This paper tackles the information of 133 RNA viruses available in public databases under the light of several mathematical and computational tools. First, the formal concepts of distance metrics, Kolmogorov complexity and Shannon information are recalled. Second, the computational tools available presently for tackling and visualizing patterns embedded in datasets, such as the hierarchical clustering

Whenever a disease emerges, awareness in susceptibles prompts them to take preventive measures, which influence individuals’ behaviors. Therefore, we present and analyze a time-delayed epidemic model in which class of susceptible individuals is divided into three subclasses: unaware susceptibles, fully aware susceptibles, and partially aware susceptibles to the disease, respectively, which emphasizes

Rotordynamic systems are central to many aerospace and heavy-duty industrial applications. The vibrational response of such systems is usually associated with forward whirl (FW) and backward whirl (BW) precessions. It is well known in the literature that the BW precession generally precedes the passage through the critical FW resonance precession. Therefore, it can be named as a pre-resonance BW frequency

In the present study, the definition of discrete Mittag–Leffler stability is derived to characterize convergence rule of the pseudostates for nabla discrete fractional-order dynamic systems. Applying the Lyapunov stability theory, some new criteria are proposed to determine asymptotic stability of the zero equilibrium. In addition, by applying fractional comparison principle, the results are extended

An active robust adaptive fault-tolerant control protocol is studied for reducing vibration of crane bridge system and handling actuator faults and output constraints simultaneously based on a partial differential equation model. The closed-loop system subject to environmental perturbations and actuator failures can be stabilized with proposed control laws. Furthermore, output constraints of trolley

A new two-component Sasa–Satsuma equation associated with a \(4\times 4\) matrix spectral problem is proposed by resorting to the zero-curvature equation. Riemann–Hilbert problems are formulated on the basis of spectral analysis of the \(4\times 4\) matrix Lax pair for the two-component Sasa–Satsuma equation, from which zero structures of the Riemann–Hilbert problems are investigated. As applications

A combination nonlinear dynamic reduction method is developed to obtain the steady-state dynamic responses of the complex jointed structures having local hysteresis nonlinearity. The harmonic balance method is used to reformulate the nonlinear dynamical governing equations as a set of nonlinear algebraic equations. The local nonlinearity transformation reduction strategy is used to decrease the dimensions

A fusion control strategy, including probability density function (PDF) compensation and gain-scheduled control, is proposed for discrete-time stochastic systems with randomly occurring nonlinearities. Usually, it is difficult to drive the tracking error strictly to zero in a random environment. So the proposed method aims to stabilize the closed-loop system in the exponentially mean square sense and

In the active magnetic bearings (AMBs) supported rotating machinery, touchdown bearings are considered as safety devices to support the rotor in the deficiency of electromagnetic field. Generally, the industrial AMB machines do not have force sensors for touchdown bearings and the system is only equipped with the position sensors to monitor the rotor displacement that disables the opportunity to measure

Aging transition refers to the manifestation of the homogeneous steady state beyond a critical ratio of the inactive oscillators in a network of active and inactive oscillators. In contrast, symmetry breaking in coupled dynamical systems always results in heterogeneous states. In this work, surprisingly, we find that the symmetry breaking coupling facilitates the onset of the homogeneous steady state

The dynamics modeling and trajectory optimization of a segmented linkage cable-driven hyper-redundant robot (SL-CDHRR) become more challenging, since there are multiple couplings between the active cables, passive cables, joints and end-effector. To deal with these problems, this paper proposes a dynamic modeling and trajectory tracking control methods for such type of CDHRR, i.e., SL-CDHRR. First

To better understand the dynamic behaviors of cable-stayed bridges, this study investigates the dynamic behaviors of a cable-stayed shallow arch subjected to two external harmonic excitations using the analytical approach. First, dimensionless planar vibration equations of the system are obtained by applying the Hamilton principle, and three ordinary differential equations of the arch and the two cables

It was found that spatially confined spin–orbit (SO) coupling, which can be induced by illuminating Bose–Einstein condensates (BECs) with a Gaussian laser beam, can help trap a spinor Bose gas in multi-dimensional space. Previous works on this topic were all based on a Boson gas featuring an attractive interaction. In this paper, we consider the trapping effect in the case in which the Boson gas features

Policy makers around the world are facing unprecedented challenges in making decisions on when and what degrees of measures should be implemented to tackle the COVID-19 pandemic. Here, using a nationwide mobile phone dataset, we developed a networked meta-population model to simulate the impact of intervention in controlling the spread of the virus in China by varying the effectiveness of transmission

In this paper, we consider a 5-dimensional Hindmarsh–Rose neuron model. This improved version of the original model shows rich dynamical behaviors, including a chaotic super-bursting regime. This regime promises a greater information encoding capacity than the standard bursting activity. Based on the Krasovskii–Lyapunov stability theory, the sufficient conditions (on the synaptic strengths and magnetic

We analyze the dynamics of a nonlinear mechanical system under the influence of an external harmonic force. The system consists of a linear oscillator (primary mass) and attached nonlinear dynamic absorber. It is supposed that the frequency of the external force is close to the natural frequency of the main mass. Assuming that the parameters of the system are uncertain, the stability conditions of

Subjected to dynamic excitations, bolted joint interfaces exhibit nonlinear characteristics that significantly affect the dynamic response of assembled structures. In this paper, a novel modeling method is developed to improve the prediction accuracy of the tangential contact behavior of bolted joint interfaces. This method is based on the framework of the Iwan model and builds the relationship between

As the COVID-19 outbreak is developing the two most frequently reported statistics seem to be the raw confirmed case and case fatalities counts. Focusing on Italy, one of the hardest hit countries, we look at how these two values could be put in perspective to reflect the dynamics of the virus spread. In particular, we find that merely considering the confirmed case counts would be very misleading

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World Health Organization (WHO) has declared COVID-19 a pandemic on March 11, 2020. As of May 23, 2020, according to WHO, there are 213 countries, areas or territories with COVID-19 positive cases. To effectively address this situation, it is imperative to have a clear understanding of the COVID-19 transmission dynamics and to concoct efficient control measures to mitigate/contain the spread. In this

Due to the strong infectivity of COVID-19, it spread all over the world in about three months and thus has been studied from different aspects including its source of infection, pathological characteristics, diagnostic technology and treatment. Yet, the influences of control strategies on the transmission dynamics of COVID-19 are far from being well understood. In order to reveal the mechanisms of

The outbreak of the novel coronavirus (COVID-19), which was firstly reported in China, has affected many countries worldwide. To understand and predict the transmission dynamics of this disease, mathematical models can be very effective. It has been shown that the fractional order is related to the memory effects, which seems to be more effective for modeling the epidemic diseases. Motivated by this

This paper considers the event-triggered sliding mode control problem of uncertain active vehicle suspension systems. A more comprehensive polytope approach is employed to model the uncertainties which generally exist in the sprung and unsprung masses. Moreover, the corresponding mathematical model is constructed for the quarter-vehicle active suspension system. Meanwhile, the event-triggered transmission

A discrete-time model of a structured population dynamics considering both density-dependent regulation and natural selection is studied. In the model, the dynamics of two population groups corresponding to different development stages is described, and birth rate limitation is considered. Fertility is assumed to change during microevolution. The stability loss of nontrivial fixed points was shown

How do group dynamics affect individuals within the group? How do individuals, in turn, affect group dynamics? As society comes together, individuals affect the group dynamics and vice versa. Social dynamics look at group dynamics, its effect on individuals, conformity, leadership, networks, and more. In the past two decades, the game theoretic Parrondo’s paradox has been used to model and explain

This paper proposes a new theoretical method to investigate the thermal behaviors of the inter-shaft bearing considering the nonlinear dynamic characteristics of a dual-rotor system by combining heat transfer and nonlinear dynamics. The nonlinearities of the inter-shaft bearing, including the Hertzian contact and the radial clearance, are considered during the dynamic modeling for the system. The dynamic

Recently, COVID-19 has attracted a lot of attention of researchers from different fields. Wearing masks is a frequently adopted precautionary measure. In this paper, we investigate the effect of behavior of wearing masks on epidemic dynamics in the context of COVID-19. At each time, every susceptible individual chooses whether to wear a mask or not in the next time step, which depends on an evaluation

This study proposes two improved gradient descent parameter estimation algorithms for rational state-space models with time-delay. These two algorithms, based on intelligent search method and momentum method, can simultaneously estimate the time-delay and parameters without the matrix eigenvalue calculation in each iteration. Compared with the traditional gradient descent algorithm, the improved algorithms

Analysis of electrostatic floating potential fluctuations associated with multiple anodic double layer revealed a complexity dynamic coexisting with chaotic behavior. These externally controllable nonequilibrium quasi-stationary multiple anodic double layers were created in a cold cathode dc discharge setup in front of an extra anode which was used to supplement additional ionization. Despite the fact

A new nonlinear integrable fifth-order equation with temporal and spatial dispersion is investigated, which can be used to describe shallow water waves moving in both directions. By performing the singularity manifold analysis, we demonstrate that this generalized model is integrable in the sense of Painlevé for one set of parametric choices. The simplified Hirota method is employed to construct the

The delay and network are incorporated to describe the spatiotemporal behavior of a food-limited population dynamical system. By using the standard approach of upper and lower solutions, we have shown the global existence and uniqueness of solutions to the system. By analyzing eigenvalue spectrum, we show that the delay can cause the long-term behavior of the system from stability to instability, that

This paper mainly investigates dynamical analysis and anti-oscillation-based adaptive control issues of the fractional-order (FO) arch microelectromechanical system (MEMS) with optimality. With the aid of phase diagram and Lyapunov exponent, the dynamical analysis reveals that chaotic oscillation originated in non-equilibrium interaction of potential energy can deteriorate the performance of the FO

Many strategies for an actuated biped gait generation have been proposed based on the passive dynamic gait. Among them, this study focuses on an impulsive excitation at the toe-off instance. The strategy offers advantages in its experimental implementation; for example, it is not required to measure and control the trajectory of the legs all the time. However, there has been no study on a realistic

In this paper, a SEIR epidemic model for the COVID-19 is built according to some general control strategies, such as hospital, quarantine and external input. Based on the data of Hubei province, the particle swarm optimization (PSO) algorithm is applied to estimate the parameters of the system. We found that the parameters of the proposed SEIR model are different for different scenarios. Then, the

To explore memcapacitors and their characteristics in chaotic oscillators, this paper proposes a logarithmic charge-controlled memcapacitor model. Using power-off plot analysis, we show that the memcapacitor possesses continuous non-volatile characteristic. Also, its dynamic route map shows the memcapacitor can rapidly switch from one memcapacitance to another by applying a single voltage pulse. Based

Predicting noise-induced critical transitions between multi-stable states of a dynamical system is of uttermost importance in various fields. This paper investigates a tri-stable model with desirable, sub-desirable and undesirable states as a prototype class of real systems. Then, two critical transitions, from the desirable state to the sub-desirable one (CT1) and from the sub-desirable state to the

In this paper, we investigate the generalized Hopf bifurcation of a non-smooth railway wheelset system. It is to note that the system is a four-dimensional non-smooth differential equation. First, we show how to overcome the non-smoothness and reduce the four-dimensional system to a two-dimensional non-smooth system by the center manifold theorem. Since the two-dimensional central manifold is still

Representative models of the nonlinear behavior of floating platforms are essential for their successful design, especially in the emerging field of wave energy conversion where nonlinear dynamics can have substantially detrimental effects on the converter efficiency. The spar buoy, commonly used for deep-water drilling, oil and natural gas extraction and storage, as well as offshore wind and wave

Lagrangian techniques, such as the finite-time Lyapunov exponent (FTLE) and hyperbolic Lagrangian coherent structures, have become popular tools for analyzing unsteady fluid flows. These techniques identify regions where particles transported by a flow will converge to and diverge from over a finite-time interval, even in a divergence-free flow. Lagrangian analyses, however, are time consuming and

In the microorganism cultivation process, delay and stochastic perturbations are inevitably accompanied, which results in complicated dynamical behaviors for microorganisms. In this paper, a mathematical model with discrete delay and random perturbation is constructed to understand how the dynamics of microorganisms in the turbidostat can be characterized. The existence, uniqueness and boundedness

Coronavirus disease 2019 is a recent strong challenge for the world. In this paper, an epidemiology model is investigated as a model for the development of COVID-19. The propagation of COVID-19 through various sub-groups of society is studied. Some critical parameters, such as the background of mortality without considering the disease state and the speed of moving people from infected to resistance

Nowadays, the novel coronavirus (COVID-19) is spreading around the world and has attracted extremely wide public attention. From the beginning of the outbreak to now, there have been many mathematical models proposed to describe the spread of the pandemic, and most of them are established with the assumption that people contact with each other in a homogeneous pattern. However, owing to the difference

We investigate the effects of cross-diffusion on pattern formation of a diffusive predator–prey system. The stability and bifurcation for the reaction diffusion system are discussed, and the conditions for the Turing instability are presented. We have found that the cross-diffusion coefficient \(d_{12}\), which reflects the tendency of preys leaving predators, suppresses the formation of Turing pattern

The pandemic of coronavirus disease 2019 (COVID-19) has threatened the social and economic structure all around the world. Generally, COVID-19 has three possible transmission routes, including pre-symptomatic, symptomatic and asymptomatic transmission, among which the last one has brought a severe challenge for the containment of the disease. One core scientific question is to understand the influence

This study proposes a novel bistable nonlinear electromagnetic actuator with elastic boundary (BEMA-EB) to enhance the actuation performance when controlled by a harmonic input signal. The structure of the BEMA-EB has an inclined spring, one end of which is supported by an elastic boundary. The inclined spring produces bistable nonlinearity to realize the large-amplitude inter-well actuation responses

This work deals with the stimulation of cardiac spiral waves in a two-dimensional FitzHugh–Nagumo model through modulational instability phenomenon in the presence of intracellular magnetic flux. The nonlinear generic model is firstly transformed into a two-dimensional complex Ginzburg–Landau equation with a small real damping term. Then, the latter is explored to perform the linear stability analysis

To model the nonlinear and complex dynamics of financial systems, a new model for the formation of financial prices is developed, taking into account heterogeneity in the communication range of market agents. Specifically, one type of agents can potentially gather and disseminate information via additional long-distance contacts compared to the other type, and interactions among these agents are imitated

The modified Korteweg–de Vries–sine-Gordon (mKdV–sG) equation is one of the models describing few-cycle-pulse optical solitons beyond the slowly varying envelope approximation. By introducing the velocity resonance mechanism to multiple soliton/breather solutions, it is found that the mKdV–sG model possesses abundant soliton molecule (SM), breather molecule (BM) and breather–soliton molecule (BSM)

We consider the NLS equation with a linear double-well potential. Symmetry breaking, i.e. the localisation of an order parameter in one of the potential wells that can occur when the system is symmetric, has been studied extensively. However, when the wells are asymmetric, only a few analytical works have been reported. Using double Dirac delta potentials, we study rigorously the effect of such asymmetry

In 2017, an efficient chaotic image cipher with dynamic lookup table driven by bit-level permutation strategy (ICDLT) was proposed (Hu et al. Nonlinear Dyn 87:1359–1375). The chaotic cipher adopts a plaintext-related image encryption mechanism as an efficient measure against chosen-plaintext/ciphertext attack. ICDLT is composed of four basic parts: inter-pixel permutation, sequential addition, intra-pixel

In this paper, an adaptive model-free control method is designed to synchronize a class of fractional-order neural networks which has a vast application in engineering and industry. The theoretical and analytical concepts of the method are based on the fractional-order version of the Lyapunov stability theorem and using adaptive control theory. Moreover, it is worth to mention that, because of using

We develop an advanced model of bistable perception based on the interplay of noise and adaptation. The model describes the decision-making process in the brain consisting in involuntary switches between perceptual states. We study the effects of noise and the stimulus duty cycle on the dominance of a particular externally biased perceptual state. We discuss the biological relevance of our model and

This paper is concerned with the application of the spectral tau and collocation methods to delay multi-order fractional differential equations with vanishing delay \(rx\ (0

The aim of this comment is to show that discovery of hyperchaos in three systems investigated in Li et al. (Nonlinear Dyn 94(3):1703–1720, 2018) is not correct. It is justified both theoretically and numerically. Corrected calculations of Lyapunov exponents and corresponding bifurcation diagram are given. Examples of hyperchaotic Hamiltonian multiple pendulum systems are presented.

In the presence of uncertain dynamic terms and external disturbances, the problem of trajectory tracking with application to an underactuated underwater vehicle is addressed in this paper. Based on Lyapunov theory and properties of neural networks, a nonlinear neural controller is designed, where multilayer neural networks are adopted to approximate the unmodeled dynamic terms and external disturbances

The convergence of the fractional difference logistic map is studied in this paper. A computational technique based on the visualisation of the algebraic complexity of transient processes is employed for that purpose. It is demonstrated that the dynamics of the fractional difference logistic map is similar to the behaviour of the extended invertible logistic map in the neighbourhood of unstable orbits

The main purpose of this article is to demonstrate that bursting oscillations can be exploited to enhance the harvested electrical power. A vibration-based bistable Duffing energy harvester, a tristable energy harvester and an asymmetric bistable energy harvester are examined, and bursting oscillations are observed in the energy-harvesting systems with periodic excitation when an order gap exists between

To analyze the dynamic characteristics of gear systems supported by squeeze film dampers (SFD), the nonlinear oil-film force of SFD is usually obtained by the short bearing approximation (SBA), long bearing approximation (LBA) or finite difference method (FDM). However, the SBA and LBA methods only hold for the cases of infinitely short and infinitely long SFD, which may be not true in practice. Additionally

This study presents an advanced algorithm for controlling the web longitude and tension of nonlinear roll-to-roll systems in the form of a cascade structure. Parameter variation and disturbance attenuation problems are addressed systematically. The features of this article are divided into two parts. First, active damping terms are injected to stabilize the system nonlinear dynamics so that the first-order

Many systems of biological interest can be modeled as pointlike oscillators whose coupling is mediated by the diffusion of some substance. This coupling occurs because the dynamics of each oscillator is influenced by the local concentration of a substance which diffuses through the spatial medium. The diffusion equation, on its hand, has a source term which depends on the oscillator dynamics. We derive