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In this paper, we develop a non-autonomous delay differential equation model for mosquito population suppression. After establishing the positiveness and boundedness of the solutions, we study the dynamical behaviours of the model with or without Wolbachia-infected male mosquitoes. More specifically, for the model without infected male mosquitoes, we analyse the asymptotic stability of the equilibria and demonstrate that the model undergo Hopf bifurcations under certain conditions. For the model incorporating infected male mosquitoes, we derive sufficient conditions for the global asymptotic stability of the origin. Numerical examples are provided to illustrate and support our theoretical findings. [ABSTRACT FROM AUTHOR]

Alopecia areata (AA) is an autoimmune disease whose clinical phenotype is characterized by the formation of distinct hairless patterns on the scalp or other parts of the body. In this paper, we study a three-component chemotaxis model for AA, which describes the complex interactions among CD 4 + T cells, CD 8 + T cells and interferon-gamma (IFN- γ ). Our first purpose is to establish the uniform boundedness of classical solutions for the model by self-map method, which extends the corresponding results of Lou and Tao (J Differ Equ 305:401–427, 2021, JDE) and Zhang et al. (Math Biosci Eng 20(5):7922–7942, 2023, MBE) to the case of arbitrary spatial dimensions and non-equidiffusive coefficients. Another purpose is to consider the globally asymptotic stability and convergence rate of the positive equilibrium under either (i) small proliferation rate and large degradation parameters or (ii) weak chemoattractive effect or strong random motions. It is shown under the above two cases that sparse patches occur in or around diseased hair follicles, gradually develop into diffuse or total hair loss and ultimately induce AA. [ABSTRACT FROM AUTHOR]

This paper deals with the modelling and stabilization of a flexible clamped beam controlled with a piezoelectric actuator in the self-sensing configuration. We derive the model starting from general principles, using the general laws of piezoelectricity. The obtained model is composed by a PDE, describing the flexible deformations dynamics, interconnected with an ODE describing the electric charge dynamics. Firstly, we show that the derived linear model is well-posed and the origin is globally asymptotically stable when a voltage control law, containing the terms estimated in the self-sensing configuration, is applied. Secondly, we make the more realistic assumption of the presence of hysteresis in the electrical domain. Applying a passive control law, we show the well-posedness and the origin's global asymptotic stability of the nonlinear closed-loop system. [ABSTRACT FROM AUTHOR]

Gross Domestic Product (GDP) growth and national debt are like two faces of the same coin. The national debt is the major source of growth of GDP. GDP is completely paralyzed in the absence of national debt. The national debt in turn is hugely dependent on foreign funding. The GDP is growing faster as a result of these investments. It is believed that the external debt will never be entirely settled. It takes some time for the agreement to mature before external investments become available in response to demand. The primary topic of this study is the delay in foreign investment’s real arrival and how it affects the dynamics of GDP and national debt. We investigate this impact with a delay parameter τ. The stability analysis is done on the system and the nonzero equilibrium is computed. For a crucial delay parameter value, Hopf bifurcation is seen. The research plays a significant role in economic growth. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying the initial-boundary value problem for the radiative full Euler equations, which are a fundamental system in the radiative hydrodynamics with many practical applications in astrophysical and nuclear phenomena, with the non-slip boundary condition on an impermeable wall. Due to the difficulty from the disappearance of the velocity on the impermeable boundary, quite few results for compressible Navier-Stokes equations and no result for the radiative Euler equations are available at this moment. So the asymptotic stability of the rarefaction wave proven in this paper is the first rigorous result on the global stability of solutions of the radiative Euler equations with the non-slip boundary condition. It also contributes to our systematical study on the asymptotic behaviors of the rarefaction wave with the radiative effect and different boundary conditions such as the inflow/outflow problem and the impermeable boundary problem in our series papers including [5,6]. [ABSTRACT FROM AUTHOR]

Under study is the stability of Persidskii systems with distributed delay. We assume that the sector-type functions on the right-hand sides of the system are essentially nonlinear. Also, we propose some original construction of the Lyapunov–Krasovskii functional of use in deriving new asymptotic stability conditions of the zero solution. The approach is applied to the stability analysis of the Lurie indirect control system and a mechanical system with essentially nonlinear positional forces. Using some development of the averaging method, we obtain the conditions that guarantee stability under nonstationary perturbations with zero mean values for the systems under study. [ABSTRACT FROM AUTHOR]

For the issue of tracking control of motor servo system with input dead-zone, a novel robust adaptive prescribed performance control is proposed. Firstly, a smooth dead-zone inverse model is introduced and parameterized, which can help compensate for dead-zone. Secondly, the prescribed performance function is used to constrain the convergence process of tracking error. Then, a robust adaptive controller is designed based on the estimation of the upper bound of disturbance to weaken the influence from disturbance. Comparative tracking verification under two position command cases is carried out and the simulation results show that the proposed controller can improve the tracking accuracy well. [ABSTRACT FROM AUTHOR]

This article considers the problem of output feedback stabilization for a class of stochastic high‐order nonlinear time‐delay systems with unknown output function. For stochastic high‐order nonlinear time‐delay systems, based on the Lyapunov stability theorem, by combining the addition of one power integrator and homogeneous domination method, the maximal open sector Δ$\Delta$ of output function is given. As long as output function belongs to any closed sector included in Δ$\Delta$, an output feedback controller can be developed to guarantee the closed‐loop system globally asymptotically stable in probability. [ABSTRACT FROM AUTHOR]

We provide the well-posedness for a partially dissipative viscous system of balance laws in smooth Sobolev spaces under the same assumptions as in the case of inviscid balance laws. A priori estimates for coupled hyperbolic-parabolic linear systems with coefficients having limited regularity are derived using Friedrichs regularization and Moser-type estimates. Local existence for nonlinear systems will be established using the results of the linear theory and a suitable iteration scheme. The local existence theory is then applied to the Kuznetsov–Westervelt equation with damping for nonlinear wave acoustic propagation. Existence of global solutions for small data and their asymptotic stability are established. [ABSTRACT FROM AUTHOR]

This paper is devoted to the asymptotic stability of diverging traveling waves for reaction–advection–diffusion equation u t - Δ u + α (t , y) u x = f (t , y , u) in cylinders. By the sliding method, we first establish a Liouville-type result. Then, using the Liouville-type result and truncation technique, we prove the asymptotic stability of the diverging traveling wave. [ABSTRACT FROM AUTHOR]

We prove the asymptotic stability of a finite sum of well-ordered solitary waves for the Zakharov–Kuznetsov equation in dimensions two and three. We also derive a qualitative version of the orbital stability result, which will be useful for studying the collision of two solitary waves in a forthcoming paper. The proof extends the ideas of Martel, Merle and Tsai for the sub-critical gKdV equation in dimension one to the higher-dimensional case. It relies on monotonicity properties on oblique half-spaces and rigidity properties around one solitary wave introduced by Côte, Muñoz, Pilod and Simpson in dimension two, and by Farah, Holmer, Roudenko and Yang in dimension three. [ABSTRACT FROM AUTHOR]

This work focuses on the asymptotic stability of nonlocal diffusion equations in N$$ N $$‐dimensional space with nonlocal time‐delayed response term. To begin with, we prove L2$$ {L}^2 $$ and L∞$$ {L}^{\infty } $$‐decay estimates for the fundamental solution of the linear time‐delayed equation by Fourier transform. For the considered nonlocal diffusion equation, we show that if l>p$$ l>\left|p\right| $$, then the solution u(t,x)$$ u\left(t,x\right) $$ converges globally to the trivial equilibrium time‐exponentially. If l=p$$ l=\left|p\right| $$, then the solution u(t,x)$$ u\left(t,x\right) $$ converges globally to the trivial equilibrium time‐algebraically. Furthermore, it can be proved that when r>q$$ r>\left|q\right| $$, the solution u(t,x)$$ u\left(t,x\right) $$ converges globally to the positive equilibrium time‐exponentially, and when r=q$$ r=\left|q\right| $$, the solution u(t,x)$$ u\left(t,x\right) $$ converges globally to the positive equilibrium time‐algebraically. Here, l,p,r$$ l,p,r $$, and q$$ q $$ are the coefficients of each term contained in the linear part of the nonlinear term f$$ f $$. All convergence rates above are L2$$ {L}^2 $$ and L∞$$ {L}^{\infty } $$‐decay estimates. The comparison principle and low‐frequency and high‐frequency analyses are significantly effective in proofs. Finally, our theoretical results are supported by numerical simulations in different situations. [ABSTRACT FROM AUTHOR]

In this paper, we consider the two-species chemotaxis-competition system with loop and nonlocal kinetics { u t = Δ u − χ 11 ∇ ⋅ (u ∇ v) − χ 12 ∇ ⋅ (u ∇ z) + f 1 (u , w) , x ∈ Ω , t > 0 , 0 = Δ v − v + u + w , x ∈ Ω , t > 0 , w t = Δ w − χ 21 ∇ ⋅ (w ∇ v) − χ 22 ∇ ⋅ (w ∇ z) + f 2 (u , w) , x ∈ Ω , t > 0 , 0 = Δ z − z + u + w , x ∈ Ω , t > 0 , subject to homogeneous Neumann boundary conditions in a smooth bounded domain Ω ⊂ R n (n ≥ 1) , where χ i j > 0 (i , j = 1 , 2) , f 1 (u , w) = u (a 0 − a 1 u − a 2 w − a 3 ∫ Ω u d x − a 4 ∫ Ω w d x) , f 2 (u , w) = w (b 0 − b 1 u − b 2 w − b 3 ∫ Ω u d x − b 4 ∫ Ω w d x) with a i , b i > 0 (i = 0 , 1 , 2) , a j , b j ∈ R (j = 3 , 4). It is shown that if the parameters satisfy certain conditions, then the corresponding initial boundary value problem admits a unique global-in-time classical solution in any spatial dimension, which is uniformly bounded. Moreover, based on the construction of suitable energy functionals, the globally asymptotic stabilization of coexistence and semi-coexistence steady states is considered. Our results generalize and improve some previous results in the literature. [ABSTRACT FROM AUTHOR]

We study the long time behavior of the generalized solution of the flow and thermal explosion model of the reactive real micropolar gas. The dynamics of the chemical reaction involved and the usual laws of conservation of mass, momentum, angular momentum, and energy generate a complex governing system of partial differential equations. The fluid is nonideal and non‐Newtonian. In this work, we prove that the problem can be solved in an infinite time domain and establish the asymptotic properties of the solution. Namely, we conclude that for certain parameter values, the solution stabilizes exponentially to a steady‐state solution, while for others the stabilization occurs but at power decay rate. At the end, we conducted a few numerical tests whereby we experimentally confirmed theoretical findings about long‐term behavior of the solution. [ABSTRACT FROM AUTHOR]

On the basis of the known equations of motion of the system of coupled gyrostats by P.V. Kharlamov and the functions of state by S.L. Sobolev, the equations of rotation in a medium with resistance of a free system of two elastically connected rigid bodies with cavities completely filled with an ideal incompressible fluid were derived. Rigid bodies are connected by an elastic restoring spherical joint. Assuming that the center of mass of the rigid bodies is located on the third main axis of inertia and the fluid is ideal, the equation of disturbed motion of the considered mechanical system is obtained in the form of a countable system of ordinary differential equations. In the case of two Lagrangian gyroscopes with arbitrary axisymmetric cavities filled with an ideal fluid, a transcendental characteristic equation has been derived. Taking into account the fundamental tone of liquid oscillations, a characteristic equation of the sixth order was obtained, and on the basis of the Lenard–Schipar criterion, it was written in the innor form, and the conditions for the asymptotic stability of uniform rotation of Lagrange gyroscopes with a liquid were written out in the form of a system of five inequalities. These inequalities are presented in the form of the first, third, sixth, and eighth powers with respect to the coefficient of the spherical joint elasticity. It was proved that if the first tones of liquid oscillations in two cavities are greater than one and do not coincide, then this is sufficient for the higher inequality coefficients to be positive. It was shown that if the first oscillation tones coincide, only the degree of the last inequality decreases, while the higher inequality coefficients remain positive; therefore, internal resonance is impossible. Thus, when the first tones of fluid oscillations are greater than one, the asymptotic stability will always be possible with the increase in the elasticity coefficient. For ellipsoidal cavities, this means that they must be oblate along the axis of rotation. It was shown that in the absence of the spherical joint elasticity, the characteristic equation has a zero root, and the conditions of stability are already presented in the form of a system of four inequalities, which are only necessary. [ABSTRACT FROM AUTHOR]

The present paper proposes the use of fractional derivatives in the definition of sliding function, giving a new mode control applied to induction motor drives in electric vehicle (EV) applications. The proposed Fractional-Order Sliding Mode Direct Torque Control-Space Vector Modulation (FOSM-DTC-SVM) strategy aims to address the limitations of conventional control techniques and mitigate torque and flux ripples in induction motor systems. The paper first introduces the motivation for using fractional-order control methods to handle the nonlinear and fractional characteristics inherent in induction motor systems. The core describes the proposed FOSM-DTC-SVM control strategy, which leverages a fractional sliding function and the associated Lyapunov stability analysis. The efficiency of the proposed strategy is validated via three scenarios. (i) The first scenario, where the acceleration of the desired speed is defined by pulses, leading to Dirac impulses in its second derivative, demonstrates the advantage of the proposed control approach in tracking the desired speed while minimizing flux ripples and generating pulses in the rotor pulsation. (ii) The second scenario demonstrates the effectiveness of filtering the desired speed to eliminate Dirac impulses, resulting in smoother rotor pulsation variations and a slightly slower speed response while maintaining similar flux ripples and stator current characteristics. (iii) The third scenario consists of eliminating the fractional derivatives of the pulses existing in the expression of the control, leading to the elimination of Dirac impulses. These results demonstrate the potential of the FOSM-DTC-SVM to revolutionize the performance and efficiency of EVs. By incorporating fractional control in the control scheme for PV-powered EVs, the paper showcases a promising avenue for sustainable transportation. [ABSTRACT FROM AUTHOR]

The Jungle Game is used in population dynamics to describe cyclic competition among species that interact via a food chain. The dynamics of the Jungle Game supports a heteroclinic network whose cycles represent coexisting species. The stability of all heteroclinic cycles in the network for the Jungle Game with four species determines that only three species coexist in the long-run, interacting under cyclic dominance as a Rock–Paper–Scissors Game. This is in stark contrast with other interactions involving four species, such as cyclic interaction and intraguild predation. We use the Jungle Game with four species to determine the success of a fourth species invading a population of Rock–Paper–Scissors players. [ABSTRACT FROM AUTHOR]

We consider the problem of stability of nonzero integral manifolds of a nonlinear finitedimensional system of ordinary differential equations whose right-hand side is a periodic vector-valued function of the independent variable containing a parameter. We assume that the system has a trivial integral manifold for all values of the parameter and the corresponding linear subsystem does not possess the property of exponential dichotomy. The aim of this work is to find sufficient conditions for stability, instability, and asymptotic stability of a local nonzero integral manifold. For this purpose, we use the method of Lyapunov functions modified to the problem considered and singularities of the right-hand sides of the system. [ABSTRACT FROM AUTHOR]

The stability of systems of linear autonomous functional differential equations of neutral type is studied. The study is based on the well-known representation of the solution in the form of an integral operator, the kernel of which is the Cauchy function of the equation under study. The definitions of Lyapunov, asymptotic, and exponential stability are formulated in terms of the corresponding properties of the Cauchy function, which allows us to clarify a number of traditional concepts without loss of generality. Along with the concept of asymptotic stability, a new concept of strong asymptotic stability is introduced. The main results are related to the stability with respect to the initial function from the spaces of summable functions. In particular, it is established that strong asymptotic stability with initial data from the space L1 is equivalent to the exponential estimate of the Cauchy function and, moreover, exponential stability with respect to initial data from the spaces Lp for any p ≥ 1. [ABSTRACT FROM AUTHOR]

For several species of microorganisms, a competition model described by a system of nonlinear differential equations with an infinite distributed delay is considered. The asymptotic stability of the equilibrium point corresponding to the survival of only one species and extinction of the others is studied. Conditions on the initial species population sizes and the initial nutrient concentration are indicated under which the system reaches the equilibrium. Additionally, the stabilization rate is estimated. The results are obtained using a Lyapunov–Krasovskii functional. [ABSTRACT FROM AUTHOR]

We address the stability of stationary solutions to a class of 2D non-newtonian fluid equations, when the external force contains hereditary characteristics involving unbounded delays. Firstly, when the unbounded variable delay is driven by a continuously differential function, we establish the stability of nontrivial weak stationary solutions and the asymptotic stability of trivial stationary solution. Then when the general unbounded delay is continuous with respect to time, the stability of nontrivial strong stationary solutions is also obtained. Eventually, when the proportional delay is considered, the polynomial stability of trivial stationary solution is verified. [ABSTRACT FROM AUTHOR]

This paper investigates the Cauchy problem for time‐space fractional Keller‐Segel‐Navier‐Stokes model in ℝd(d≥2)$$ {\mathrm{\mathbb{R}}}^d\kern0.1em \left(d\ge 2\right) $$, which can describe the memory effect and anomalous diffusion of the considered system. The local and global existence and uniqueness in weak Lp$$ {L}^p $$ space are obtained by means of abstract fixed point theorem. Moreover, we explore the asymptotic stability of solutions as time goes to infinity. [ABSTRACT FROM AUTHOR]

This present work develops a nonlinear SIRS fractional-order model with a system of four equations in the Caputo sense. This study examines the impact of positive and negative attitudes towards vaccination, as well as the role of government actions, social behavior and public reaction on the spread of infectious diseases. The local stability of the equilibrium points is analyzed. Sensitivity analysis is conducted to calculate and discuss the sensitivity index of various parameters. It has been established that the illness would spread across this system when the basic reproduction number is larger than 1, the system becomes infection-free when the reproduction number lies below its threshold value of 1. Numerical figures depict the effects of positive and negative attitudes towards vaccination to make the system disease-free sooner. A comprehensive study regarding various values of the order of fractional derivatives together with integer-order derivatives has been discussed in the numerical section to obtain some useful insights into the intricate dynamics of the proposed system. The Pontryagin principle is used in the formulation and subsequent discussion of an optimum control issue. The study also reveals the significant role of government actions in controlling the epidemic. A numerical analysis has been conducted to compare the system's behavior under optimal control and without optimal control, aiming to discern their differences. The policies implemented by the government are regarded as the most adequate control strategy, and it is determined that the execution of control mechanisms considerably diminishes the ailment burden. [ABSTRACT FROM AUTHOR]

In this paper, a viscous shock wave under space-periodic perturbation of 1-D isentropic Navier-Stokes system in the half space is investigated. It is shown that if the initial periodic perturbation around the viscous shock wave is small, then the solution time asymptotically tends to a viscous shock wave with a shift partially determined by the periodic oscillations. Moreover the strength of shock wave could be arbitrarily large. This result essentially improves the previous work Matsumura and Mei (1999) [14] where the strength of shock satisfies some restrictions and the initial periodic oscillations vanish. [ABSTRACT FROM AUTHOR]

This paper presents various bifurcations of the McMillan map under perturbations of its coefficients, such as period-doubling, pitchfork, and hysteresis bifurcation. The associated existence regions are located. Using the quasi-Lyapunov function method, the existence of asymptotically stable fixed point is also demonstrated. [ABSTRACT FROM AUTHOR]

Several types of linear and nonlinear singularly perturbed time-delay differential systems are considered. Asymptotic stability of the linear systems and asymptotic stability of the trivial solution of the nonlinear systems, valid for any sufficiently small value of the parameter of singular perturbation, are analyzed. For the stability analysis in the linear case, a partial exact slow–fast decomposition of the original system and an application of the Symmetric Matrix Riccati Equation method are proposed. Such an analysis yields parameter-free conditions, providing the asymptotic stability of the considered linear singularly perturbed time-delay differential systems for any sufficiently small value of the parameter of singular perturbation. Using the asymptotic stability results for the considered linear systems and the method of asymptotic stability in the first approximation, parameter-free conditions, guaranteeing the asymptotic stability of the trivial solution to the considered nonlinear systems for any sufficiently small value of the parameter of singular perturbation, are derived. Illustrative examples are presented. [ABSTRACT FROM AUTHOR]

We extend the detailed study of the linearized dynamics obtained for cnoidal waves of the Korteweg–de Vries equation by Rodrigues [J. Funct. Anal. 274 (2018), pp. 2553–2605] to small-amplitude periodic traveling waves of the generalized Korteweg–de Vries equations that are not subject to Benjamin–Feir instability. With the adapted notion of stability, this provides for such waves, global-in-time bounded stability in any Sobolev space, and asymptotic stability of dispersive type. When doing so, we actually prove that such results also hold for waves of arbitrary amplitude satisfying a form of spectral stability designated here as dispersive spectral stability. [ABSTRACT FROM AUTHOR]

We consider a system of autonomous nonlinear ordinary differential equations for which the existence conditions for an invariant manifold are satisfied in the case where this manifold is central. It is well known that the theorem on the existence of a central invariant manifold cannot be supplemented with the statement of its uniqueness. We obtain sufficient conditions that guarantee the uniqueness of the central invariant manifold. [ABSTRACT FROM AUTHOR]

To solve the control problem of time-varying state-scale nonlinear systems whose initial state is not affected by settling time, fixed-time convergence algorithms are proposed for first-order systems and higher-order systems in this paper. First, a scalar model is used to illustrate how the time-varying feedback parameter can guarantee that the system achieves asymptotic stability while achieving finite-time convergence, and it is proved that the settling time obtained in this paper is only related to the prescribed boundary. This allows us to design the settling time with an appropriate parameter based on the prescribed boundary. To exhibit the effectiveness and extensibility of the proposed algorithm for first-order scalar systems, the results are subsequently extended to general higher-order systems based on the backstepping method. By introducing numerical simulation results, this paper verifies that the proposed algorithm will make the system achieve asymptotic stability and its output can converge to a given boundary, regardless of the system's initial states. [ABSTRACT FROM AUTHOR]

This paper proposes a novel stable economic model predictive control (EMPC) strategy for constrained nonlinear systems with changing economic criteria. The traditional EMPC may lead to infeasibility and even instability of the closed-loop system when the criterion has been changed. Firstly, a generalised terminal constraint is introduced to ensure the recursive feasibility of the economic optimisation problem, which enforces the terminal states to converge to an arbitrary equilibrium state rather than a predetermined fixed one at the initial time. Then the stability constraint is constructed by solving an auxiliary optimisation problem online, which is the key to guaranteeing the asymptotic stability of the closed-loop system. Finally, sufficient conditions for feasibility and asymptotic stability are derived in the context of changing economic criteria. The main feature of the proposed strategy is that it does not need to know the changes of economic criterion in advance, and its properties and effectiveness are exemplified by simulations on a nonlinear chemical process example. [ABSTRACT FROM AUTHOR]

Atherosclerosis, as a chronic inflammatory disease, has been a threat to human health. How to diagnose and prevent this disease has long been the focus of medical and biomathematics study. In this paper, we investigate a free boundary model of an atherosclerotic plaque formation in the presence of reverse cholesterol transport, which includes low-density lipoprotein, high-density lipoprotein, endothelial stimulating cytokines, pro-inflammatory and anti-inflammatory macrophages, as well as foam cells. For this model, we use the Holling type-III response function instead of the usual Holling type-II to describe the change of the concentration of each substance. We first introduce the auxiliary function ξ (r) to prove the existence and uniqueness of small radially symmetric stationary plaque for appropriate L 0 and H 0 by using the contraction mapping principle and maximum principle, and then establish a condition to ensure their asymptotic stability behavior by expanding the corresponding steady-state solution. [ABSTRACT FROM AUTHOR]

This article investigates the asymptotic stability of fractional-order (FO) systems with uncertainty and time-varying delay based on the sliding mode control (SMC) method. First, based on the SMC method, a suitable integral type fractional-order sliding mode surface (FOSMS) is designed and the dynamic equations of FO systems under SMC are obtained. Second, by inequality techniques, the condition for asymptotic stability of the FO system has been mathematically established. Then, a novel adaptive SMC law is introduced, which can make sure the accessibility of sliding mode surfaces (SMS). Finally, the feasibility of the results obtained in this paper is verified through a simulation. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the dynamics of Hopfield neural networks with impulsive effects, focusing on Poisson stable rates, synaptic connections, and unpredictable external inputs. Through the symmetry of impulsive and differential compartments of the model, we follow and extend the principal dynamical ideas of the founder. Specifically, the research delves into the phenomena of unpredictability and Poisson stability, which have been examined in previous studies relating to models of continuous and discontinuous neural networks with constant components. We extend the analysis to discontinuous models characterized by variable impulsive actions and structural ingredients. The method of included intervals based on the B-topology is employed to investigate the networks. It is a novel approach that addresses the unique challenges posed by the sophisticated recurrence. [ABSTRACT FROM AUTHOR]

This work presents a new fuzzy logic parameter tuning-based fractional order sliding mode control (F-FOSMC) strategy for the trajectory tracking of robotic systems. The primary objective is to achieve an optimal control compromise seeking to minimize energy consumption for required motions, all while increasing both accuracy and rapidity of the transient response, addressing therefore a critical challenge in the field of robotics. Our approach integrates a sophisticated fuzzy logic fractional order mechanism to dynamically fine-tune the noninteger derivation parameter of the FOSMC, offering adaptability to varying operational conditions. This intelligent fuzzy logic controller tuning optimizes the FOSMC performance, demonstrates a remarkable capacity to handle uncertainties and disturbances intrinsic to robotic applications and allows to optimize the trade-off between the energy consumption and transient response efficiency throughout the robot's motion. The effectiveness of the proposed study is thoroughly examined via simulations conducted on a 3 DOF manipulator robotic system. Results showcase that F-FOSMC significantly reduces control energy consumption while preserving rapid and efficient transient response characteristics. [ABSTRACT FROM AUTHOR]

In this work, we prove a nonlocal Halanay inequality with an exact decay rate. This enables us to analyze behavior of solutions to some classes of nonlocal ODEs and PDEs involving unbounded delays. The obtained results extend and improve the previous ones proved for fractional differential equations and other nonlocal subdiffusion equations. [ABSTRACT FROM AUTHOR]

In this paper, we construct center stable manifolds of unstable line solitary waves for the Zakharov–Kuznetsov equation on R × T L and show the orbital stability of the unstable line solitary waves on the center stable manifolds, which yields the asymptotic stability of unstable solitary waves on the center stable manifolds near by stable line solitary waves. The construction is based on the graph transform approach by Nakanishi and Schlag (SIAM J Math Anal 44:1175–1210, 2012). Applying the bilinear estimate on Fourier restriction spaces by Molinet and Pilod (Ann Inst H Poincaré Anal Non Lineaire 32:347–371, 2015) and modifying the mobile distance in Nakanishi and Schlag (2012), we construct a contraction map on the graph space. [ABSTRACT FROM AUTHOR]

This paper investigates the asymptotic stability of neutral stochastic pantograph systems with Markovian switching (NSPSMS). The stochastic LaSalle theorem has been set up to locate the attractive sets for NSPSMS without linear growth condition. Subsequently, combining the stochastic LaSalle theorem and uniformly continuous theory, almost surely asymptotic stability and pth moment asymptotic stability are analysed. Furthermore, we also present one new criterion on the pth moment polynomial stability and almost surely polynomial stability for NSPSMS, where the coefficients of the delay term are time invariable. Finally, three examples are provided to exhibit the efficiency of the proposed 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]

The stabilization problem for uncertain discrete‐time singular Markovian jump systems (DSMJSs) with time‐varying delays is comprehensively covered in this paper. An updated Lyapunov–Krasovskii functional is presented via a discrete state decomposition method. With the help of this constructed Lyapunov–Krasovskii functional, some delay‐ and mode‐dependent sufficient conditions for the open‐loop DSMJSs are derived. Based on these circumstances, a memory mode‐dependent state feedback control is used to create a closed‐loop DSMJS with parameter uncertainties that is regular and causal. And then, the stochastically admissible conditions are attained. Through the exact calculation of each decomposition component for the designed memory state feedback controller, the intended memory state feedback controller settings are determined. It should be mentioned that the algorithm suggested in this article expands the controller design's feasibility and flexibility. The numerical results show how the approach is superior to previous ones, and the given results are less conservative. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of designing secure control for networked multi-agent systems (MASs) under Denial-of-Service (DoS) attacks. We propose a constructive design method based on the interaction topology. The MAS with a non-attack communication topology, modeled by quasi-Abelian Cayley graphs subject to DoS attacks, can be represented as a switched system. Using switching theory, we provide easily implementable sufficient conditions for the networked MAS to remain asymptotically stable despite DoS attacks. Our results are applicable to both continuous-time and discrete-time systems, as well as to discrete-time systems with variable steps or systems that combine discrete and continuous times. [ABSTRACT FROM AUTHOR]

We develop two neural network models for computing the quaternion singular value decomposition (QSVD), which can be shown to arise as gradient flows or Riemannian-gradient flows on the product of Stiefel manifold over the quaternion skew-field and their geometric and dynamical properties are investigated. Numerical experiments including color image compression indicate the feasibility and effectiveness of the proposed neural network models. • Establish the parameterization optimization formula for computing QSVD. • Propose the neutral network models and algorithms for solving the optimization model, and give the convergence analysis. • The neutral network models have the local asymptotically stable under suitable assumptions. • The color image compression illustrates the effectiveness of the QSVD neutral dynamical system models. [ABSTRACT FROM AUTHOR]

We study the asymptotic stability of a front connecting two unstable states. Such a structure typically appears when the stable state behind a Fisher--Kolmogorov--Petrovskii--Piskunov front destabilizes when going through an essential Turing bifurcation, giving rise to oscillating patterns. Despite the instability of both end-states, we obtain for the first time stability of such a structure against suitably localized perturbations, with algebraic temporal decay t-3/2. To deal with the instability behind the front, we simultaneously control the error in two different norms. In the first norm, enhanced diffusive decay is obtained at a linear level through pointwise resolvent estimates. In the second norm, better suited for nonlinear analysis, we show that the error stays bounded in time by use of mode filters. [ABSTRACT FROM AUTHOR]

In this paper, the optimal formation control issue with collision avoidance and connectivity assurance is investigated for a class of second-order uncertain nonlinear multi-agent systems. First, the neural networks are employed in order to deal with the unknown nonlinear dynamics of the system. Then, an optimal formation control scheme is developed in the framework of the identifier–actor–critic. By constructing a new performance metric function containing collision avoidance and connectivity constraints, it is demonstrated that asymptotic convergence of the tracking error can be achieved under the proposed control scheme. Finally, the effectiveness of the proposed control method is validated by the numerical simulation example. [ABSTRACT FROM AUTHOR]

Summary: Ensuring nominal asymptotic stability of the nonlinear model predictive control (NMPC) controller is not trivial. Stabilizing ingredients such as terminal penalty term and Terminal Region (TR) are crucial in establishing the asymptotic stability. Approaches available in the literature provide limited degrees of freedom for the characterization of the TR for the discrete time quasi infinite horizon NMPC formulation. Current work presents alternate approaches namely arbitrary controller based approach and linear quadratic regulator (LQR) based approach, which provide larger degrees of freedom for enlarging the TR. Both the approaches are scalable to system of any dimension. Approach from the literature provides a scalar whereas proposed approaches provide two additive matrices as tuning parameters for shaping of the TR. Proposed approaches involve solving modified Lyapunov equations to compute terminal penalty term, followed by explicit characterization of the TR. Efficacy of the proposed approaches is demonstrated using benchmark two state system. TR obtained using the arbitrary controller based approach and LQR based approach are approximately 10.4723 and 9.5055 times larger by area measure when compared to the largest TR obtained using the approach from the literature. As a result, there is significant reduction in the prediction horizon length while retaining the feasibility of the controller. [ABSTRACT FROM AUTHOR]

This paper studies the problem of event-triggered impulsive control for discrete-time systems. A novel periodic event-triggering scheme with two tunable parameters is presented to determine the moments of updating impulsive control signals which are called event times. Sufficient conditions are established to guarantee asymptotic stability of the resulting impulsive systems. It is worth mentioning that the event times are different from the impulse times, that is, the control signals are updated at each event time but the actuator performs the impulsive control tasks at a later time due to time delays. The effectiveness of our theoretical result with the proposed scheme is illustrated by three examples. [ABSTRACT FROM AUTHOR]

In this study, a novel unified stability criterion is first proposed for general fractional-order systems with time delay when the fractional order is from 0 to 1. Such a new unified criterion has the advantage of having an initiative link with the fractional orders. A further advantage is that the corresponding asymptotic stability theorem, derived from the proposed criterion used to analyze the asymptotic stability, is only slightly affected by the change of the fractional order. In addition, the unified stability criterion is applied to general multi-dimensional nonlinear fractional-order systems with time delays, the corresponding asymptotic stability criterion is applied by combining the vector Lyapunov function with the M-matrix method. Compared with the traditional stability criterion, the unified stability criterion is slightly influenced by the changing fractional order and large time delays. The reliability and effectiveness of the novel uniform stability criterion were verified through three representative examples. [ABSTRACT FROM AUTHOR]

We study the dynamics of solutions of nonlinear Schrödinger equation (NLS) near unstable ground states. The existence of the local center stable manifold around ground states and the asymptotic stability for the solutions on the manifold is proved. The novelty of our result is that we allow the existence of internal modes. [ABSTRACT FROM AUTHOR]

We establish some properties of the Proximal Difference-of-Convex functions decomposition algorithm in indefinite quadratic programming under linear constraints. The first property states that any iterative sequence generated by the algorithm is root linearly convergent to a Karush–Kuhn–Tucker point, provided that the problem has a solution. The second property says that iterative sequences generated by the algorithm converge to a locally unique solution of the problem if the initial points are taken from a suitably chosen neighbourhood of it. Through a series of numerical tests, we analyse the influence of the decomposition parameter on the rate of convergence of the iterative sequences and compare the performance of the Proximal Difference-of-Convex functions decomposition algorithm with that of the Projection Difference-of-Convex functions decomposition algorithm. In addition, the performances of the above algorithms and the Gurobi software in solving some randomly generated nonconvex quadratic programs are compared. [ABSTRACT FROM AUTHOR]