The management of COVID-19 appears to be a long-term challenge, even in countries that have managed to suppress the epidemic after their initial outbreak. In this paper, we propose a model predictive approach for the constrained control of a nonlinear compartmental model that captures the key dynamical properties of COVID-19. The control design uses the discrete-time version of the epidemic model,

We theoretically and experimentally examine the effect of forcing and damping on systems that can be described by the nonlinear Schrödinger equation (NLSE), by making use of the phase-space predictions of the three-wave truncation. In the latter, the spectrum is truncated to only the fundamental frequency and the upper and lower sidebands. Our experiments are performed on deep water waves, which are

In this work, we study the Kundu-nonlinear Schrödinger (Kundu-NLS) equation (so-called the extended NLS equation), which can describe the propagation of the waves in dispersive media. A Lax spectral problem is used to construct the Riemann–Hilbert problem, via a matrix transformation. Based on the inverse scattering transformation, the general solutions of the Kundu-NLS equation are calculated. In

Two-DOF nonlinear system under stochastic excitation is considered. It is assumed that the system allows from two up to four nonlinear normal modes (NNMs) with rectilinear trajectories in the system configuration space. Influence of the random excitation to the NNMs stability is analyzed by using the analytical–numerical test, which is an implication of the well-known stability definition by Lyapunov

This paper deals with the inherent instability observed in the speed of a planing type craft. In the case of displacement craft, the systems governing the speed are stable hence closed-loop control is trivial. In the case of planing craft, however, there may exist instability in their speed. By using the Qualitative Theory of Dynamical Systems (QTDS), this paper shows that there may exist a set of

An iterative convergence control method (ICCM) based on the support vector regression (SVR) is proposed to realize the position–posture control of the planar four-link underactuated manipulator with a passive second link. Firstly, the particle swarm optimization (PSO) algorithm is used to obtain the target angles of all links according to the position–posture control objective. Then, two prediction

Recently, it has been shown that DC–AC and AC–DC power converters whose dynamics is governed by two vastly different frequencies lead to a special class of piecewise smooth models characterized by a practically unpredictable number of switching manifolds between partitions in the state space associated with different dynamics. In the previous publications, we have shown that transformations of chaotic

Triadic interactions are the fundamental mechanism of energy transfer in fluid flows. This work introduces bispectral mode decomposition as a direct means of educing flow structures that are associated with triadic interactions from experimental or numerical data. Triadic interactions are characterized by quadratic phase coupling which can be detected by the bispectrum. The proposed method maximizes

In this study, a method of measuring the added mass for an object oscillating in a viscous fluid using nonlinear self-excited oscillations was developed. The added mass produces an additional inertial effect on the vibrating object. In previous methods, the added mass is obtained experimentally from the response frequency and amplitude at the peak in the frequency response curve under a harmonically

In this paper, a novel implicit family of composite two sub-step algorithms with controllable dissipations is developed to effectively solve nonlinear structural dynamic problems. The primary superiority of the present method over other existing integration methods lies that it is truly self-starting and so the computation of initial acceleration vector is avoided, but the second-order accurate acceleration

In this paper, we propose a model for the transverse oscillation of a square-section cylinder under flow. The fluctuating transverse force due to vortex shedding is represented using a coupled nonlinear wake oscillator, while the unsteady force for galloping caused by the varying incidence angle effects is modelled using the quasi-steady approach. First, we analytically investigate the lift behavior

A 2-dimensional coupled logistic map lattice model and a 2-dimensional Logistic-nested-Sine map are proposed in this paper. In order to strengthen complexity of 2-dimensional coupled logistic map lattice, chaotic sequences are transformed to binary sequences, and new decimal sequences are constructed by perturbed binary sequences. Numerical experimental results demonstrate that this method can increase

Origami has recently received wide attention, and the study on its dynamic characteristics remains a nascent field. The waterbomb origami is a common subtype of origami, and its base structure is treated as a bi-stable configuration in the literature. The systematical framework for modeling, simulation and dynamic analysis of the vibration for the waterbomb origami base is established in this paper

The main purpose of this paper is to study both the underdamped and the overdamped dynamics of the nonlinear Helmholtz oscillator with a fractional-order damping. For that purpose, we use the Grünwald–Letnikov fractional derivative algorithm in order to get the numerical simulations. Here, we investigate the effect of taking the fractional derivative in the dissipative term in function of the parameter

This paper investigates the string stability and traffic flow stability based on an improved quadratic spacing policy for heterogeneous vehicular platoons with actuator faults. Due to the occurrence of actuator faults, the maximum acceleration changes, which may invalid the traditional quadratic spacing policy. To tackle the dilemma, an improved quadratic spacing policy with the lower bound of fault

Invariant manifolds are important sets arising in the stability theory of dynamical systems. In this article, we take a brief review of invariant sets. We provide some results regarding the existence of invariant lines and parabolas in planar polynomial systems. We provide the conditions for the invariance of linear subspaces in fractional-order systems. Further, we provide an important result showing

All possible one- and two-component delocalized nonlinear vibrational modes (DNVMs) in triangular lattice are analyzed. DNVMs are obtained considering solely upon the symmetry of the triangular lattice, and thus, they exist regardless the type of interactions between particles. In this work, the nearest-neighbor inter-particle interactions are described by the \(\beta \)-FPU potential. The one-component

This paper develops a fixed-time trajectory tracking control scheme for Mars entry vehicle under uncertainty. First, a novel fixed-time nonsingular terminal sliding mode (FTNTSM) surface with bounded convergence time independent on the initial conditions is developed, which not only averts the singularity problem but also assures fast convergence. Second, based on the FTNTSM surface and adaptive technique

This study examines the effect of vehicle–bridge interaction (VBI) on the vibration of coupled train–bridge systems and proposes a consistent approach to decouple the VBI problem; the Extended Modified Bridge System (EMBS) method. This constitutes an extension of the formerly developed, for simply supported bridges, Modified Bridge System method. The analysis considers a generic, multi-degree of freedom

Darboux and Bäcklund transformations on integrable couplings are formulated and generalized. The generalization of the theory pertains to spectral problems where the spatial spectral matrix is a polynomial in \(\lambda \) of any order. A specific application to a generalized D-Kaup–Newell integrable couplings system is worked out, along with an explicit formula for the associated Bäcklund transformation

In this paper, the weight of the rotor is considered in a 16-pole rotor active magnetic bearing system with constant stiffness. The equations of motion are derived to show the asymmetry between the rotor’s horizontal and vertical displacements. Accordingly, the rotor may exhibit forward, backward, intermediate, or hybrid whirls. The possibility to overcome the backward whirl and to symmetrize the rotor’s

The phase reduction approach has manifested its power in analyzing the rhythmic behaviors for limit cycle oscillators. For coherent oscillation purely induced by noise, e.g., the coherence resonance oscillator, the stochastic dynamics exhibit almost deterministic limit cycle phenomenon which inspires the application of the phase reduction approach to this kind of systems. In this paper, the FitzHugh–Nagumo

This paper examines the oscillations of a spherical pendulum with horizontal Lissajous excitation. The pendulum has two degrees of freedom: a rotational angle defined in the horizontal plane and an inclination angle defined by the pendulum with respect to the vertical z axis. The results of numerical simulations are illustrated with the mathematical model in the form of multi-colored maps of the largest

The application of external electromagnetic stimulation to regulate the electrophysiological activities of specific brain regions can provide an ideal control or treatment scheme for some non-organic mental diseases. To further explore the effectiveness of electromagnetic stimulation in the treatment of mental illnesses, the regulatory abilities of external electromagnetic stimulation on the pattern

With nonlinear systems extensively studied for applications in vibration isolation, energy harvesting, etc., most of the studies focused on the response of the nonlinear oscillator defined by some explicit equations, namely the typical oscillator. Rare studies or approaches are devoted to the non-typical nonlinear oscillator for which the stiffness profile is possible defined by an arbitrary curve

In this paper, a class of switched fractional-order continuous-time systems with order \(0<\alpha <1\) is investigated. First, an interesting property of fractional calculus is revealed, that is, unlike integer-order integral, it does not hold that \(_{t_{0}}D^{-\alpha }_{t}f(t)={_{t_{0}}}D^{-\alpha }_{t_1}f(t)+{_{t_{1}}}D^{-\alpha }_{t}f(t)\) for \(\alpha >0,~t_0

A pendulum with an attached permanent magnet swinging in the vicinity of a conductor is a typical experiment for the demonstration of electromagnetic braking and Lenz’ law of induction. When the conductor itself moves, it can transfer energy to the pendulum. An exact analytical model of such an electromagnetic interaction is possible for a flat conducting plate. The eddy currents induced in the plate

Reconstructing a pitchfork bifurcation that is destroyed by an exogenous disturbance is important to control it. This paper extends the equivalent-input-disturbance (EID) approach to solve the problem of reconstructing a pitchfork bifurcation when there is an exogenous disturbance for the first time. A nonlinear term and a bifurcation parameter are designed in the system to reconstruct the pitchfork

This paper focuses on the problem of fixed-time chaos suppression and stabilization of a class of Lorenz systems with uncertain parameters. Based on the fixed-time stability theory, adaptive control and backstepping algorithm, a novel adaptive practical fixed-time controller is proposed. It is shown that the presented control scheme can guarantee that all the signals of the closed-loop system are bounded

This paper addresses the problem of consensus tracking with fixed-time convergence, for leader–follower multi-agent systems with double-integrator dynamics, where only a subset of followers has access to the state of the leader. The control scheme is divided into two steps. The first one is dedicated to the estimation of the leader state by each follower in a distributed way and in a fixed-time. Then

The nonlinear vortex-induced vibration of a rectangular section with an aspect ratio B/D = 6 is investigated in this study, aiming at explanation of the phenomenon of double lock-in ranges. First, numerical results by two-dimensional CFD simulation are compared with experimental results; then flow field characteristics, aerodynamic loadings and structural motion properties are presented and discussed;

The classical local impact laws of Newton and Poisson are able to capture the behaviour observed in single-impact collisions in many situations. However, in the case of collisions with multiple impacts, the simultaneous enforcement of local impact laws does not reproduce essential features of the physical process, such as propagation effects. The aim of this work is to broaden the applicability of

Memristors are widely considered to be promising candidates to mimic biological synapses. In this paper, by introducing a non-ideal flux-controlled memristor model into a Hopfield neural network (HNN), a novel memristive HNN model with multi-double-scroll attractors is constructed. The parity of the number of double scrolls can be flexibly controlled by the internal parameters of the memristor. Through

The signal transmission phenomenon in an underdamped fractional system composed of two harmonically coupled particles, but only the first particle, which is driven by a periodic force, is studied. We obtain the analytical expressions for the steady-state response of the two coupled particles by applying the stochastic averaging method and define the signal transmission factor to characterize signal

A high-speed rotating rotor system mounted on a moving vehicle is inevitably subjected to parametric excitations and exciting forces induced by base motions. Dynamic characteristics of a rotor-bearing system supported by squeeze-film damper with retainer spring subjected to unbalance and support motions are investigated. Using Lagrange’s principle, equations of motion for rotor system relative to a

In this paper, we introduce a generalization of Lyapunov’s direct method for dynamical systems with fractional damping. Hereto, we embed such systems within the fundamental theory of functional differential equations with infinite delay and use the associated stability concept and known theorems regarding Lyapunov functionals including a generalized invariance principle. The formulation of Lyapunov

Buoyant, finite-size, or inertial particle motion is fundamentally unlike neutrally buoyant, infinitesimally small, or Lagrangian particle motion. The de-jure fluid mechanics framework for the description of inertial particle dynamics is provided by the Maxey–Riley equation. Derived from first principles—a result of over a century of research since the pioneering work by Sir George Stokes—the Maxey–Riley

Chaotic maps are widely used in the designs of different security applications due to their series of attractive features, but many commonly used chaotic maps have several weaknesses such as limited chaotic range, small Lyapunov exponent and heavy computational cost. Although there have been many methods to overcome these shortcomings, most of them lack theoretical analysis and the improvement effect

This paper addresses the problem of trajectory tracking control of an underactuated surface vessel moving in a two-dimensional space in the presence of unknown disturbances. In a preliminary stage, a couple of nonlinear observers is derived to obtain an estimate of the perturbations, which are assumed to originate from unmodeled time-varying dynamics and/or exogenous disturbances. Secondly, we resort

Periodic synchronous patterns induced by the traveling waves in coupled discontinuous map lattices are investigated by numerical simulation. The formation mechanism of this behavior is analyzed in detail. The results show that the periodic synchronous patterns arise from the competition between different homogeneous states and are a function of their relative sizes. Periodic synchronous patterns can

Aiming to isolate disturbance vibration for heavy machines with low frequency, a novel hydro-pneumatic vibration isolator with high-static and low-dynamic (HSLD) stiffness is proposed, which contains bellows structure as elastic element and pressurized gas and incompressible liquid as working media. Due to that the natural frequency of isolation system with such isolator is close to zero and loading

This paper presents a stochastic model for performing the uncertainty and sensitivity analysis of a Jeffcott rotor system with fixed-point rub-impact and multiple uncertain parameters. A probabilistic nonlinear formulation is developed based on the combination of the harmonic balance method and an alternate frequency/time procedure (HB-AFT) in stochastic form. The non-intrusive generalized polynomial

Infinite dimensions always challenge the analysis of multiple stability in nonlinear time-delayed systems, as the computation and visualization of conventional basin of attraction are hampered by the increase in systems’ dimensions. To address this issue, this paper introduces an orthonormal basis to approximate the delayed states, uses their signal energy to represent them, and generalises the concept

Theoretical studies suggest that dispersion and repulsion are two important interactions that occur within non-polar particles. Enlightened by this, we propose a simple model for flocking of autonomous agents interacting by physicochemically inspired dispersion and repulsion interactions. This interdisciplinary effort provides a generic framework for design and analysis of distributed flocking by introducing

This paper investigates the trajectory tracking problem of the quadrotor unmanned aerial vehicles (UAV) with consideration of both attitude and position dynamics. First of all, the trajectory tracking problem is divided into the commands tracking in position and attitude loops by introducing the virtual attitude angle commands. Secondly, the high-order sliding mode observers (HSMOs) are introduced

The friction-induced vibration of a novel 5-DoF (degree-of-freedom) mass-on-oscillating-belt model considering multiple types of nonlinearities is studied. The first type of nonlinearity in the system is the nonlinear contact stiffness, the second is the non-smooth behaviour including stick, slip and separation, and the third is the geometrical nonlinearity brought about by the moving-load feature

In this paper, an adaptive prescribed performance controller, consisting of a novel scalarly virtual parameter adaptation (SVPA) technique, is developed for a class of single-input and single-output high-order nonlinear pure-feedback systems in the presence of model uncertain yet locally Lipschitz nonlinearities. The objective of this work is to improve the transient and steady performance of pioneering

In this work, we estimate the total number of infected and deaths by COVID-19 in Brazil and two Brazilian States (Rio de Janeiro and Sao Paulo). To obtain the unknown data, we use an iterative method in the Gompertz model, whose formulation is well known in the field of biology. Based on data collected from the Ministry of Health from February 26, 2020, to July 2, 2020, we predict, from July 3 to 9

This paper is devoted to investigate the nonlinear vibration characteristics and active control of composite lattice sandwich plates using piezoelectric actuator and sensor. Three types of the sandwich plates with pyramidal, tetrahedral and Kagome cores are considered. In the structural modeling, the von Kármán large deflection theory is applied to establish the strain–displacement relations. The nonlinear

We study the integrability of the Hamiltonian normal form of 1:2:2 resonance. It is known that this normal form truncated to order three is integrable. The truncated to order four normal form contains many parameters. For a generic choice of parameters in the normal form up to order four, we carry on non-integrability analysis, based on the Morales–Ramis theory using only first variational equations

Though contradicting with natural selection, cooperative behaviors widely exist in practice and seem to be an effective measure to maintain the functioning of complex systems. As revealed by previous studies, punishment is capable of promoting cooperation and therefore various types of punishment are proposed. Previously, scholars mainly focus on investigating either peer punishment or pool punishment

During epidemic outbreaks, there are various types of information about epidemic prevention disseminated simultaneously among the population. Meanwhile, the mass media also scrambles to report the information related to the epidemic. Inspired by these phenomena, we devise a model to discuss the dynamical characteristics of the co-evolution spreading of multiple information and epidemic under the influence

We provide the maximum number of limit cycles of some classes of discontinuous piecewise differential systems formed by two differential systems separated by a straight line, when these differential systems are linear centers or three families of cubic isochronous centers, giving rise to ten different classes of discontinuous piecewise differential systems. These maximum number of limit cycles vary

Low-power devices used in Internet-of-things networks have been short of security due to the high power consumption of random number generators. This paper presents a low-power hyperchaos-based true random number generator, which is highly recommended for secure communications. The proposed system, which is based on a four-dimensional chaotic system with hidden attractors and oscillators, exhibits

The primary and subharmonic simultaneous resonance of Duffing oscillator with fractional-order derivative is studied. Firstly, the approximately analytical solution of the resonance is obtained by the method of multiple scales, and the correctness and satisfactory precision of the analytical solution are verified by numerical simulation. Then, the amplitude–frequency curve equation and phase–frequency

The centrifugal pendulum vibration absorber (CPVA) is a device whose purpose is the reduction in torsional vibrations in rotating and reciprocating machinery. Over the last decades, CPVA nonlinear behavior has been thoroughly investigated. In particular, the performance and the local stability of cycloidal, epicycloidal and tautochronic CPVAs have been extensively analyzed. In this paper, on the basis

The present work studies the dynamics of chaotic Rössler oscillators in a star network, where the central node or relay system is controlled by an external and similar system. Without the outer systems, the middle oscillator of the network is an amplified observer of the driver. Varying both amplification and coupling parameters leads the outer systems and the driver–relay to various behaviors. To

We formulate and experimentally validate a theoretical reduced-order model for the transverse galloping of nonlinear structures, namely a pair of identical, parallel-oriented cantilever beams whose free ends are attached to square prisms. We derive the structural nonlinearities from (a) a single-mode approximation of the nonlinear (truncated at cubic order) equation of motion, calculated for conservative

The dynamics of chains of interacting active particles with Rayleigh-type dissipation and coupled by a Morse potential were previously studied. In this work we introduce an on-site potential to transform this system into a chain of oscillators. We study the evolution of modes previously found in a chain of active particles as a consequence of the on-site force. Beside this, a new class of modes, dissipative

In this paper, a novel fixed-time second-order sliding mode (SOSM) controller has been developed for a class of nonlinear systems with output constraints. Based on the output constraint condition, a new barrier Lyapunov function, which can be used to deal with the output constraint, is first constructed. Then, with the help of adding a power integrator technique, the SOSM algorithm can be constructed