural networks (MNNs) with stochastic disturbances, spatial diffusions and distributed delays. The spatial diffusions are not assumed to be symmetric and distributed delays are relaxed to be unbounded. Then, the presented MNNs are modeled as a class of stochastic partial systems with hybrid delays. Based on nonsmooth analysis, the Lyapunov–Krasovskii functional and inequality approach, some simple algebraic criteria are derived for the global exponential stability as well as the stabilization via two kinds of designed feedback controllers. The derived criteria are easily verified and the obtained results are available for other delayed systems with or without stochastic disturbances and spatial diffusions. Finally, the stability and stabilization results are validated by numerical simulations. • The stochastic model with spatial diffusions and distributed delays is discussed. • The derived results are generalized and they contain previous ones as special cases. • The method is available for other stochastic delayed partial differential systems. • The space set of the spatial diffusions in our model is not symmetrical. • The distributed delays are unbounded. [ABSTRACT FROM AUTHOR]

Continuous stirred tank reactor (CSTR) is a common reactor in the chemical industry. The accurate observation of the concentration conversion rate of the mixture and the internal temperature of the reaction vessel is a prerequisite for obtaining the desired mixture. This paper proposes a novel observer based on residual neural networks for CSTR systems. Firstly, the mathematical model of the CSTR reaction is given, as well as a detailed description of the structure and equations of the residual neural networks and the designed observer. Then the matrix method is used for the nonlinear isolation of the residual neural networks and the theory of quadratic constraints for nonlinear activation functions of the neural networks is applied. Thus, the convergence of the proposed observer is analyzed theoretically in detail. Finally, the numerical simulations are implemented to demonstrate that the proposed residual neural network-based observer can quickly and accurately observe the state changes during the CSTR reaction. • A novel residual neural network-based observer for CSTR is proposed. • The convergence analysis of the proposed observer is presented. • The selection of hyperparameters of the residual neural networks is given. • The effectiveness of the proposed observer is verified by numerical simulations. [ABSTRACT FROM AUTHOR]

In Electro-Osmotic Pumps (EOPs), a micro fluid flow is formed by applying an external electric field via two electrodes immersed in the electrolyte. The immersed electrodes, due to lying in the fluid flow path, can consider an obstacle that can negatively affect the flow inside the microchannel. This issue is usually neglected in studies performed on the electroosmotic flows. Concerning this motivation, in this paper, a novel concept of a multi-stage EOP (introduced earlier by the researchers) was investigated numerically where the electrodes were attached to the wall of the micropump so as not to obstruct the fluid flow and to facilitate the serialization of micropumps. A two-dimensional numerical code is developed to analyze the steady-state performance of the multi-stage EOP. The governing equations for the fluid flow, internal and external electric fields, and ion concentration distribution are solved using the Finite Volume method. The results showed that in the multi-stage EOP consisting of multiple micropumps connected in series, the maximum pressure of EOP will enhances by increasing the number of micropumps. In contrast, the maximum flow rate remains approximately constant. The relationship between the maximum pressure, and the strength of the applied external electric field, was also investigated based on the electric field strength, and the results were expressed as a mathematical correlation. [ABSTRACT FROM AUTHOR]