In this paper, we establish the nonlinear orbital stability of the traveling wave solution of deterministic and stochastic delayed reaction–diffusion equation. Employing the deterministic phase shift and establishing a delayed-integral inequality, we obtain the exponential stability of the traveling wave solution for the deterministic delayed reaction–diffusion equation. Applying a stochastic phase

In this paper, the nonlinear dynamics of fractional viscoelastic polyethylene terephthalate (PET) membranes with linearly varying density are elaborated. The viscoelasticities of the PET membranes are characterized with the fractional Kelvin-Voigt model, and the density distribution is considered a linear fluctuation in the lateral direction. The geometrically nonlinear formulation is established with

In this paper we apply Cimmino algorithm for common fixed point problems with a countable family of quasi-nonexpansive operators in an arbitrary normed space and show its convergence. Our results are an extension of the recent results by T. Y. Kong , H. Pajoohesh and G. T. Herman obtained for operators which are projections on convex closed sets in a finite-dimensional Euclidean space.

In the simulation of microstructural evolutions, detailed priori knowledge for the model parameters and initial states is difficult to be observed by experiments. For an improved simulation, we present a data assimilation framework for the phase field crystal model with the effect of stochastic noise. A sequential data assimilation method based on the ensemble Kalman filter is applied to integrate

Non-equilibrium models are applicable in various physical situations, including phase transitions, hysteresis, and chemical reactions, among others. To model the dynamics of such phenomena, partial differential equations are employed with source terms, as seen in Eq. (1.1). This work focuses on situations where we connect states in equilibrium while allowing for non-equilibrium times. In our model

In this article, the phase field sintering model, which is composed of a Cahn–Hilliard type equation and several Allen–Cahn type equations, has been considered. On the scalar auxiliary variable framework, we propose a theoretically efficient and stable method for solid-state sintering. In order to overcome the nonlinear issues, we define a stabilized scalar auxiliary variable method and reformulate

In this paper, the resilient distributed filtering problem is studied for time-varying nonlinear multi-rate systems (TVNMRSs) with integral measurements over sensor networks, where the lifting technology is utilized during the analysis of the TVNMRSs. In order to reduce unnecessary data transmissions, the memory-event-triggered communication mechanism (METCM) is adopted to determine whether the sensor

When a subject is at rest and meals have not been eaten for a relatively long time (e.g. during the night), presumably near-constant, zero-order glucose production occurs in the liver. Glucose elimination from the bloodstream may be proportional to glycemia, with an apparently first-order, linear elimination rate. Besides glycemia itself, unobserved factors (insulinemia, other hormones) may exert second

Understanding the role of age structure and the spatial heterogeneity on disease spreading and vanishing is a vital question in the transmission of diseases. In this paper we construct a reaction–diffusion vector-borne disease model on a bounded domain subject to the no-flux boundary condition, with two novel features: age-space structure and multiple transmission routes. The contribution of mathematical

Solving quasi-periodic (QP) responses of nonlinear dynamical systems, particularly when multiple self-excited fundamental frequencies have to be determining, has been a challenging task. The presence of unknown frequencies usually leads to an under-determined problem, where the number of unknowns exceeds that of equations, as obtained through harmonic balancing or difference techniques, for instance

In this paper, the adaptive tracking control problem is investigated of uncertain nonlinear systems with input saturation, asymmetric state-function constraints and unknown control gains (UCG). The hyperbolic tangent function is used to deal with input saturation, and the original system is equivalent to a new system with explicit control input. Nussbaum function and fuzzy logic system (FLS) are simultaneously

This paper studies the synchronously discrete-time feedback control of large-scale systems. Given an unstable complex networks (the ith subsystem is ẋi(t)=Aixi(t)+∑j=1NaijΓxj(t) ), we will design a discrete time feedback control Biei(tττ) to stabilize it. These discrete times are 0,τ,2τ,…, where τ>0 is the duration between two consecutive observations. When τ is sufficiently small, these discrete

In this paper we investigate analytically and numerically the nonlinear Kelvin lattice, namely a chain of masses and nonlinear springs, as in the α-Fermi-Pasta–Ulam-Tsingou (FPUT) chain, where, in addition, each mass is connected to a nonlinear resonator, i.e., a second mass free to oscillate. Both nonlinearities are quadratic in the equations of motion. This setup represents the simplest prototype

In this paper, an accelerated subgradient extragradient algorithm with a new non-monotonic step size is proposed to solve bilevel variational inequality problems involving non-Lipschitz continuous operator in Hilbert spaces. The proposed algorithm with a new non-monotonic step size has the advantage of requiring only one projection onto the feasible set during each iteration and does not require prior

Nonlinear metamaterial structures may provide extensive applications in low-frequency and broadband vibration attenuation. Recently, there has been growing interest in nonlinear resonator design towards vibration attenuation of metamaterial structures. This work is focused on investigating the working mechanism of meta-beam by periodically attaching nonlinear coupling multi-frequency resonators for

We observe Poisson stable solutions for nonlinear stochastic functional differential equations (SFDEs) with finite delay. Firstly, we prove the existence and uniqueness of bounded (in square-mean sense) solutions and solution maps for SFDEs with finite delay by remoting start (or dissipative method) and classical pull-back attraction method. Then, based on the relationship between the solution and

6-revolute (6R) robot manipulators with offset wrists are widely applied in industrial scenarios. However, the autonomous and highly-precise manipulations of these robots are restricted for online industrial uses due to the lack of effective inverse kinematic methods. The inverse kinematic problem for 6R robot manipulators with offset wrists is addressed with a novel kinematic modelling and elimination

We develop an interior penalty virtual element method (IPVEM) for solving a Kirchhoff plate contact problem, which can be described by a fourth-order elliptic hemivariational inequality (HVI). The virtual element space in IPVEM is constructed by modifying the H2-conforming virtual element space, and the number of degrees of freedom is greatly reduced. To force the C1 continuity, the interior penalty

The distributed consensus is considered for multi-agent systems (MASs), which characterized by fractional reaction–diffusion partial differential equations (RDPDEs) in this paper. Based on Lyapunov technique and linear matrix inequalities (LMIs) theory, the consensus can be realized via two novel event-triggered boundary control schemes. Firstly, a novel convergence principle subject to finite time

Sharp transitions in relation to the variation of system parameters are frequently encountered in many multiple-timescale systems, and they have been found to be an important factor related to the generation of mixed-mode oscillations (MMOs). The present paper aims to report a novel type of sharp transition, referred to as step-shaped sharp transition, in a nonlinear gyroscope oscillator with multiple-frequency

The microstructural-dependent nonlinear in-plane stability characteristics of functionally graded (FG) sandwich shallow micro-arches subjected to a uniformly distributed lateral load in conjunction with a temperature rise are investigated in the current study. In this regard, the third-order shear flexible arch formulations are established within the framework of the modified strain gradient continuum

This paper focuses on observability and observer design for nonlinear complex dynamical systems described by a class of hyperbolic partial differential equations (PDEs) with nonlinear van de Pol type boundary conditions. The systems exhibit complex dynamics due to its imbalance of energy flows. Both the exact observability and approximate observability of the systems with different boundary output

This paper focuses on the mean-square finite-time synchronization (MFTS) of stochastic competitive neural networks with infinite time-varying discrete delays and reaction–diffusion terms (IRSCNNs). Different from other articles, this paper presents a new approach, which does not use finite-time stability theorem but uses integral inequality, Gronwall-type inequality and comparison strategy to study

Nonlinear vibration isolators with stiffness nonlinearity show promise for a broadband isolation performance without degrading the load capacity. An analytical method is proposed to predict all the possible frequency responses of nonlinear stiffness isolators under different damping. The vibration equation is transformed into an algebraic equation through harmonic balance method. The equation is regarded

The problem of heteroclinic chaos detecting is considered with the help of the Melnikov method. This paper presents the Melnikov method adaptation based on investigation of a nanosatellite attitude dynamics in the presence of internal dissipation properties. The need for this adaptation is determined by dynamical aspects of perturbing oscillations acting with damping amplitudes. In this case formal

This paper aims to incorporate a high order diffusion term into a SIQR epidemic model with transient prophylaxis and lasting prophylaxis. The existence and uniqueness of the global positive solution is proven and we find a condition ensuring the extinction of an infectious disease. The existence of a stationary distribution for the stochastic epidemic model is investigated as well. Numerical simulations

In this paper, we construct two kinds of exponential SAV approach with relaxation (R-ESAV) for dissipative system. The constructed schemes are linear and unconditionally energy stable. They can guarantee the positive property of SAV without any assumption compared with R-SAV and R-GSAV approaches, preserve all the advantages of the ESAV approach and satisfy dissipation law with respect to a modified

In this work, we extend an antibiotic resistance mathematical model in hospitals spatially on a two-dimensional coupled map lattice. The complex dynamics of the resultant space–time discrete model are investigated. An invasion reproduction number Rar and two control parameters Rsc and Rrc for sensitive bacteria and resistant bacteria, respectively, are defined. The three numbers play an important role

A non-axisymmetric granular vortex ring is generated by penetration into a loose granular bed, and its structure is found to be much more complex than the vortex rings observed in fluid flows. Herein, the properties of granular vortex ring are studied via CFD-DEM, and its transient structure is carefully identified by applying several parameters, including the equivalent radius of vortex core, the

An efficient numerical scheme is developed for coupled hydrodynamic and scalar transport systems to guarantee the conservation and the positivity-preserving properties for water depth and scalar concentration. A second-order well-balanced positivity-preserving central-upwind scheme based on the finite volume method is adopted to discretize both the Saint-Venant system and the advective fluxes in the

Formation flight is the most typical collaborative scenario of Unmanned Aerial Vehicles (UAVs) clusters, which can be used to perform various complex tasks. The most fundamental issue in UAVs formation flying is the consistency problem. In this paper, we study the predefined-time group generalized projective synchronization of the leader-follower multi-agent systems with different dimensions of the

In this work, we consider the multiplicity two dynamic transitions of a broad class of problems. The first main assumption is the existence of two critical eigenmodes of the linear operator which depend on at least two wave indices one of which are consecutive m, m+1 and the other identical n. The second main assumption is an orthogonality condition on the nonlinear interactions of the basis vectors

The Swift–Hohenberg (SH) equation is an important model in the study of pattern formation. In this paper, we propose two full-rank splitting schemes and a low-rank approximation for the SH equation. We first employ a second-order finite difference method to approximate the space derivatives. Based on the resulting semi-discrete system, two full-rank splitting schemes are derived. The convergences of

Effects of nonlinear dynamics of solitary waves and wave modulations within the modular (also known as quadratically cubic) Korteweg–de Vries equation are studied analytically and numerically. Large wave events can occur in the course of interaction between solitons of different signs. Stable and unstable (finite-time-lived) breathers can be generated in inelastic collisions of solitons and from perturbations

We present a new approach for solving partial differential equations (PDEs) based on randomized neural networks and the Petrov–Galerkin method, which we call the RNN-PG methods. This method uses randomized neural networks to approximate unknown functions and allows for a flexible choice of test functions, such as finite element basis functions, Legendre or Chebyshev polynomials, or neural networks

In this paper we present the inverse problem of determining a time dependent heat source in a two-dimensional heat equation accompanied with Dirichlet–Neumann–Wentzell boundary conditions. The model is of significant practical importance in applications where the time dependent internal source is to be controlled from total energy measurements in the case when the boundary is defined with partially

This paper is dedicated to fixed-time (FXI) output synchronization for multi-layer complex networks (MLCNs) with output coupling. By designing two kinds of dynamic event-triggering control strategies based on nodes’ output information, the FXI output synchronization of MLCNs with or without specified synchronization target is discussed, and further the Zeno behavior is excluded. In particular, the

This work aims to demonstrate some common fixed point results in light of certain common limit range properties. Such results are associated with certain weakly compatible mappings in intuitionistic fuzzy metric spaces that meet a specific implicit relation. In particular, the accomplished results in this paper generalize several significant theorems reported in the literature. As an application of

This work is concerned with convergence rate of Euler–Maruyama scheme for distribution-independent and distribution-dependent stochastic differential equations, where the drifts involved are Dini continuous and unbounded. Via introducing a new Zvonkin-type’s transformation, we investigate convergence rate of Euler–Maruyama scheme for stochastic differential equations with singular coefficients which

Understanding the behaviour of nonlinear dynamical systems is crucial in epidemiological modelling. Stability analysis is one of the important concepts in assessing the qualitative behaviour of such systems. This technique has been widely implemented on deterministic models involving ordinary differential equations (ODEs). Nevertheless, the application of stability analysis to distinct complex systems

This paper deals with the following critical nonlocal Choquard equation on the Heisenberg group: −(a−b∫Ω|∇Hu|2dξ)ΔHu=μ|u|q−2u+∫Ω|u(η)|Qλ∗|η−1ξ|λdη|u|Qλ∗−2uinΩ,u=0on∂Ω,where Ω⊂HN is a smooth bounded domain, ΔH is the Kohn-Laplacian on the Heisenberg group HN, 10, μ>0, 0<λ<4, and Qλ∗=2Q−λQ−2 is the critical exponent. Existence results are obtained by using the Ekeland variational principle, Clark critical

A simple electromagnetic energy harvester with a cubic nonlinear stiffness is proposed and dynamic responses as well as the potential power harvested are studied in this paper. The proposed nonlinear electromagnetic vibration energy harvester can be installed on a host base that is rotating at a constant speed and vibrating vertically. Considering the combination of the vertically vibrating and rotating

This article studies the lattice long-wave–short-wave resonance equations in weighted spaces. The authors first prove the global well-posedness of the initial value problem and the existence of the pullback attractor for the process generated by the solution mappings in the weighted space. Then they establish that the process possesses a family of invariant Borel probability measures supported by the

On the basis of the recent group classification of the one-dimensional magnetohydrodynamics (MHD) equations in cylindrical geometry, the construction of symmetry-preserving finite-difference schemes with conservation laws is carried out. New schemes are constructed starting from the classical completely conservative Samarsky–Popov schemes. In the case of finite conductivity, schemes are derived that

Magnetic skyrmions widely exist in a diverse range of magnetic systems, including chiral magnets with a non-centrosymmetric structure characterized by Dzyaloshinkii–Moriya interaction (DMI). In this study, we propose a generalized semi-implicit backward differentiation formula projection method, enabling the simulations of the Landau–Lifshitz (LL) equation in chiral magnets in a typical time step-size

The higher order commutators of fractional integral operator Iζ(⋅),Vm of variable order is shown to be bounded from the grand variable Herz spaces K̇p(⋅)a(⋅),u,θ(Rn) into the weighted space K̇ρ,q(⋅)a(⋅),u,θ(Rn), where ρ=(1+|z1|)−λ and 1q(z)=1p(z)−β(z)n when p(z) is not necessarily constant at infinity.

This paper addresses the problems of robust stability of fractional-order systems with mixed uncertainties, including multi-parameter uncertainties and norm-bounded uncertainties. The problems are relevant because on the one hand, uncertainties are common in real systems and the uncertainties in different components of systems may be of different types, and on the other hand, the non-convex and decoupling

Abstract not available

In this paper, we develop an adaptive neural strategy based on optimized backstepping (OB) technology for strict-feedback systems with unknown control directions and pre-set performance. First, the OB technique is used to construct each optimized virtual controller and optimized actual controller in backstepping, so as to achieve global optimization. Second, the problem of unknown control directions

Real life networks heavily rely on higher-order interactions. This paper studies the diffusibility of novel quasi-star higher-order networks from two aspects. When the coupling strengths of the lower-order and higher-order coupling parts are less than 1, the diffusibility can be maximized by choosing the intermediate values of these coupling strengths. When they are far greater than 1, there exists

The research work focuses on development of mathematical models to study on the dynamic behaviour of a multi-stage crash energy absorption system (MSCEAS) suitable for cars. The proposed energy absorption system can be attached in the front overhang of the vehicle, which comprises of a bumper, magneto-rheological absorber (MRA), friction spring, and piston-cylinder with shear plate assembly (PCSPA)

We present methods for excitation of bushes of nonlinear normal modes in the dynamical system, whose symmetry is described by any point or space group, with the aid of acting on the individual atoms periodic external forces with the frequency of some normal mode of the considered system. It is shown that these methods allow one to excite all bushes of nonlinear modes possible in this system. The application

This paper is concerned with the quasi-uniform synchronization (Q-US) issues of discrete fractional fuzzy neural networks (DFFNNs) with time delays. Firstly, we analyze the neural network systems with fuzzy time delays in discrete cases, complementing the neglected factors in the current literatures. Secondly, we use discrete fractional calculus including discrete Hölder inequality, discrete Gronwall

This paper studies Lp stabilization problem of the positive neural networks (NNs) with multiple time-varying delays. The delays can be bounded or unbounded. Firstly, a system solution-based new method is proposed, from which new Lp stabilization criteria are obtained. This method does not need to establish any Lyapunov–Krasovskii functional, which can greatly reduce the amount of calculations. The

Though the discrete delay has been extensively studied in the field of network topology identification, little attention has been paid to the distributed delay. In this paper, we address the partial topology identification problem of complex dynamical networks with distributed delay. By constructing a response network having fewer nodes than the drive network, partial topology of networks with distributed

In this paper we construct a family of Hamilton–Jacobi separable non-linear S1×S1 Sigma models for which the kink variety can be analytically identified and for which the linear stability of the emerging kinks is ensured. Furthermore, a model with only one vacuum point is found, where all kinks are forced to be non-topological. The non-simply connectedness of the torus guarantees the global stability

Since the immune function of AIDS patients infected with SARS-CoV-2 is impaired, it is easier for SARS-CoV-2 to reproduce, replicate, and even mutate in the host. Therefore, the co-infection of SARS-CoV-2 and HIV in vivo deserves our attention. In this paper, a series of co-infection dynamic models of HIV, wild-type, and variant SARS-CoV-2 are developed and studied for four co-infected patients in

This paper introduces a consistent projection finite method for the non-stationary incompressible thermally coupled MHD equations, which buoyancy affects because temperature differences in the flow cannot be neglected. It is a fully discrete projection method. The unconditional stability and error estimates of the velocity, pressure, temperature, and magnetic field under some assumptions are given

Sparse identification of nonlinear dynamical systems is a topic of continuously increasing significance in the dynamical systems community. Here we explore it at the level of lattice nonlinear dynamical systems of many degrees of freedom. We illustrate the ability of a suitable adaptation of Physics-Informed Neural Networks (PINNs) to solve the inverse problem of parameter identification in such discrete