We provide rigorous computer-assisted proofs of the existence of different dynamical objects, like stable families of periodic orbits, bifurcations and stable invariant tori around them, in the paradigmatic Hénon–Heiles system. There are in the literature a large number of articles with numerical simulations on this system, and other open Hamiltonians, but only a few give a rigorous guarantee of simulations

In this paper, a second-order numerical scheme for the time-fractional phase field models is proposed. In this scheme, the fractional backward difference formula is used to approximate the time-fractional derivative and the extended scalar auxiliary variable method is used to deal with the nonlinear terms. The energy dissipation property for the numerical scheme is proved. Our discussion includes the

In this paper, the autonomous landing control issue on moving shipboard is investigated for unmanned helicopters subject to disturbances. The issue is studied by stabilizing the error system of the helicopter and the shipboard. The landing process is divided into two phases, i.e., homing phase, where a hierarchical double-loop control scheme is developed such that the helicopter is forced to hover

A nonlinear energy sink (NES), conceived to mitigate the vibrations of a multi-degree-of-freedom host mechanical system, is considered. The high-dimensional slow invariant manifold (SIM) describing the high-amplitude slow dynamics of the system is derived and exploited to interpret its transient regimes caused by impulsive excitation. It is shown that algebraic expressions derived from the SIM formulation

This paper proposes an improved transfer-matrix method (TMM) for investigating the steady-state response of complex rotor-bearing systems. The internal damping of the shafts is considered to enhance the accuracy of the method. A transfer matrix of ball bearings with clearance and Hertzian contact is established. In addition, the incremental harmonic balance method is combined with the TMM to obtain

In this paper, a generalized fractional-order SEIR model is proposed, denoted by SEIQRP model, which divided the population into susceptible, exposed, infectious, quarantined, recovered and insusceptible individuals and has a basic guiding significance for the prediction of the possible outbreak of infectious diseases like the coronavirus disease in 2019 (COVID-19) and other insect diseases in the

Iterative learning control (ILC) is a well-established methodology which has proved successful in achieving accurate tracking control for repeated tasks. However, the majority of ILC algorithms require a nominal plant model and are sensitive to modelling mismatch. This paper focuses on the class of gradient-based ILC algorithms and proposes a data-driven ILC implementation applicable to a general class

A long-standing question in applications of dynamical systems theory is how to distinguish noisy signals from chaotic steady states. Information-theoretic measures hold promise to resolve this problem. We apply two such measures to numerically computed phase-space trajectories of continuous-state nonlinear oscillators: forecasting or statistical complexity, which quantifies the minimum memory required

This paper presents a feedforward technique for arresting motion in nonlinear systems based on two-scale command shaping (TSCS). The advantages of the proposed technique arise from its feedforward nature and ease of implementation in linear and nonlinear systems. Using the TSCS strategy, the control input required to arrest motion is decomposed into two scales—the first arrests dynamics associated

We investigate a (3 + 1)-dimensional nonlinear evolution equation which is a higher-dimensional generalization of the Korteweg–de Vries equation. On the basis of the decomposition approach, the N-antidark soliton solution on a finite background is constructed by using the Darboux transformation together with the limit technique. The asymptotic analysis for the N-antidark soliton solution is performed

In this paper, the flow switching theory of discontinuous dynamical systems is used as the main tool to study the dynamical behaviors of a two-degree-of-freedom friction oscillator with elastic impacts, where considering that the inequality of static and kinetic friction forces results in the existence of flow barriers at the relative velocity between the mass and conveyor belt tending to zero. The

The nonlinear dynamics of the six-pole rotor active magnetic bearings system is studied in this article for the first time. Two control configurations based on a proportional-derivative feedback current controller are proposed to mitigate lateral vibrations of the considered system. The first configuration is designed in such a way that only four electromagnetic poles are responsible for the system

Distribution entropy has been proved to reveal stability for short time series and to distinguish different classes of series by complexity. However, there still exists some drawbacks. For example, it does not consider the possible causality underlying the data, which may not precisely identify deterministic from stochastic processes. In addition, cumulative residual entropy can successfully solve

This paper describes a rapid and efficient nonlinear non-resonance mechanism for low-to-high-frequency energy scattering, which is referred to as intermodal targeted energy transfer (IMTET). To present the IMTET mechanism in the most basic setting, a blast-excited two-DOF linear system with a single clearance is considered. The impact interactions facilitate rapid transfer of oscillation energy from

This note comments on the questionable approach and claims made in “Study of mixed-mode oscillations in a nonlinear cardiovascular system” [Nonlinear Dyn, doi: 10.1007/s11071-020-05612-8]. Although the author of the above paper attempts to discuss a nonlinear cardiovascular system and its dynamics, the conductance model used, is that of the well-known Cassie–Mayr model of electric arcs, known in the

This paper investigates a logistic map derived from a difference equation in the framework of discrete fractional calculus. Through the Poincaré plots and Julia sets, the map’s chaotic and fractal characteristics are studied comparing with those of a quadratic map to be proposed. The memory effect of fractional difference maps is reflected in these dynamics, and some reasonable explanations are given

This paper focuses on security control of nonlinear networked control systems with parameter uncertainties. Interval type-2 T–S fuzzy model is used to represent the original nonlinear system, so as to capture the parameter uncertainties. Stochastic deception attacks are considered in the sensor to controller channel and the controller to actuator channel. By constructing Lyapunov–Krasovskii functional

This paper deals with two problems: the identification and compensation of hysteresis nonlinearity in dynamical systems using nonlinear polynomial autoregressive models with exogenous inputs (NARX). First, based on gray-box identification techniques, some constraints on the structure and parameters of NARX models are proposed to ensure that the identified models display a key feature of hysteresis

The dynamics of spiking and bursting activities have attracted interest from scientists due to their significance in the brain and neural systems. In this work, the effects of processing delay, specifically the time delay in coupling, on the dynamical behaviors of the coupled Hindmarsh–Rose neurons with resting state are investigated. The results reveal that the processing delay can induce rich spiking

Phase-locked loops are important engineering systems that are widely used in electronic communication systems. Although, in almost all the engineering applications they operate in coupled conditions; however, most of the studies explored their dynamics in the isolated condition. In this paper, we explore in detail the collective dynamics of a network of coupled time-delay digital tanlock loops (TDTLs)

The three-degree-of-freedom (3D) pendulum has been used as a benchmark in the field of nonlinear dynamics and control. Nonetheless, the attitude control of 3D pendulum is still an open problem presently since some issues remain not well addressed. In this paper, a robust adaptive finite-time attitude control method is proposed for the attitude tracking control of a 3D pendulum with external disturbance

With the unfolding of the COVID-19 pandemic, mathematical modelling of epidemics has been perceived and used as a central element in understanding, predicting, and governing the pandemic event. However, soon it became clear that long-term predictions were extremely challenging to address. In addition, it is still unclear which metric shall be used for a global description of the evolution of the outbreaks

We use the Liénard–Wiechert potential to show that very violent fluctuations are experienced by an electromagnetic charged extended particle when it is perturbed from its rest state. The feedback interaction of Coulombian and radiative fields among different charged parts of the particle makes uniform motion unstable. Then, we show that radiative fields and radiation reaction produce dissipative and

In this paper, a variable-coefficient cubic–quintic nonlinear Schrödinger equation involving five arbitrary real functions of space and time is analyzed from the point of view of symmetry analysis by using Lie’s invariance infinitesimal criterion. The infinitesimal generators of corresponding equivalence transformations are presented. The first-order differential invariants are constructed to identify

We investigate the emergence of amplitude and frequency chimera states in ring–star networks consisting of identical Chua circuits connected via nonlocal diffusive, bidirectional coupling. We first identify single-well chimera patterns in a ring network under nonlocal coupling schemes. When a central node is added to the network, forming a ring–star network, the central node acts as the distributor

The large-scale use of the Internet brings the problem of the rapid spread of computer malware over the network. Aiming at the relationship between malware, propagation paths and users in network propagation, this paper proposes a perception propagation model of computer malware based on a tripartite graph. First of all, aiming at the driving and influence of malware, propagation paths and users’ association

This paper investigates the global stability analysis of two-strain epidemic model with two general incidence rates. The problem is modelled by a system of six nonlinear ordinary differential equations describing the evolution of susceptible, exposed, infected and removed individuals. The wellposedness of the suggested model is established in terms of existence, positivity and boundedness of solutions

System identification of dynamical systems is often posed as a least squares minimization problem. The aim of these optimization problems is typically to learn either propagators or the underlying vector fields from trajectories of data. In this paper, we study a first principles derivation of appropriate objective formulations for system identification based on probabilistic principles. We compare

The stability and bifurcation behavior of the electromagnet-track beam coupling system of the electromagnetic suspension maglev vehicle are studied by the theoretical and numerical analyses. The stability domain of three key dynamics parameters of the track beam as well as the Lyapunov coefficient at the degenerated equilibrium point is calculated. The topological structure of the solution to the coupling

A (3 + 1)-dimensional Gross–Pitaevskii equation with partially nonlocal distributed coefficients under a linear potential is followed with interest. The mapping procedure from the distributed-coefficient to the constant-coefficient equations is provided. Via the procedure with solution of constant-coefficient NLSE from the variational principle, an approximate vortex soliton solution is reported. With

We report the novel colliding dynamics of the rogue waves (RWs) for a three-component transient stimulated Raman scattering system arising from nonlinear optics. The N-order RW solutions are constructed by utilizing the generalized Darboux transformation scheme. Then, the dynamics of the RWs are analyzed. As \(N\ge 2\), the multiple RWs collide towards a central point. During the collisions and interactions

Paradoxical enhancement rather than reduction in firing activity induced by inhibitory effect is very important for both nonlinear dynamics and neuroscience. In the present paper, to build a more comprehensive viewpoint related to excitatory effect, a paradoxical phenomenon modulated by the excitatory self-feedback of autapse is extended to bursting activity in a modified Morris–Lecar model. With increasing

This work is based on the observation that the first Poincaré–Lyapunov constant is a quadratic function of the coefficients of the two-dimensional vector field at a Hopf bifurcation. From a given parameter point, we find the distance to the “Hopf quadric.” This distance provides a measure of the criticality of the Hopf bifurcation. The viability of the approach is demonstrated through numerical examples

The internal resonances between the longitudinal and transversal oscillations of a forced Timoshenko beam with an axial end spring are studied in depth. In the linear regime, the loci of occurrence of 1 : ir, \(ir \in \mathbb {N}\), internal resonances in the parameters space are identified. Then, by means of the multiple time scales method, the 1 : 2 case is investigated in the nonlinear regime, and

Damping is largely increasing with the vibration amplitude during nonlinear vibrations of rectangular plates. At the same time, soft materials present an increase in their stiffness with the vibration frequency. These two phenomena appear together and are both explained in the framework of the viscoelasticity. While the literature on nonlinear vibrations of plates is very large, these aspects are rarely

Recent studies in passively isolated systems have shown that mode coupling is desirable for better vibration suppression, thus refuting the long-standing rule of modal decoupling. However, these studies have ignored the nonlinearities in the isolators. In this work, we consider stiffness nonlinearity from pneumatic isolators and study the nonlinear forced damped vibrations of a passively isolated ultra-precision

Countries in Europe took different mobility containment measures to curb the spread of COVID-19. The European Commission asked mobile network operators to share on a voluntarily basis anonymised and aggregate mobile data to improve the quality of modelling and forecasting for the pandemic at EU level. In fact, mobility data at EU scale can help understand the dynamics of the pandemic and possibly limit

This paper proposes a non-intrusive interval uncertainty analysis method for estimation of the dynamic response bounds of nonlinear systems with uncertain-but-bounded parameters using polynomial chaos expansion. The conventional interval arithmetic and Taylor series methods usually lead to large overestimation because of the intrinsic wrapping effect, especially for the multidimensional and non-monotonic

Robust testing and tracing are key to fighting the menace of coronavirus disease 2019 (COVID-19). This outbreak has progressed with tremendous impact on human life, society and economy. In this paper, we propose an age-structured SIQR model to track the progression of the pandemic in India, Italy and USA, taking into account the different age structures of these countries. We have made predictions

Harvesting ultra-low frequency random vibration, such as human motion or turbine tower oscillations, has always been a challenge, but could enable many potential self-powered sensing applications. In this paper, a methodology to effectively harness this type of energy is proposed using rotary-translational motion and bi-stability. A sphere rolling magnet is designed to oscillate in a tube with two

The outbreak of COVID-19 in Italy took place in Lombardia, a densely populated and highly industrialized northern region, and spread across the northern and central part of Italy according to quite different temporal and spatial patterns. In this work, a multi-scale territorial analysis of the pandemic is carried out using various models and data-driven approaches. Specifically, a logistic regression

The objective of this contribution is to compare two methods proposed recently in order to build efficient reduced-order models for geometrically nonlinear structures. The first method relies on the normal form theory that allows one to obtain a nonlinear change of coordinates for expressing the reduced-order dynamics in an invariant-based span of the phase space. The second method is the modal derivative

The current work is primarily devoted to the asymptotic analysis of the instability zones existing in the bi-linear Mathieu equation. In this study, we invoke the common asymptotical techniques such as the method of averaging and the method of multiple time scales to derive relatively simple analytical expressions for the transition curves corresponding to the 1:n resonances. In contrast to the classical

Due to the poor security level in current industrial network, the control performance of robots may be severely affected by cyber attacks. This paper studies the sensor attack reconstruction problem of mobile robots, where a switching Kalman fusion mechanism is proposed to reconstruct the sensor attacks online. It is shown that the proposed mechanism is better than the existing extended state observer

In this paper, we generalize the Preisach model to the case when parameters of elementary relays are random variables. We show that an output state of the stochastic Preisach operator can be treated as a random process. For this random process the first and second statistical moments are obtained in an explicit form. We prove also the correctness of the definition of such an operator. Illustrative

The paper introduces a technique that decomposes the dynamics of a nonlinear system about an equilibrium into low-order components, which then can be used to reconstruct the full dynamics. This is a nonlinear analogue of linear modal analysis. The dynamics is decomposed using Invariant Spectral Foliation (ISF), which is defined as the smoothest invariant foliation about an equilibrium and hence unique

A new simple formulation of the orientation constraints for very flexible bodies is introduced in this investigation. This constraint formulation avoids using the tangent or cross-section frames previously used in the literature by directly using two position-gradient vectors to define the orientation constraint equations that eliminate the relative rotations between two bodies. The orientation constraints

In this work, the generalized \((3+1)\)-dimensional variable coefficients Kadomtsev–Petviashvili equation, widely used in fluids or plasmas, is analyzed via the unified method and its general form. The multi-soliton rational solutions are obtained including single- and double-soliton rational solutions. Single-soliton shaping and the interactions of double-soliton are graphically discussed in different

We consider the two-dimensional map introduced in Bischi et al. (J Differ Equ Appl 21(10):954–973, 2015) formulated as a model for a renewable resource exploitation process in an evolutionary setting. The global dynamic scenarios displayed by the model are not so often encountered in smooth two-dimensional dynamical systems. We explain the occurrence of such scenarios at the light of the theory of

On the title page, author Oleg Shiryavev should be spelled as Oleg Shiryayev.

The COVID-19 disease significantly has threatened the human lives and economy. It is a dynamic system with transmission and control as factors. Modeling the dynamics of the spread of COVID-19 based on the reported data can predict the growing trend of such a disease. In this paper, the dynamic evolution of COVID-19 in Spain is studied, and a comprehensive SEIR model is adopted to fit the obtained clinical

Autoloaders that replace the human loaders performing ammunition transferring tasks in main battle tanks have been confronted with the problem of poor compliance abilities. To solve this problem, a novel autoloader with novel compliant actuators-SEAs (series elastic actuators) is firstly proposed in this paper. However, compliant actuators will lead to the problem of flexible vibrations. Moreover,

Nonlinear flutter of variable stiffness composite plates—using a reduced-order model benefiting from a large-enough number of modes or degrees of freedom—is the subject of this research. Dynamic of such plates is enriched by different scenarios including period-n (un)stable limit cycle oscillations, quasi-periodic or chaotic solutions, along with Hopf, symmetry breaking and period doubling bifurcations

Fractional derivatives of Prabhakar type are capturing an increasing interest since their ability to describe anomalous relaxation phenomena (in dielectrics and other fields) showing a simultaneous nonlocal and nonlinear behaviour. In this paper we study the asymptotic stability of systems of differential equations with the Prabhakar derivative, providing an exact characterization of the corresponding

COVID-19 has spread around the world since December 2019, creating one of the greatest pandemics ever witnessed. According to the current reports, this is a situation when people need to be more careful and take the precaution measures more seriously, unless the condition may become even worse. Maintaining social distances and proper hygiene, staying at isolation or adopting the self-quarantine method

In this paper, an indirect dual ascent method with an exponential convergence rate is proposed for a general resource allocation problem with convex objectives and weighted constraints. By introducing the indirect dual variables, the dual dynamics can be executed in a decentralized manner by all nodes over the network. In contrast to the conventional methods, consensus on all the dual variables is

The stability of synchronous states is analyzed in the context of two populations of inhibitory and excitatory neurons, characterized by two different pulse-widths. The problem is reduced to that of determining the eigenvalues of a suitable class of sparse random matrices, randomness being a consequence of the network structure. A detailed analysis, which includes also the study of finite-amplitude

The objective of this manuscript is to elucidate the role of topology on the nonlinear response of resonators. The resonators are composed of two beams and designed to exhibit two-to-one internal resonances. The manuscript explores the sensitivity to variations in the topological parameters, i.e., the relative orientation, and the ratio of lengths and heights, on the modal frequencies of the structure

In this paper, two new control methods based on a Lyapunov-like function and a vector Lyapunov function separately were put forward to solve the asymptotic stabilization problem of general fractional-order nonlinear systems with multiple time delays. First, we deduced a new asymptotic stabilization control criterion based on a Lyapunov-like function after discussing the asymptotic stability criterion

Motivated by the many diverse responses of different countries to the COVID-19 emergency, here we develop a toy model of the dependence of the epidemics spreading on the availability of tests for disease. Our model, that we call SUDR+K, grounds on the usual SIR model, with the difference of splitting the total fraction of infected individuals in two components: patients that are still undetected and