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The rapid depletion of fossil fuels, oil, and natural gas due to their excessive use is a source of motivation for finding alternative solutions. Global warming is also an important issue caused by the emission of harmful gases. Consequently, extensive research has been conducted on Fuel Cell-based Hybrid Electric Vehicles (FCEVs) to address the twin challenges of resource depletion and harmful emissions. This study presents a novel model comprising of four sources i.e. Fuel Cell (FC), Photo Voltaic panel (PV), battery, and Supercapacitor (SC). The Proton exchange membrane fuel cell (PEMFC) in which hydrogen is used as fuel is the primary source whereas the other three sources act as secondary sources. These sources are interconnected via DC converters to a DC bus. To regulate this Hybrid Energy Storage System (HESS), a Super-Twisting Sliding Mode Controller (ST-SMC) has been developed, ensuring global stability through the application of Lyapunov criteria. In addition, the proposed controller is compared with a conventional Sliding Mode Controller (SMC) and Integral Sliding Mode Controller (ISMC). Both simulation (MATLAB/Simulink 2021b) and hardware tests (MicroLabBox dSPACE RTI1202) confirm the system's stability, resilience, and efficient functionality across various dynamic scenarios. Comparative analysis between the three demonstrates the superiority of ST-SMC over the SMC and ISMC, as verified by the results. [Display omitted] • Proposed of a novel multi power source-based hybrid energy storage system for electric vehicles. • Design of Super Twisting Sliding Mode Controller. • Comparative assessment with conventional Sliding Mode Controller and Integral Sliding Mode Controller. • Systems global asymptotic stability assurance through Lyapunov criteria. • Validation using both simulation and hardware results. [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]

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]

This paper presents a study on a Lotka-Volterra ammensalism model that incorporates the fear effect, which can potentially decrease the birth rate and raise the mortality rate of the species. For the autonomous case, equilibrium points' local and global stability are discussed. For the nonautonomous case, sufficient conditions which ensure the persistence and extinction, and global asymptotic stability of the positive solutions are obtained, respectively. The study has shown that with the increase of the fear effect, the final density of the affected population will decrease, and when the fear effect is large enough, it will cause population's extinction. [ABSTRACT FROM AUTHOR]

This work investigates the dynamics of discrete reaction-diffusion Gierer-Meinhardt system as mathematical models of biological pattern formation. We study the system's local asymptotic behaviour with and without the diffusion once developing the discrete integer variant of the well-known Gierer-Meinhardt model and proving that the model has a unique equilibrium. The requirements for the steady-state solution's local and global stability are found with the help of relevant approaches and the Lyapunov technique. Two large biological models and simulations are used throughout the work to validate the utility of the suggested technique. [ABSTRACT FROM AUTHOR]

This paper proposes a two-dimensional modified Leslie–Gower predator–prey model with carry-over effects, fear, prey protection and additional food, including prey harvesting. For this, it assumes the carry-over effect with delay incorporated in the birth rate of the prey population and gestation delay in Leslie–Gower term of a predator, and supposes that the predator consumes the prey according to Holling type II functional response. This dynamical system is split into two groups, namely non-delayed and delayed systems, respectively. In the non-delayed system, first, we discuss positivity, boundedness solutions, and the existence of equilibria, especially finding the coexistence of interior equilibrium points under certain conditions. After that, local and global stabilities are systematically analyzed. In addition, we obtain the conditions of Hopf-bifurcation in terms of the growth rate of prey species, prey protection and preference rate of predator for the non-delayed system. Whereas in the delayed system, both the delays have an essential role in governing the dynamical system discussed in three cases, and each case found the Hopf-bifurcation parameters for which the system changes stability behavior into instability. At last, the numerical simulations have been carried out to verify the theoretical findings. [ABSTRACT FROM AUTHOR]

The virus infections pose a significant threat to human health, necessitating a profound comprehension of these diseases to effectively manage epidemics and avert fatalities. This study delves into a comprehensive analysis of a mathematical model that incorporates the age of infection and distributed time delays in the context of pathogenic epidemics. The framework of this model accommodates the nonlocal diffusion of the pathogen within cells. Our investigation showcases the well‐posed nature of the model and establishes the compactness of the solutions. We derive the basic reproduction number, denoted as R0$$ {R}_0 $$, and substantiate that when R0$$ {R}_0 $$ is less than 1, the disease‐free equilibrium (E0$$ {E}^0 $$) achieves global asymptotic stability. Furthermore, we construct a global attractor within a bounded set and affirm the existence of the complete trajectory (ψ$$ \psi $$). This research also delves into scenarios where R0$$ {R}_0 $$ surpasses 1, illustrating the presence of the endemic steady state (E∗$$ {E}^{\ast } $$) through the utilization of super‐subsolutions. We establish the globally asymptotic stability of E∗$$ {E}^{\ast } $$ for cases where R0$$ {R}_0 $$ is greater than 1 by employing a well‐suited Lyapunov function. To validate the robustness of our mathematical computations, we conclude by presenting a set of numerical results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the asymptotic behavior of a modified chemostat model. We first demonstrate the existence of equilibria. Then, we present a mathematical analysis for the model, the invariance, the positivity, the persistence of the solutions, and the asymptotic global stability of the interior equilibrium. Some numerical simulations are carried out to illustrate the main results. [ABSTRACT FROM AUTHOR]

In this paper, we propose a diffusive prey-predator model with saturated hunting cooperation and predator-taxis. We first establish the global classical solvability and boundedness, and provide some sufficient conditions to assure the existence of a unique positive homogeneous steady state and the global uniform asymptotic stability of the predator-free homogeneous steady state. Secondly, we study the pattern formation mechanism and reveal that pattern formation is driven by the joint effect of predator-taxis, hunting cooperation, and slow diffusivity of predators. Moreover, we find that a strong predator-taxis can annihilate the spatiotemporal patterns, but a weak predator-taxis supports the pattern formation when diffusion-driven instability is present in the model without predator-taxis. However, if diffusion-driven instability is absent, predator-taxis cannot destabilize the unique positive spatially homogeneous steady state. Additionally, we highlight that spatially heterogeneous steady states do not exist when the diffusion coefficient ratio of predators to prey is sufficiently large under specific parametric conditions. To explore the various types of spatially heterogeneous steady states, we derive amplitude equations based on the weakly nonlinear analysis theory. Finally, numerical simulations, including the hexagonal pattern, stripe pattern, a mixed pattern combining hexagons and stripes, and the square pattern, are presented to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

In this study, a mathematical model for the transmission dynamics of malaria among different socioeconomic groups in the human population interacting with a susceptible-infectious vector population is presented and analysed using a fractional-order derivative of the Caputo type. The total human population is stratified into two distinguished classes of lower and higher income individuals, with each class further subdivided into susceptible, infectious, and recovered populations. The socio hierachy-structured fractional-order malaria model is analyzed through the application of different dynamical system tools. The theory of positivity and boundedness based on the generalized mean value theorem is employed to investigate the basic properties of solutions of the model, while the Banach fixed point theory approach is used to prove the existence and uniqueness of the solution. Furthermore, unlike the existing related studies, comprehensive global asymptotic dynamics of the fractional-order malaria model around both disease-free and endemic equilibria are explored by generalizing the usual classical methods for establishing global asymptotic stability of the steady states. The asymptotic behavior of the trajectories of the system are graphically illustrated at different values of the fractional (noninteger) order. [ABSTRACT FROM AUTHOR]

This paper is concerned with a cross-diffusion tumor invasion model with double-taxis effect. We first investigate the global existence of classical solutions of this model in two-dimensional space. The essential difficulty lies in the second-level taxis effect of immune cells on tumor cells, where chemotactic factor (tumor cells) exhibit their own taxis behavior, the double-taxis effect makes us have to use more detailed analysis and calculation, and some new estimation techniques are used. Subsequently, we also investigate the stability of some equilibria. For small proliferation coefficient, we prove the global asymptotic stability or local asymptotic stability of a semitrivial equilibrium point. While, for the other equilibria, the stability analysis is complicated even for some special cases, and both the double chemotactic coefficients will affect the stability of the solution. [ABSTRACT FROM AUTHOR]

We investigate the influence of streamwise-elongated and spanwise-periodic roughness arrays on the supersonic boundary-layer instability under the assumption of a high Reynolds number. The main focus is on the lower-branch viscous instability modes, and the spanwise spacing of the roughness arrays is taken to be comparable to the characteristic wavelength of the modes (which is on the triple-deck scale), so that most significant effects can be generated. The streamwise length scale of the elements is much greater than the spanwise length scale. The roughness height is determined by requiring the change of the wall shear to be O(1). The equations governing the nonlinear roughness-induced streaky flow are deduced from the standard triple-deck theory. These equations are parabolic in the streamwise direction and are solved using a streamwise marching method to characterize the evolution of streaky structures. The linear stability of the streaky flow is analyzed. By exploiting the asymptotic structure, the bi-global eigenvalue problem is reduced to a one-dimensional one, where the stability is found to be controlled by the spanwise-dependent wall shear. The reduced eigenvalue problem is solved numerically. The results show that roughness arrays inhibit instability modes with moderate frequencies but promote high-frequency modes. Roughness elements of greater height have stronger effects on the linear stability. The shape of roughness elements plays an important role. A significant feature, different from the subsonic case, is that fundamental and superharmonic resonance modes radiate sound waves spontaneously into the far field. [ABSTRACT FROM AUTHOR]

This work is devoted to investigate the global asymptotic stability of equilibriums for a reaction–diffusion susceptible-infected-susceptible (SIS) epidemic model with spatial heterogeneity and mass-action-type nonlinearity. By discretizing the spatial variables of the model, first, Lyapunov functions are constructed for the corresponding ordinary differential equations (ODEs) model of the original SIS PDEs model, and then the construction method is generalized to the PDEs model in which either the susceptible or the infectious individuals are spreading in spatial heterogeneity environment. For both the cases, we obtained the standard threshold dynamics results. [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]

This paper addresses the electromagnetic separation problem for mass-unknown spacecraft in elliptical orbits that play a significant role in on-orbit assembly and other future space missions. First, the relative motion dynamics model between the platform (target spacecraft) and module (chaser spacecraft) is presented with the lumped disturbance resulting from external disturbances, elliptical eccentricity and unknown mass, and a compliant reference trajectory is designed by applying the idea of trigonometric-function. Then, an improved sliding mode controller is developed to ensure that the tracking errors of relative motion can converge to near the equilibrium point. In order to avoid adverse impacts, the elliptical eccentricity and unknown mass are fully considered by using the developed control approach, and the global asymptotic stability of the closed-loop system is analyzed by strict theoretical proof. Combined with spacecraft electromagnetic docking technology, the electromagnetic separation scheme can make on-orbit assembly easy to achieve with certain advantages, e.g., it doesn't consume propellant and thus doesn't cause plume contamination, and has reversible, continuous and non-contact characteristics. Finally, numerical simulations are performed to illustrate the effectiveness and feasibility of the developed control approach. [ABSTRACT FROM AUTHOR]

This paper investigates a two-species amensalism model that includes the fear effect on the first species and the Beddington–DeAngelis functional response. The existence and stability of possible equilibria are investigated. Under different parameters, there exist two stable equilibria which means that this model is not always globally asymptotically stable. Together with the existence of all possible equilibria and their stability, saddle connection and close orbits, we derive some conditions for transcritical bifurcation and saddle-node bifurcation. Furthermore, global dynamics analysis of the model is performed. It is observed that under certain parameter conditions, when the intensity of the fear effect is below a certain threshold value, as the fear effect increases it will only reduce the density of the first species population and will have no influence the extinction or existence of the first species population. However, when the fear effect exceeds this threshold, the increase of the fear effect will accelerate the extinction of the first species population. Finally, numerical simulations are performed to validate theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we propose and study a discretized one‐predator two‐prey system along with prey refuge and Michaelis–Menten‐type prey harvesting. The interaction among the species is considered as Holling type III functional response. Firstly, existence and local stability of all the fixed points are derived under certain parametric conditions. Furthermore, a special consideration is made to global asymptotic stability of the interior fixed point. Then, we have shown that the system undergoes different types of bifurcations including transcritical bifurcation, flip bifurcation, and Neimark–Sacker bifurcation by using center manifold theorem, bifurcation theory, and normal form method. Also, Feigenbaum's constant of the system is calculated. It is observed that both harvesting and refuge have a stabilizing effect on the system, and the stabilizing effect of harvesting dominates the stabilizing effect of refuge. Of most interest is the finding of coexisting attractors and multistability. In particular, optimal harvesting policy has been obtained by extension of Pontryagin's maximum principle to discrete system. Finally, some intriguing numerical simulations are provided to verify our analytic findings and rich dynamics of the three species system. [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]

Terrorist activity in the Sahel region has been on the increase for almost a decade. Groups advocating extremist ideologies with a political or religious base are carrying out attacks against states with the aim of imposing a totalitarian ideology, sometimes against a backdrop of political crisis and famine. In this state of crisis and sometimes communal conflict, it is questionable whether ideological terrorism can really be eradicated in the Sahel. In this study, we develop a model of the dynamics of ideological terrorism based on the terrorism situation in the Sahel. In particular, this model incorporates popular resistance to terrorism through the class of volunteers for the defense of the homeland, but we also take into account the indoctrination of certain sections of the population vulnerable to fanatical ideology. We estimate R0, the number of elementary replications of extremist behavior, which enables us to predict the evolution of extremism. We also identify four thresholds R1, R2, R3 and R4 of sufficient conditions for the eradication of ideological terrorism and brigandage. A multi-objective optimal control of a counter-terrorism strategy is also presented. Finally, we perform a numerical simulation of the analysis and control results to test our hypotheses. [ABSTRACT FROM AUTHOR]

This research relies on several kinds of Volterra-type integral differential systems and their associated stability concerns under the impulsive effects of the Volterra integral terms at certain time instants. The dynamics are defined as delay-free dynamics contriobution together with the contributions of a finite set of constant point delay dynamics, plus a Volterra integral term of either a finite length or an infinite one with intrinsic memory. The global asymptotic stability is characterized via Krasovskii–Lyapuvov functionals by incorporating the impulsive effects of the Volterra-type terms together with the effects of the point delay dynamics. [ABSTRACT FROM AUTHOR]

It is beyond dispute that cytotoxic T-lymphocytes (CTLs) exert a vital function in the host's antiviral defense mechanism. With the idea of the above factor and the logistic proliferation of CD4 + T-cells, we establish a HTLV-I (human T-cell leukemia virus type-I) mathematical model. First, two threshold parameters ℛ 0 and ℛ c (the basic reproduction numbers for viral infection and CTL immune response, respectively) are obtained. Second, sufficient criteria for local and global asymptotic stabilities of the feasible equilibria of the model are deduced, respectively. Third, the sensitivity analyses of ℛ 0 and ℛ c are performed to better understand the effective strategies for HTLV-I infection. Finally, not only numerical simulations are given to illustrate the stability conclusions, but also the biological significance is stated. [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]

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]

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]

We consider a general impulsive reaction-diffusion equation with shifting environment and birth pulse, both induced by climate changes, to capture essential features of the dynamics of species exhibiting distinct stages of reproduction and dispersal. We convert this model into a discrete-time semiflow, and hence to a discrete-time recursion system. We establish the existence of forced waves and asymptotic spreading properties of solutions, and obtain sufficient conditions for the global asymptotic stability of the forced waves. [ABSTRACT FROM AUTHOR]

A new viral infection model with cell-to-cell infection and periodic antiretroviral therapy was proposed and analyzed. With the help of defined basic reproduction number ℜ 0 , we proved that if ℜ 0 < 1 , then the infection-free steady state is globally attractive. If ℜ 0 > 1 , then the infection is uniformly persistent. Furthermore, the globally asymptotical stability of infection-free steady state has been established for the critical case of ℜ 0 = 1. Also, the global asymptotic stability of the infection steady state for a special case of the model has been established by applying the method of Lyapunov. Numerical simulations show that increasing the drug efficacy for blocking virus-to-cell infection, cell-to-cell infection and producing non-infectious virus contributes to weakening the severity of viral infection. [ABSTRACT FROM AUTHOR]

In this paper, an anti-unwinding adaptive robust backstepping control law is proposed to solve the attitude control problem of rigid spacecraft with external disturbances and inertia uncertainties. A new variable based on hyperbolic sine functions is designed to prevent the unwinding phenomenon, and then a novel robust backstepping controller is developed. Initially, a nonlinear tracking law is designed to obtain the desired angular velocity and to ensure that the attitude maneuvering system could have two equilibrium points. Subsequently, an adaptive robust control law is devised, which incorporates the adaptive estimation method to update the inertial parameters in real-time. Moreover, the bounded external disturbances are taken into account in the design of the control law, and thus the robustness of the attitude control system is improved. Furthermore, the global asymptotic stability of the attitude control system is verified by the Lyapunov-Krasovskii theorem. Finally, numerical simulations are carried out to demonstrate the effectiveness and robustness of the proposed control law, as well as the anti-unwinding characteristics are perfectly validated during the attitude maneuver of rigid spacecraft. [ABSTRACT FROM AUTHOR]

In this article, the tracking control problem for a class of nonlinear time‐delay systems is investigated. In particular, a new methodology for the design and the digital implementation of observer‐based tracking controllers is provided for a class of control‐affine nonlinear systems with state delays. First, a procedure for the design of continuous‐time observer‐based tracking controllers ensuring the global asymptotic stability of the corresponding closed‐loop tracking error system is provided for the considered class of systems. Then, sufficient conditions are provided for the existence of a suitably fast sampling and of an accurate quantization of the input/output channels such that the digital implementation of the proposed continuous‐time observer‐based tracking controller ensures the semi‐global practical stability property of the related sampled‐data quantized closed‐loop tracking error system, with arbitrarily small final target ball of the origin. Moreover, it is shown that, in the special case of delay‐free nonlinear systems, the sufficient conditions provided for the digital implementation of the proposed continuous‐time observer‐based tracking controller can be strongly relaxed. In the theory here developed, time‐varying sampling periods and nonuniform quantization of the input/output channels are taken into account. The proposed results are validated through examples concerning a class of neural networks systems and a class of time‐delay systems including, as a special case, a delay‐free actuated inverted pendulum. [ABSTRACT FROM AUTHOR]

A nonlinear optimal (H-infinity) control approach is proposed for the dynamic model of multi-DOF redundant robotic manipulators. Because of the complicated kinematics and dynamics and the high dimensionality of the state-space model of such robots, the related control problem is of elevated difficulty. In the present article, a three-link planar robotic manipulator it considered. The article's approach relies first on approximate linearization of the state-space model of the redundant robotic manipulator, according to first-order Taylor series expansion and the computation of the related Jacobian matrices. For the approximately linearized model of the manipulator, a stabilizing H-infinity feedback controller is designed. To compute the controller's gains an algebraic Riccati equation is solved at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. The proposed control method retains the advantages of typical optimal control, that is fast and accurate tracking of the reference setpoints under moderate variations of the control inputs. [ABSTRACT FROM AUTHOR]

This study focuses on enhancing the control precision and efficiency of a two-degree-of-freedom (2-DOF) space manipulator used for active space debris removal. The unpredictable space environment introduces large uncertainties, which introduces unique challenges beyond the capabilities of a standalone computed torque controller and degrades control performance. To address this problem, a robust controller is developed, integrating traditional techniques such as sliding mode and computed torque control with a Neural Network framework. This synergy leverages both methods' strengths—conventional controls' accuracy and Neural Network's adaptability. The integration of Neural Network-based sliding mode control complements the robustness of computed torque control by actively mitigating uncertainties and disturbances inherent in the space environment. The 2-DOF manipulator's state variables model the system dynamics, necessitating accurate relative motion estimation between the manipulator and debris. The global asymptotic stability of the developed algorithm is demonstrated through the Lyapunov theorem, guaranteeing error convergence to zero. The convergence, stability, precision, tracking errors, and responsiveness of the controller have been analysed and validated by the MATLAB Simulink simulations. The novel approach's performance effectiveness is substantiated by numerical simulations and a comparative analysis with conventional computed torque control. Outcomes highlight the superior precision and efficiency in manipulator tracking the trajectory, validating the integrated controller's potential for successful active space debris removal. • Neural network-based sliding mode computed torque control (NSMCTC) approach ensures precise space manipulator position tracking. • NSMCTC reduces chattering and improves convergence for enhanced trajectory control in dynamic space environments. • Lyapunov stability theorem validates uniform and ultimate boundedness, ensuring global asymptotic stability. • Self-learning capability and low computational complexity distinguish NSMCTC from traditional computed torque control methods. • Potential applications extend to spacecraft manipulator attitude control, offering adaptability for safe debris capture in multidimensional dynamics. [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]

In this paper, we consider a food chain model with ratio-dependent functional response and prey-taxis. We first investigate the global existence and boundedness of the unique positive classical solutions of the system in a bounded domain with smooth boundary and Neumann boundary conditions. Then, we analyze the local stability of the system and the existence of Hopf bifurcation. In addition, we prove the global asymptotic stability of steady states under some conditions by constructing a Lyapunov functional, and investigate convergence rates. Finally, we present several numerical simulations to illustrate the results. [ABSTRACT FROM AUTHOR]

We formulate a mathematical model of social media addiction and depression (SMAD) in this study. Key aspects, such as social media addiction and depression disease-free equilibrium point (SMADDFEP), social media addiction and depression endemic equilibrium point (SMADEEP), and basic reproduction number (R0), have been analyzed qualitatively. The results indicate that if R0 < 1, the SMADDFEP is locally asymptotically stable. The global asymptotic stability of the SMADDFEP has been established using the Castillo-Chavez theorem. On the other hand, if R0 > 1, the unique endemic equilibrium point (SMADEEP) is locally asymptotically stable by Lyapunov theorem, and the model exhibits a forward bifurcation at R0 = 1 according to the Center Manifold theorem. To examine the model's sensitivity, we calculated the normalized forward sensitivity index and conducted a Partial Rank Correlation Coefficient (PRCC) analysis to describe the influence of parameters on the SMAD. The numerical results obtained using the Fourth-order Runge-Kutta (RK-4) scheme show that increasing the number of addicted individuals leads to an increase in the number of depressed individuals. [ABSTRACT FROM AUTHOR]

In many smart systems, such as cloud computing, networked control, manufacturing, and telecommunication, the effects of time delays are unavoidable. Saturation nonlinearity is common in many smart systems (e.g. electric systems with limited actuator power supplies, mechanical systems with position and speed constraints, fixed-point digital filters, etc.). Therefore, the study of stability of discrete-time systems (DTSs) with time delay and saturation is of high importance in practice. The global asymptotic stability (GAS) problem of such systems is investigated in this paper. The saturation nonlinearity is constrained by a convex hull with a free matrix whose infinity norm is smaller than or equal to unity. A new Lyapunov-based GAS criterion for DTSs with time-varying delay and state saturation is established. The GAS problem for DTSs with constant delay and saturation is also discussed. The obtained results can be used to ensure the absence of overflow oscillations in the considered system. In comparison to several existing criteria, the approach yields improved stability results. An example is provided to demonstrate the importance of the presented results. [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]

Summary: This paper discusses the global asymptotic stability and strong passivity analysis of fourth‐order nonlinear and time‐varying dynamical systems by utilizing the Lyapunov direct method. The mathematical model of the main system is obtained from a non‐linear and aging RLC circuit that we have designed before. RLC circuits play an excellent role in the stability of modern system theory. Without the concept of storage elements, the construction of Lyapunov or energy functions for nonlinear and time‐varying systems may be difficult. Because of this, although there are many studies on the stability concept, but the subject has not been completed yet. Therefore, this study may present some mathematical technicalities to the Lyapunov stability with physical considerations. The Lyapunov functions obtained from RLC circuits are natural storage functions, and they satisfy the dissipation inequality. The theoretical stability results of the system are also discussed by Lyapunov's linearization method. The relationship between stability and passivity is also given. Meanwhile, we realized that linear system analysis is not a guaranteed way for determining the stability properties of a full system. Finally, the correctness and availability of the proposed approach are verified through simulation results. [ABSTRACT FROM AUTHOR]

To explore the rumor propagation dynamics in online social networks (OSNs) and propose the corresponding control strategies, a novel Ignorants-Spreaders-1-Spreaders-2-Removers (I2SR) rumor-spreading model with general incidence is first formulated in heterogeneous networks. This model covers the bilinear incidence and nonlinear incidence, and considers the time delay in the rumor-spreading process, which is universal and practical. We analytically derive the basic reproduction numbers, which determine the existence of rumor-spreading equilibria but also the global dynamics of the model. Moreover, the Lyapunov–LaSalle principle and the graph-theoretic approach prove the global asymptotic stability of the rumor-free/rumor-spreading equilibria in detail. Significantly, the effects of various strategies, including uniform control, targeted control, and acquaintance control, are implemented and compared. Finally, the developed theoretical results are tested via numerical simulations and a real case data of rumors, showing that the model can more accurately simulate rumor-spreading in OSNs. [ABSTRACT FROM AUTHOR]

Summary: Single‐inductor dual‐output (SIDO) boost converters are used extensively in modern power systems because of their small circuit volume and high efficiency. However, SIDO boost converters exhibit non‐minimum phase property, and the coupling of the inductor current results in coupled dual outputs leading to cross‐regulation, which seriously affects the dynamic performance and stability of the system. To settle the non‐minimum phase issue and suppress the cross‐regulation of SIDO boost converters, proposed herein is a robust control method, which combines the exact feedback linearization (EFL) theory, adaptive technology, and sliding mode control (SMC) method. A nonlinear mathematical model is established, and a set of output functions for full linearization are constructed based on EFL theory. Furthermore, the output functions are linearized, and two single‐input single‐output linear subsystems are obtained. The SMC technologies are used to control the linear subsystems to improve the robustness of the system, and an adaptive mechanism is adopted to update the sliding mode switching gain to reduce chattering. Furthermore, the global asymptotic stability of the control system is proved based on the Lyapunov theory, and the robustness of the closed‐loop system is verified. Simulation and experimental results show that the proposed approach provides better dynamic regulation performance compared with the existing method. [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]

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]

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 focuses on the stability problem of networked control systems (NCSs) under denial‐of‐service (DoS) attacks and bandwidth limitation. Firstly, the periodic dynamic quantization mechanism is extended to insecure systems, and a periodic‐like quantization strategy is proposed. Due to the designable period, such mechanism allows a trade‐off between better system performance and less energy consumption. With finite quantization levels, a reasonable parametric design is given to avoid quantizer saturation under general energy‐constrained DoS attacks. Secondly, a suitable quantized controller is designed for the system affected by DoS attacks. The relationship between the quantized controller and the DoS attacks is analyzed, and the criterion for NCSs achieving global asymptotic stability is derived. Finally, two numerical examples are given to verify the correctness of the theoretical result. [ABSTRACT FROM AUTHOR]

To address the nonlinear stabilization problem and improve the tracking control feature of ball on plate system (BPS), this paper puts forward a novel Takagi Sugeno (TS) fuzzy control augmented with the current cycle feedback iterative learning control (CCF-ILC) scheme. According to Bode's sensitivity integral, the performance of linear controllers is always a trade-off between reference tracking and robustness. Hence, to deal with the so-called 'waterbed' effect, this work exploits the capability of TS fuzzy to handle the nonlinear dynamics and synthesizes a learning control scheme based on current iteration error to capitalize the information rich error signal for enhancing the robustness and trajectory tracking features. The global asymptotic stability of the proposed TS fuzzy augmented ILC scheme is proved using the Lyapunov function and linear matrix inequalities (LMIs). Moreover, the monotonic convergence of ILC is presented based on the singular value condition. For identifying the rolling mass from the video stream, a background subtraction algorithm based on thresholding technique is implemented. Finally, the robustness and tracking features of the proposed scheme are evaluated on a two degrees of freedom (DoF) laboratory scale BPS system through hardware in loop (HIL) testing for three realistic test cases. The tracking performance quantified using the root mean square error (RMSE) and power spectral density plot corroborates that the proposed scheme can offer better setpoint tracking and robustness feature compared to state-of-the-art fuzzy and ILC control techniques implemented on BPS. [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]

Considering the influence of sublethal concentration of pesticides on pests and natural enemies, we propose a pest-management model with impulsive effect on chemical control and biological control strategies–periodic spraying pesticide and releasing predatory natural enemies. By using the Floquet theory and the comparison theorem of impulsive differential equations, a sufficient condition for the global asymptotic stability of the pest-eradication periodic solution is obtained. The persistence of the system is further studied, and a sufficient condition for the persistence of the system is obtained. Finally, some numerical simulations are shown to verify our theoretical works. Our works indicate that the sublethal effects of insecticides and the release of predatory natural enemies play significant roles in pest control in agricultural production. [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]

Hepatitis B is a viral infection that can cause inflammation of the liver and lead to severe liver damage and even death. The study of hepatitis in Burkina Faso is crucial for several reasons. Indeed, understanding the epidemiology of hepatitis in Burkina Faso can help develop effective prevention and control strategies. Its study can also contribute to a better understanding of the global burden of the disease and the development of effective interventions in other parts of the world. To this aim, a new differential susceptibility and infectivity mathematical model of Hepatitis B transmission was developed in order to simulate the potential spread of the Hepatitis B virus in the population of Burkina Faso. Once the mathematical model is presented, the existence and uniqueness of non-negative solutions are proved. The model has a globally asymptotically stable disease-free equilibrium when the basic reproduction number R0 < 1 and a globally asymptotically stable endemic equilibrium when R0 > 1. The global asymptotic stability of the disease-free equilibrium has been studied using the Castillo Chavez method. The Lyapunov function and the LaSalle invariance principle are used to prove the global asymptotic stability of the endemic equilibrium. To simulate the proposed model, a Matlab numerical code has been developed. Numerical simulations are performed using data of Burkina Faso. The obtained numerical results confirm analytical results as well as the evolution of hepatitis B in Burkina Faso. [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]