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The global robust stability of uncertain delayed fuzzy cellular neural networks (UDFCNNs) was analyzed in this paper. The major results of this paper provided some new criteria for the existence and uniqueness of the equilibrium point of UDFCNN. Furthermore, suitable Lyapunov-Krasovskii functionals was designed for obtaining the adequate conditions for the global asymptotic robust stability and global exponential robust stability of UDFCNN. Finally, several numerical examples was provided to verify the validity of the results. [ABSTRACT FROM AUTHOR]

This paper investigates rumor propagation in a multilingual environment, taking into account language usage variations. Firstly, a 2I2S2R model is proposed within a heterogeneous network framework that incorporates both immunologic and cross-transmitted mechanisms. Secondly, the paper calculates the basic reproduction number R0 by the next-generation matrix method. Thirdly, the local asymptotic stability and the global asymptotic stability are further explored, which indicate that whether the rumor continuously spreads or becomes extinct is determined by the threshold. Finally, the numerical simulation and sensitivity analysis are given to illustrate the effectiveness of theoretical results and the influence of model parameters on rumor spreading. [ABSTRACT FROM AUTHOR]

Abstract: This paper studies the general nonautonomous single-species Kolmogorov systems with delays. The sufficient conditions on the persistence and permanence of species, global asymptotic stability and the existence of positive periodic solutions are established. As applications of these results, the permanence, global asymptotic stability and the existence of positive periodic solutions for a series of special single-species growth systems with delays are discussed. [Copyright &y& Elsevier]

A significant proportion of malaria infections in humans exhibit no symptoms, but it is a reservoir for maintaining malaria transmission. A time periodic reaction-diffusion model for malaria spread is introduced in this paper, incorporating spatial heterogeneity, incubation periods, symptomatic and asymptomatic carriers. This paper introduces the concept of the basic reproduction number R 0 , which is defined as the spectral radius of the next generation operator, and we present some preliminary results by elementary analysis. The threshold dynamic behavior analysis shows that when R 0 < 1 , the disease is extinct, and when R 0 > 1 , the disease is persistent. We investigate the case of constant system parameters, focusing on the global asymptotic stability of the disease-free steady state when R 0 = 1 . In the numerical simulation section, we validate the theoretical results obtained, and then use elasticity analysis methods to explore the influence of parameters on the output solution. In addition, sensitivity analysis of the basic reproduction number under homogeneous conditions indicates direction of controlling malaria transmission. And several control measures are evaluated in the following steps. [ABSTRACT FROM AUTHOR]

This paper studies the global asymptotic stabilization problem of strict-feedforward nonlinear systems with state and input delays. We will first transform the considered system into an equivalent system by constructing the novel parameter-dependent state feedback controller and introducing the appropriate coordinate transformation. After that, the global asymptotic stability of the closed system is proved by giving the proper Lyapunov-Krasovskii functional and using the stability criterion of time-delay system. [ABSTRACT FROM AUTHOR]

This paper studies a delayed rumor propagation model with logistic growth and saturation incidence. The next generation matrix method, some inequality techniques, the Lyapunov-LaSalle invariance principle, and the Lyapunov method are used in this paper. Our results indicate that if the basic regeneration number (which is analogous to the basic reproduction number in disease transmission models) is less than 1, the rumor-free equilibrium point (which is analogous to the disease-free equilibrium point in disease transmission models) is globally stable. If the basic regeneration number is greater than 1, then the rumor is permanent, and some sufficient conditions are obtained for local and global asymptotic stability of the rumor prevailing equilibrium point (which is analogous to the endemic equilibrium point in disease transmission models). Finally, three examples with numerical simulations are presented to illustrate the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the overflow oscillation elimination problem in the fixed-point two-dimensional (2D) digital filter (DF) based on Roesser model subjected to two's complement overflow (TCO) nonlinearities. By utilizing the system information and behavior of TCO nonlinearities more effectively, a new global asymptotic stability (GAS) criterion for 2D DFs is presented. A comparison of the obtained criterion with existing criteria is made with the help of examples. [ABSTRACT FROM AUTHOR]

In this paper, a nonlinear mathematical model for tuberculosis transmission, which incorporates multiple saturated exogenous reinfections, is proposed and explored. The existence of disease-free and endemic steady states is investigated. Disease-free equilibrium (DFE) is locally asymptotically stable (LAS) but not globally asymptotically stable (GAS) when the basic reproduction number, ℛ 0 < 1. However, it is GAS only when there is no exogenous reinfection. The local asymptotic stability and global asymptotic stability of the unique endemic equilibrium point (EEP) are established under certain conditions when ℛ 0 > 1. Further, the EEP is GAS when ℛ 0 > 1 , provided there is no exogenous reinfection. When ℛ 0 is below unity, the presence of multiple endemic equilibria is found which leads to backward bifurcation. It is demonstrated that the system encounters a Hopf-bifurcation when the transmission rate β crosses a critical value, resulting in the formation of limit cycles, i.e. periodic solutions bifurcate around the EEP when β passes a critical value. The stability and direction of Hopf-bifurcation are also studied. The results of the analytical work are validated through numerical simulations. A numerical simulation illustrates that EEP losses its stability via Hopf-bifurcation for specific parameters. However, when the bifurcation parameter β is increased further, the EEP regains its stability. In addition, Hopf-bifurcation occurs due to exogenous reinfection rates p and . Thus, our model shows some important nonlinear dynamical behaviors. [ABSTRACT FROM AUTHOR]

In this article, a reaction–diffusion model of HIV immunity with chemotaxis and absorption effect is constructed. The paper proves the existence and boundedness of the global classical solution of this mode when the chemotactic coefficient is kept in a suitable range. Five equilibrium points are established based on the different ranges of the basic regeneration number, two immune reproduction numbers and the immune competitive reproduction number. The global asymptotic stability of each equilibrium point is established by constructing an appropriate Lyapunov function when the chemotactic coefficient is kept in a small interval. [ABSTRACT FROM AUTHOR]

This paper investigates the global asymptotic stability problem for a class of quaternionvalued Takagi-Sugeno fuzzy BAM neural networks with time-varying delays. By applying Takagi-Sugeno fuzzy models, we first consider a general form of quaternion-valued Takagi-Sugeno fuzzy BAM neural networks with time-varying delays. Then, we apply the Cauchy-Schwarz algorithm and homeomorphism principle to obtain sufficient conditions for the existence and uniqueness of the equilibrium point. By utilizing suitable Lyapunov-Krasovskii functionals and newly developed quaternion-valuedWirtinger-based integral inequality, some sufficient criteria are obtained to guarantee the global asymptotic stability of the considered networks. Further, the results of this paper are presented in the form of quaternion-valued linear matrix inequalities, which can be solved using the MATLAB YALMIP toolbox. Two numerical examples are presented with their simulations to demonstrate the validity of the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, the mean square locally and globally asymptotic stability problem of discrete-time fractional order stochastic neural networks(DFOSNNs) with multiple time-varying delays are investigated. Firstly, the DFOSNNs model with multiple time-varying delays are established. Then, the general framework for the mixed delays Halanay-type inequality has been established with no harsh assumption. Further, the locally and globally asymptotic stability of DFOSNNs with multiple time-varying delays in mean square sense are proved via Halanay-type inequality respectively. In addition, the sufficient condition for globally asymptotic stability of DFOSNNs with multiple time-varying delays in mean square sense is derived via Lyapunov–Krasovskii functional method. From the results obtained in this paper, the two theorems of global asymptotic stability are complement each other. Finally, three numerical examples are given to show the validity of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we investigated a new heroin–cocaine epidemic model which incorporates spatial heterogeneity and nonlinear incidence rate. The main project of this paper is to explore the threshold dynamics in terms of the basic reproduction number $ \mathcal {R}_0 $ R 0 , which was defined by applying the next-generation operator. The threshold type results shown that if $ \mathcal {R}_0 \lt 1 $ R 0 < 1 , then the drug-free steady state is globally asymptotically stable. If $ \mathcal {R}_0 \gt 1 $ R 0 > 1 , then heroin–cocaine spread is uniformly persistent. Furthermore, the globally asymptotic stability of the drug-free steady state has been established for the critical case of $ \mathcal {R}_0=1 $ R 0 = 1 by analysing the local asymptotic stability and global attractivity. [ABSTRACT FROM AUTHOR]

Many phenomena in nature can be described by establishing differential equation models. To be more practical, we extend the instantaneous impulsive delay differential equations proposed by Faria and Oliveira to the non-instantaneous impulsive delay differential equations. This paper proposes a class of non-instantaneous impulsive delay differential equations which satisfy Yorke-type condition. With the help of the definitions of stability, sufficient conditions for stability and the global asymptotic stability of the zero solution of this model are given. Finally, we give some examples and numerical simulations. [ABSTRACT FROM AUTHOR]

Malaria is a fever condition that results from Plasmodium parasites, which are transferred to humans by the attacks of infected female Anopheles mosquitos. The deterministic compartmental model was examined using stability theory of differential equations. The reproduction number was obtained to be asymptotically stable conditions for the disease-free, and the endemic equilibria were determined. More so, the qualitatively evaluated model incorporates time-dependent variable controls which was aimed at reducing the proliferation of malaria disease. The reproduction number R o was determined to be an asymptotically stable condition for disease free and endemic equilibria. In this paper, we used various schemes such as Runge–Kutta order 4 (RK-4) and non-standard finite difference (NSFD). All of the schemes produce different results, but the most appropriate scheme is NSFD. This is true for all step sizes. Various criteria are used in the NSFD scheme to assess the local and global stability of disease-free and endemic equilibrium points. The Routh–Hurwitz condition is used to validate the local stability and Lyapunov stability theorem is used to prove the global asymptotic stability. Global asymptotic stability is proven for the disease-free equilibrium when R 0 ≤ 1 . The endemic equilibrium is investigated for stability when R 0 ≥ 1 . All of the aforementioned schemes and their effects are also numerically demonstrated. The comparative analysis demonstrates that NSFD is superior in every way for the analysis of deterministic epidemic models. The theoretical effects and numerical simulations provided in this text may be used to predict the spread of infectious diseases. [ABSTRACT FROM AUTHOR]

The Gilpin-Ayala (GA) ecosystem is one of the most important biological mathematical models. The exploration of various kinetics behaviours of GA-ecological model has attracted the attention of many mathematicians. This paper focuses on a nonlinear periodic GA-predation ecosystem with infinite distributed lags on time scales. In the sense of time scale, our model unifies the difference model and differential model of GA-predation ecosystem. We first discuss a class of auxiliary functions with only two real roots. By using these auxiliary functions, coincidence degree and some inequality techniques, we next obtain some existence conditions of periodic solution. Furthermore, we explore the global asymptotic stability of periodic solution on account of Lyapunov stability theory. An example and its simulation are provided to inspect the correctness and availability of our main results at last. [ABSTRACT FROM AUTHOR]

This paper investigates new sufficient conditions for the stability, asymptotic stability, and global asymptotic stability of nonlinear autonomous systems, specifically in cases where the first derivative of the Lyapunov function candidate may have both positive and negative values on its domain. The main contribution of this approach is the introduction of a new auxiliary function that relaxes the stability conditions, allowing the first derivative of the Lyapunov function candidate to be less than or equal to a nonnegative function. The suggested auxiliary function should be integrable within our first theorem. Meanwhile, our first corollary presents a technique that simplifies the task by establishing specific conditions related to differential inequalities. This weaker condition in the proposed results enables the establishment of stability properties in cases where the Lyapunov function candidate is not well chosen or finding a Lyapunov function is not straightforward. Additionally, it is proven that the original Lyapunov method for autonomous systems is a special case of our first theorem. Furthermore, it is demonstrated that assumptions in previous studies, such as Matrosov's theorem or results on higher-order derivatives of the Lyapunov function, guarantee the existence of our auxiliary function. Finally, lemmas are provided to construct these auxiliary functions, and examples are presented to demonstrate the effectiveness of this approach. This work will contribute to the development of stability analysis techniques for nonlinear autonomous systems. [ABSTRACT FROM AUTHOR]

In this paper, the impact of the strong Allee effect and ratio-dependent Holling–Tanner functional response on the dynamical behaviors of a predator–prey system is investigated. First, the positivity and boundedness of solutions of the system are proved. Then, stability and bifurcation analysis on equilibria is provided, with explicit conditions obtained for Hopf bifurcation. Moreover, global dynamics of the system is discussed. In particular, the degenerate singular point at the origin is proved to be globally asymptotically stable under various conditions. Further, a detailed bifurcation analysis is presented to show that the system undergoes a codimension- 1 Hopf bifurcation and a codimension- 2 cusp Bogdanov–Takens bifurcation. Simulations are given to illustrate the theoretical predictions. The results obtained in this paper indicate that the strong Allee effect and proportional dependence coefficient have significant impact on the fundamental change of predator–prey dynamics and the species persistence. [ABSTRACT FROM AUTHOR]

Space manipulators are expected to perform more challenging missions in on-orbit service (OOS) systems, but there are some unique characteristics that are not found on ground-based robots, such as dynamic coupling between space bases and manipulators, limited fuel supply, and working with unfixed bases. This paper focuses on trajectory-tracking control and internal force control for free-floating close-chain manipulators. First, the kinematics and dynamics of free-floating close-chain manipulators are given using the momentum conservation and spatial operator algebra (SOA) methodologies, respectively. Furthermore, an adaptive fuzzy integral sliding mode controller (AFISMC) based on time delay estimation (TDE) was designed for trajectory-tracking control, and a proportional-integral (PI) control strategy was adopted for internal force control. The global asymptotic stability of the proposed controller was proven by using the Lyapunov methodology. Three cases were conducted to verify the efficiency of the controller by using numerical simulations on two six-link manipulators with a free-floating base. The controller presents the desired tracking capability. [ABSTRACT FROM AUTHOR]

In this paper, a dynamic HIV model with cell-to-cell transmission, two immune responses, and induced apoptosis is proposed and studied. First, the non-negativity and boundedness of the solutions of the model are given, and then the exact expression of the basic reproduction number R0 is obtained by using the next generation matrix method. Second, criteria are obtained for the local stability of the disease-free equilibrium, immune response-free equilibrium, and the infected equilibrium with both humoral and cellular immune responses. Furthermore, the threshold conditions are also derived for the global asymptotic stability of the disease-free equilibrium, immune responsefree equilibrium, and the infected equilibrium with both humoral and cellular immune responses by constructing the suitable Lyapunov function. Finally, some numerical simulations are conducted to verify the theoretical results; the numerical simulation results show that the increase of apoptosis rate had a positive role in the control of viral infection. [ABSTRACT FROM AUTHOR]

In this paper, we study three stochastic two-species models. We construct the stochastic models corresponding to its deterministic model by introducing stochastic noise into the equations. For the first model, we show that the system has a unique global solution starting from the positive initial value. In addition, we discuss the extinction and the existence of stationary distribution under some conditions. For the second system, we explore the existence and uniqueness of the solution. Then we obtain sufficient conditions for global asymptotic stability of the equilibrium point and the positive recurrence of solution. For the last model, the existence and uniqueness of solution, the sufficient conditions for extinction and asymptotic stability and the positive recurrence of solution and weak persistence are derived. And numerical simulations are performed to support our results. [ABSTRACT FROM AUTHOR]

In this paper, experimental results about the performance of a Takagi–Sugeno Fuzzy Controller (TSFC) for an EV3 Ballbot Robotic System (EV3BRS) are reported. The physical configuration of the EV3BRS has the form of an inverted pendulum mounted on a ball. The EV3BRS is an underactuated robotic system with four outputs and two control torques. In this work, following the Takagi–Sugeno (TS) fuzzy control design methodology, the Parallel Distributed Compensation (PDC) approach is used in the design of the TSFC. The EV3BRS's TS Fuzzy Model (TSFM) design comes from linearization of the nonlinear model around two operation points near the upright position of EV3BRS's body. The Linear Matrix Inequality (LMI) approach was used to obtain the feedback gains for every local linear controller, guaranteeing, via a conservative stability condition, the global asymptotic stability of the overall fuzzy control system. The main goal of the control task consists of maintaining the EV3BRS's body at its upright position. Measurement and control data from and to the EV3BRS are transferred via telecontrol and telemetry. The appropriate performance of the controller design is corroborated via experimentation. [ABSTRACT FROM AUTHOR]

In this paper, an SEAI epidemic model with asymptomatic infection is studied under the background of mass transmission of COVID-19. First, we use the next-generation matrix method to obtain the basic reproductive number R 0 and calculate the equilibrium point. Secondly, when R 0 < 1 , the local asymptotic stability of the disease-free equilibrium is proved by Hurwitz criterion, and the global asymptotic stability of the disease-free equilibrium is proved by constructing the Lyapunov function. When R 0 > 1 , the system has a unique endemic equilibrium point and is locally asymptotically stable, and it is also proved that the system is uniformly persistent. Then, the application of optimal control theory is carried out, and the expression of the optimal control solution is obtained. Finally, in order to verify the correctness of the theory, the stability of the equilibrium point is numerically simulated and the sensitivity of the parameters of R 0 is analyzed. We also simulated the comparison of the number of asymptomatic infected people and symptomatic infected people before and after adopting the optimal control strategy. This shows that the infection of asymptomatic people cannot be underestimated in the spread of COVID-19 virus, and an isolation strategy should be adopted to control the spread speed of the disease. [ABSTRACT FROM AUTHOR]

We are concerned with the time-asymptotic stability of planar rarefaction wave to a non-conservative two-phase flow system described by two-dimentional compressible Euler and Navier-Stokes equations through drag force. In this paper, we show the planar rarefaction wave to a non-conservative compressible two-phase model is asymptotically stable under small initial perturbation in H³. The main difficulties overcome in this paper come from the non-viscosity of one fluid and the interaction between two fluids caused by drag force. The stability result is proved by the energy method. [ABSTRACT FROM AUTHOR]

This paper considers the dynamical properties of a space and time discrete fractional reaction–diffusion epidemic model, introducing a novel generalized incidence rate. The linear stability of the equilibrium solutions of the considered discrete fractional reaction–diffusion model has been carried out, and a global asymptotic stability analysis has been undertaken. We conducted a global stability analysis using a specialized Lyapunov function that captures the system's historical data, distinguishing it from the integer-order version. This approach significantly advanced our comprehension of the complex stability properties within discrete fractional reaction–diffusion epidemic models. To substantiate the theoretical underpinnings, this paper is accompanied by numerical examples. These examples serve a dual purpose: not only do they validate the theoretical findings, but they also provide illustrations of the practical implications of the proposed discrete fractional system. [ABSTRACT FROM AUTHOR]

In this paper, the finite difference scheme of the spatiotemporal fractional convection-diffusion equation is established, and its stability and convergence are proved. Furthermore, this discrete technique is extended to solve nonlinear spatiotemporal fractional convection-diffusion equations. By using the Krylov subspace method to solve the discrete system, the numerical solution of the spatiotemporal fractional convection-diffusion equation can be obtained quickly. In this paper, an efficient optimal control algorithm is proposed to solve the free control problem of a class of nonlinear time-delay systems. We obtained the optimal control law of the system through the Bellman optimality principle, obtained the asymptotic stability criterion of the system in the form of LMI under the optimal control input by using the Lyapunov stability theory, and discussed the effect of the delay parameter on the system stability. Using the principle of intelligent neural network approximation function, the evaluation neural network and the execution neural network are used to approximate the optimal performance index function and optimal control input, respectively, the optimal control strategy of the system is obtained, and the convergence of the weight estimation error is proved to be optimal. On the basis of optimal state adjustment, the optimal tracking control problem is further solved. Numerical example results verify the effectiveness of the proposed method in terms of stability analysis, optimal state control, and optimal tracking control for the nonlinear time-delay system proposed in this paper. We calculate the parameters of the conveyor and select a reasonable transmission and sorting mechanism to realize the speed regulation of the driving motor of each mechanism. Through the work of each part, the design scheme of the automatic transmission system is formed, and the reliability, practicability, and economy of the system are guaranteed. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of attitude trajectory tracking of rigid bodies subject to external disturbances. The attitude control problem has been studied in the last decades and novel solutions have been proposed. Nevertheless, most of the proposed controllers only achieve local or almost global asymptotic stability without considering external disturbances. Contrary to other works, we focus on the problem of achieving almost global exponential stability of the attitude tracking errors in the presence of external disturbances using continuous control laws. We propose an attitude trajectory tracking controller based on the exponential coordinates of rotation in combination with a disturbance observer that estimates the exogenous signals. To solve this problem, we adopt a hierarchical approach, where the proposed control law is divided into a kinematic controller (outer control loop) and a velocity tracking controller (inner control loop). To design the disturbance observer, it is assumed that exogenous signals can be generated by a linear exosystem, i.e. the magnitude and phase of the disturbance are unknown. The almost global exponential stability of the closed-loop dynamics' equilibrium point was proved by a strict Lyapunov function. The performance of the proposed approach is assessed by numerical simulations and experimental tests on a low-cost quadrotor. [ABSTRACT FROM AUTHOR]

In this paper, a generalized fractional three-species food chain model with delay is investigated. First, the existence of a positive equilibrium is discussed, and the sufficient conditions for global asymptotic stability are given. Second, through selecting the delay as the bifurcation parameter, we obtain the sufficient condition for this non-control system to generate Hopf bifurcation. Then, a nonlinear delayed feedback controller is skillfully applied to govern the system's Hopf bifurcation. The results indicate that adjusting the control intensity or the control target's age can effectively govern the bifurcation dynamics behavior of this system. Last, through application examples and numerical simulations, we confirm the validity and feasibility of the theoretical results, and find that the control strategy is also applicable to eco-epidemiological systems. [ABSTRACT FROM AUTHOR]

The paper studies a class of nonlinear disturbed neutral linear fractional systems with derivatives in the the Riemann–Liouville sense and distributed delays. First, it is proved that the initial problem for these systems with discontinuous initial functions under some natural assumptions possesses a unique solution. The assumptions used for the proof are similar to those used in the case of systems with first-order derivatives. Then, with the obtained result, we derive the existence and uniqueness of a fundamental matrix and a generalized fundamental matrix for the homogeneous system. In the linear case, via these fundamental matrices we obtain integral representations of the solutions of the homogeneous system and the corresponding inhomogeneous system. Furthermore, for the fractional systems with Riemann–Liouville derivatives we introduce a new concept for weighted stabilities in the Lyapunov, Ulam–Hyers, and Ulam–Hyers–Rassias senses, which coincides with the classical stability concepts for the cases of integer-order or Caputo-type derivatives. It is proved that the zero solution of the homogeneous system is weighted stable if and only if all its solutions are weighted bounded. In addition, for the homogeneous system it is established that the weighted stability in the Lyapunov and Ulam–Hyers senses are equivalent if and only if the inequality appearing in the Ulam–Hyers definition possess only bounded solutions. Finally, we derive natural sufficient conditions under which the property of weighted global asymptotic stability of the zero solution of the homogeneous system is preserved under nonlinear disturbances. [ABSTRACT FROM AUTHOR]

Modern social networks are especially beneficial for spreading rumors since they perform as multichannel communication platforms. The spread of false information has a detrimental impact on people, communities, and businesses. Media reports significantly affect rumor propagation by providing inhibiting factors. In this paper, we propose a new ISCRM fractional-order model to analyze the law of rumor propagation and provide appropriate control strategies. First, under fractional differential equations, the boundedness and non-negativeness of the solutions are obtained. Second, the local and global asymptotic stability of the rumor-free equilibrium and rumor-permanence equilibrium are proved. Third, employing Pontryagin's maximum principle, the conditions necessary for fractional optimum control are derived for the rumor model, and the optimal solutions are analyzed. Finally, several numerical simulations are presented to verify the accuracy of the theoretical results. For instance, while media reports can mitigate the propagation of rumors across various dynamic regions, they are unable to completely restrain rumor spread. [ABSTRACT FROM AUTHOR]

This paper focuses on the global asymptotic stability (GAS) problem for Takagi–Sugeno (T-S) fuzzy quaternion-valued bidirectional associative memory neural networks (QVBAMNNs) with discrete, distributed and leakage delays by using non-separation method. By applying T-S fuzzy model, we first consider a general form of T-S fuzzy QVBAMNNs with time delays. Then, by constructing appropriate Lyapunov–Krasovskii functionals and employing quaternion-valued integral inequalities and homeomorphism theory, several delay-dependent sufficient conditions are obtained to guarantee the existence and GAS of the considered neural networks (NNs). In addition, these theoretical results are presented in the form of quaternion-valued linear matrix inequalities (LMIs), which can be verified numerically using the effective YALMIP toolbox in MATLAB. Finally, two numerical illustrations are presented along with their simulations to demonstrate the validity of the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, we present a survey about the latest results in global stability concerning the discrete-time evolutionary Ricker competition model with n species, in both, autonomous and periodic models. The main purpose is to convey some arguments and new ideas concerning the techniques for showing global asymptotic stability of fixed points or periodic cycles in these kind of discrete-time models. In order to achieve this, some open problems and conjectures related to the evolutionary Ricker competition model are presented, which may be a starting point to study global stability, not only in other competition models, but in predator–prey models and Leslie–Gower-type models as well. [ABSTRACT FROM AUTHOR]

This paper presents an SIQR patch model that combines population migration and entry–exit screening. The threshold for disease extinction is determined using the next-generation matrix method. By constructing the Lyapunov function, the global asymptotic stability of the disease-free equilibrium is demonstrated when R0 < 1. The local asymptotic stability of the endemic equilibrium is shown using the Hurwitz criterion, and it is found that the disease is uniformly persistent when R0 > 1. The influence of screening and migration on disease dynamics is discussed via numerical simulations. Our findings highlight the significance of the detection rate as a vital index in disease transmission and emphasize the effectiveness of screening strategies in preventing outbreaks. Therefore, during an outbreak, it is recommended to establish checkpoints in regions with high mobility to identify and isolate potentially infected individuals, thereby reducing the widespread dissemination of the pandemic. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the global asymptotic stability of an age-structured population dynamics model with a Ricker's type of birth function. This model is a hyperbolic partial differential equation with a nonlinear and nonlocal boundary condition. We prove a uniform persistence result for the semiflow generated by this model. We obtain the existence of global attractors and we prove the global asymptotic stability of the positive equilibrium by using a suitable Lyapunov functional. Furthermore, we prove that our global asymptotic stability result is sharp, in the sense that Hopf bifurcation may occur as close as we want from the region global stability in the space of parameter. [ABSTRACT FROM AUTHOR]

This paper is concerned with the Hall effect on the asymptotic stability of the global solutions to an initial-boundary value problem of the planar compressible MHD system. In the case when the heat conductivity depends on the temperature in the form κ (θ) = θ β with β ∈ (0 , + ∞) , we show that the global large solutions decay exponentially in time to the equilibrium states without any restriction on the Hall coefficient ε . The exponential stability of the global large solutions still holds when the heat conductivity is a positive constant, provided the Hall coefficient is suitably small. As by-products, the vanishing limit of Hall coefficient is also justified in both cases. [ABSTRACT FROM AUTHOR]

Purpose: Aiming at the problems of the strong nonlinearity, multivariable strong coupling and uncertainty parameters in the nonlinear hydro-turbine governing system, this paper proposes a neural network-based dynamic surface sliding mode fault-tolerant control method to improve the fault information monitoring and tracking control performance of hydro-turbine governing system. Methods: Firstly, the mathematical model of the nonlinear hydro-turbine governing system is simplified as a strict feedback form. The first-order pade approximation strategy is introduced, which transforms the delayed input in the transfer function into a first-order inertial link by Taylor series expansion. Secondly, based on the neural network technology, the virtual control quantity and the actual control quantity are designed by combining the dynamic surface control and the sliding mode control algorithm, respectively. Results: Finally, according to the Lyapunov function stability theorem, the global asymptotic stability of a closed-loop control system including dynamic surface inversion faulttolerant controller based on neural network is guaranteed. To verify the effectiveness and robustness of the proposed control algorithm, time-varying gain-bias faults and input time-varying delay are considered. Conclusion: The simulation results demonstrate that the generator powers angle quickly reaches stability in a short time and has a small overshoot in the existence of the actuator faults and input time-delay, which is much less than the adjustment time required by the sliding mode control and backstepping sliding mode fault-tolerant control algorithms. Therefore, we concluded that the comparison of control performance to illustrate the effectiveness and superiority of the proposed control approach. [ABSTRACT FROM AUTHOR]

This paper is concerned with the global asymptotic stability (GAS) problem of fixed-point Lipschitz nonlinear digital filters employing 2's complement overflow arithmetic. Nonlinear digital filtering finds immense applications in various fields such as adaptive systems and controllers, digital controllers and observers for nonlinear systems, realization of neural networks using digital hardware, controllers for feedback linearization, etc. Lipschitz nonlinear digital filter is considered in this paper as it is frequently employed in nonlinear digital filtering, state filtering, neural networks, feedback control, digital controllers, decision-taking systems and so on. Based on Lyapunov theory, the property of 2's complement overflow arithmetic and Lipschitz condition associated with system nonlinearities, a new criterion for the suppression of overflow oscillations in 2's complement state variable realizations of digital filters is established. Several examples along with simulation results are provided to highlight the utility of the criterion. [ABSTRACT FROM AUTHOR]

This paper investigates the global asymptotic stability problem for a class of Takagi-Sugeno fuzzy Clifford-valued delayed neural networks with impulsive effects and leakage delays using the system decomposition method. By applying Takagi-Sugeno fuzzy theory, we first consider a general form of Takagi-Sugeno fuzzy Clifford-valued delayed neural networks. Then, we decompose the considered n -dimensional Clifford-valued systems into 2 m n -dimensional real-valued systems in order to avoid the inconvenience caused by the non-commutativity of the multiplication of Clifford numbers. By using Lyapunov-Krasovskii functionals and integral inequalities, we derive new sufficient criteria to guarantee the global asymptotic stability for the considered neural networks. Further, the results of this paper are presented in terms of real-valued linear matrix inequalities, which can be directly solved using the MATLAB LMI toolbox. Finally, a numerical example is provided with their simulations to demonstrate the validity of the theoretical analysis. This paper investigates the global asymptotic stability problem for a class of Takagi-Sugeno fuzzy Clifford-valued delayed neural networks with impulsive effects and leakage delays using the system decomposition method. By applying Takagi-Sugeno fuzzy theory, we first consider a general form of Takagi-Sugeno fuzzy Clifford-valued delayed neural networks. Then, we decompose the considered -dimensional Clifford-valued systems into -dimensional real-valued systems in order to avoid the inconvenience caused by the non-commutativity of the multiplication of Clifford numbers. By using Lyapunov-Krasovskii functionals and integral inequalities, we derive new sufficient criteria to guarantee the global asymptotic stability for the considered neural networks. Further, the results of this paper are presented in terms of real-valued linear matrix inequalities, which can be directly solved using the MATLAB LMI toolbox. Finally, a numerical example is provided with their simulations to demonstrate the validity of the theoretical analysis. [ABSTRACT FROM AUTHOR]

The goal of this paper is to establish a general framework for the development of small- or medium-sized enterprises' (SMEs) growth path by using star-coupled stochastic dynamic system approach. The dynamic behaviors are related to the stochastic resonance (SR) phenomenon subject to multiplicative fluctuation and periodic force which could be interpreted as uncertain environments faced by SMEs (enterprises) during their growth process. The multiplicative noise is modeled as dichotomous noise (uncertainty under the innovation and capital paradigm) and the memory of risk environments is characterized by using fractional kernel function. By using the mathematical derivation, the analytical expressions for the first moment of the steady state response, the stability in the long-time limit in terms of (enterprises) systems' asymptotic stability is obtained. Theoretic and simulation results show the nonmonotonic dependence between the output gain and the input signal frequency, noise parameters for SMEs dynamic behaviors. Furthermore, the fluctuation noise, the number of related parties (partners) for SMEs, and the fractional-order work together, producing more complex dynamic phenomena compared with the traditional integral-order systems (for enterprises). Finally, theoretical analyses with corresponding numerical simulations results established in this paper would provide a possible fundamental mathematical framework for the study of Schumpeter's theory on the development for SMEs' growth under the "innovation and capital paradigm" and related disciplines. In particular, the framework allows us, for the first time, to logically conclude that "in general, the ratio for SMEs' growth successfully is around less than one-third", this is actually consistent with what the market has been observing commonly in general. [ABSTRACT FROM AUTHOR]

This paper deals with the global boundedness and asymptotic stability of the solution of the two-predator and one-prey systems with density-dependent motion in a n-dimensional bounded domain with Neumann boundary conditions. In a previous paper, Qiu et al. (J Dyn Differ Equ, 1–25, 2021) proved the global existence and uniform boundedness of classical solution by limiting the conditions on motility functions and the coefficients of logistic source. By contrast, we relax the limitation conditions in Qiu et al. (2021) by constructing the weight function. Moreover, under diverse competition circumstances, the global stabilities of nonnegative spatially homogeneous equilibria for the special model are established. [ABSTRACT FROM AUTHOR]

This paper deals with the diffusive epidemic model with saturated incidence and logistic growth, ∂S/∂t = dSΔS - βSI/1 + αI + rS (1 - S/K), x ∈ Ω, t > 0, ∂I/∂t = dIΔI - βSI/1 + αI - γS, x ∈ Ω, t > 0, where Ω ⊂ ℝN (N ∈ ℕ) is a bounded domain with smooth boundary and dS, dI, K, r, α, β, γ > 0 are constants. Setting R0 := Kβ/γ, Avila-Vales et al. [1] succeeded in showing that if R0 ≤ 1, then the disease-free equilibrium (K, 0) of the model with saturated treatment is globally asymptotically stable, whereas in the case R0 > 1 the model admits a constant endemic equilibrium (S*, I*) (S*, I * > 0), and it is unknown whether (S*, I*) is globally asymptotically stable or not. The purpose of this paper is to establish that the constant endemic equilibrium of the above model is globally asymptotically stable by constructing a strict Lyapunov functional. The construction is carried out by optimizing a function of two real variables through straightforward calculations, division into some cases and arrangement of several conditions. Moreover, to show that the functional is strict, some auxiliary function is introduced. [ABSTRACT FROM AUTHOR]

In this paper, a class of Clifford-valued neutral fuzzy neural-type networks with proportional delay and D operator and whose self feedback coefficients are also Clifford numbers are considered. By using the Banach fixed point theorem and some differential inequality techniques, we directly study the existence and global asymptotic stability of pseudo almost periodic solutions by not decomposing the considered Clifford-valued systems into real-valued systems. Finally, two examples are given to illustrate our main results. Our results of this paper are new. [ABSTRACT FROM AUTHOR]

This paper deals with the global asymptotic stability (GAS) of the fixed-point two-dimensional (2D) Lipschitz nonlinear digital filter (LNDF) in Fornasini–Marchesini second local state-space (FMSLSS) model with 2's complement overflow. In particular, the 2D system under study involves intrinsic system nonlinearities as well as nonlinearities due to overflow. New conditions for verifying the GAS of such LNDFs is developed in this paper. The criterion utilizes Lyapunov method and the properties of overflow arithmetic and Lipschitz nonlinearities. A criterion for the overflow stability of 2D systems (without intrinsic system nonlinearities) is also brought out. The obtained criteria are also applicable to digital filters with other frequently used overflow arithmetic (namely, saturation, zeroing, and triangular). The results presented in this paper can be used directly as criteria for elimination of overflow oscillations in 2D systems. The obtained results are compared with existing results. [ABSTRACT FROM AUTHOR]

This paper focuses on the S-asymptotically Periodic oscillation for a type of fractional-order fuzzy Cohen-Grossberg neural networks (CGNNs) by employing some properties of Mittag-Leffler mappings and fixed point theorems. Further, the global asymptotic stability of CGNNs is received. For CGNNs, our works in this paper not only enrich its theoretical achievements, but also expand its application scope. [ABSTRACT FROM AUTHOR]

A nonlinear infectious disease model with information-influenced vaccination behavior and contact patterns is proposed in this paper, and the impact of information related to disease prevalence on increasing vaccination coverage and reducing disease incidence during the outbreak is considered. First, we perform the analysis for the existence of equilibria and the stability properties of the proposed model. In particular, the geometric approach is used to obtain the sufficient condition which guarantees the global asymptotic stability of the unique endemic equilibrium E e when the basic reproduction number R 0 > 1. Second, mathematical derivation combined with numerical simulation shows the existence of the double Hopf bifurcation around E e . Third, based on the numerical results, it is shown that the information coverage and the average information delay may lead to more complex dynamical behaviors. Finally, the optimal control problem is established with information-influenced vaccination and treatment as control variables. The corresponding optimal paths are obtained analytically by using Pontryagin's maximum principle, and the applicability and validity of virous intervention strategies for the proposed controls are presented by numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper, we study the semi-cycle analysis of positive solutions and the asymptotic behavior of positive solutions of three-dimensional system of difference equations with a higher order under certain parametric conditions. Furthermore, we show the boundedness and persistence, the rate of convergence of the solutions and the global asymptotic stability of the unique equilibrium point of the proposed system under certain parametric conditions. Finally, for this system, we offer some numerical examples which support our analytical results. [ABSTRACT FROM AUTHOR]

In this paper, we will revisit the model studied in Lou and Zhao (J Math Biol 62:543–568, 2011), where the model takes the form of a nonlocal and time-delayed reaction–diffusion model arising from the fixed incubation period. We consider the infection age to be a continuous variable but without the limitation of the fixed incubation period, leading to an age-space structured malaria model in a bounded domain. By performing the elementary analysis, we investigate the well-posedness of the model by proving the global existence of the solution, define the explicit formula of basic reproduction number when all parameters remain constant. By analyzing the characteristic equations and designing suitable Lyapunov functions, we also establish the threshold dynamics of the constant disease-free and positive equilibria. Our theoretical results are also validated by numerical simulations for 1-dimensional and 2-dimensional domains. [ABSTRACT FROM AUTHOR]