The primary motor cortex (M1) contains interconnected and diverse layers that play an important role in motor execution. In recent years, M1 has emerged as one of the hot targets for optogenetic stimulation in the treatment of Parkinson’s disease (PD). In this paper, we explore potential optogenetic stimulation targets in M1 based on the M1-basal ganglia-thalamus network model. The results show that

This paper aims to investigate the three-dimensional (3-D) nonlinear dynamics of a porous functionally graded (FG) pipe subjected to lateral harmonic excitation. Material properties of the porous pipe are graded across the radius in a power-law distribution form. Based on the Euler–Bernoulli beam theory, the nonlinear equations of motion are derived employing the Hamilton’s principal to achieve third-order

African swine fever (ASF) is transmitted by the African swine fever virus (ASFV). Since the early 1900s, ASF spread across Africa, Europe, South America and the Caribbean. In 2018, ASF was found in China and quickly spread to all provinces in mainland China, which had resulted in insecurity of pig production and serious economic losses. To investigate the effect of culling on the ASFV transmission

This paper is devoted to the study of the global stability of classical solutions to an initial and boundary value problem (IBVP) of a nonlinear PDE system, converted from a model of reinforced random walks, subject to time-dependent boundary conditions. It is shown that under certain integrability conditions on the boundary data, classical solutions to the IBVP exist globally in time and the differences

In this study, we developed a fragment–asperity interaction model for earthquakes. Based on Tsallis entropy, this model can provide mathematical expression for the non-extensive entropy of fragments and asperities in the gouge area. From a statistical physics perspective, we hypothesized that non-extensive entropy decreases with energy relaxation after crustal rupture (i.e., following an earthquake)

To analyze the effect of animal spirits on economic dynamics, we construct a simple Keynesian business-cycle model with animal spirits incorporated into it. Similar to the well-known Kaldor model, we assume that each firm possesses the investment function depending on demand, in which the animal spirits are connected with the degree of the propensity to invest. However, we would like to emphasize that

In this paper, a generalized form of Shannon-Fisher (SF) index is introduced. The generalized SF index (GSF) is in view of the original SF index, which is provided with the ability to quantify the instability of time series. The key of this proposed method is to replace the original distribution with its escort distribution, whose advantage lies in its capability of scanning the properties of original

This paper is concerned with the impulsive consensus tracking problem of Lipschitz nonlinear multi-agent systems subject to deception attacks. The proposed distributed impulsive tracking algorithm allows only partial state variables of every agent to be governed by consensus impulses. The considered deception attacks are supposed to take place in the controller-actuator channel, and can be modelled

Recurrence plot is an effective tool for portraying system dynamics. However, dealing with distance matrices through the Heaviside function which is difficult to determine the threshold may lead to the loss of much important information, such as information about transitions between states. Therefore, in this paper, we propose a novel dispersion heterogeneous recurrence analysis for complex systems

The paper studies robustness with respect to time-sampling of the energy regulation for one-dimensional sine-Gordon system. Such a problem is a new to control of invariants for hyperbolic partial differential equations (PDEs). In the absence of analytic results, the problem is studied numerically. The properties of four sampled-data algorithms are computationally studied with respect to three performance

A two-degree-of-freedom nonlinear mechanical system describing a damped linear oscillator weakly coupled to a lightweight grounded bistable nonlinear energy sink is proposed to investigate the targeted energy transfer (TET) under asymmetric local nonlinear potentials. The bifurcations of equilibria are discussed to reflect the bistable and asymmetric characteristics of the system. Through projections

There is a point in predicting the past (retrodicting) because we lack information about it. To address this issue, we consider a truncated Lévy flight to model data. We build on the finding that there is a power law between truncation length and standard deviation that connects the bounded past and unbounded future. Even if a truncated Lévy flight cannot predict future extreme events, we argue that

Nonlinear dynamics and control of the galloping of elastic structures is an important research topic that has been addressed in the present paper. Some recent research has used high-frequency excitation in controlling galloping oscillations under steady wind. However, galloping under unsteady wind is potentially more dangerous because of the presence of an additional parametric instability on top of

This paper presents Turing–Hopf bifurcation analysis and the resulting spatiotemporal dynamics in a single-species reaction–diffusion model with nonlocal delay. A linear stability analysis is performed to find the conditions for the occurrence of Turing–Hopf bifurcation. The weakly nonlinear analysis is then employed to derive the amplitude equations which describe the slow-time evolution of the critical

It takes time to produce commodities, and different production technologies may take different lengths of time. Suppose that firms may switch between different production technologies that take different lengths of time. A natural implication of such a scenario is that not all firms would then offer their commodities in every period, i.e. firms’ total supply schedule would become a time-varying quantity

Neurons can be excited and inhibited by filtered signals. The filtering properties of neural networks have a huge impact on memory, learning, and disease. In this paper, the frequency selection of Hodgkin–Huxley (HH) neuron in response to band-pass filtered signals is investigated. It is found that the neuronal filtering property depends on the locking relationship between the band-pass filtered signal’s

In view of the concerns regarding contaminant transport and removal after water pollution incidents, this study focuses on the temporal and spatial evolutions of concentration distribution and removal performance in channel flows with floating vegetation islands (FVIs). For a typical case of instantaneous and uniform contaminant release, the analytical solution of the spatial concentration distribution

In this paper, we present a method that combines information-theoretical and statistical approaches to infer connectivity in complex networks using time-series data. The method is based on estimations of the Mutual Information Rate for pairs of time-series and on statistical significance tests for connectivity acceptance using the false discovery rate method for multiple hypothesis testing. We provide

Pattern formation, arising from systems of autonomous reaction–diffusion equations, on networks has become a common topic of study in the scientific literature. In this work we focus primarily on directed networks. Although some work prior has been done to understand how patterns arise on directed networks, these works have restricted their attentions to networks for whom the Laplacian matrix (corresponding

In this paper, we deal with the approximate controllability of Sobolev-type fractional stochastic evolution hemivariational inequalities of order r∈(1,2). Firstly, by using stochastic analysis, fractional calculus, sine and cosine family operators, and fixed point theorems of multivalued maps, we show the existence of mild solutions for the fractional stochastic evolution systems. Then we provide a

This paper aims to report a new route to pulse-shaped explosion (PSE) related to the limit cycle attractor in a mechanical system with multiple-frequency excitations. We show that the compound bursting connected by PSE of equilibria can be observed in this system. Then, with the decrease of the amplitude of parametric excitation, the compound bursting pattern begins to change to other types, accompanied

In this paper we consider a step function characterized by an arbitrary sequence of real-valued scalars and approximate it with a matching pursuit (MP) algorithm. We utilize a waveform dictionary with rectangular window functions as part of this algorithm. We show that the waveform dictionary is not necessary when all of the scalars are either non positive or non negative and the parameters of a wavelet

This paper investigates the interconnections between real economy and the financial market in a discrete dynamical framework. We focus on the effect of the dividend policy decided by managers and the expectations of investors about future payments. We found that an excessively high dividend payout ratio erodes the economy, while in the opposite case instability and fluctuations arise. By means of analytical

A sizable part of the water extracted is unauthorized. This phenomenon may contribute to exacerbate the problem of groundwater over-exploitation. To consider both issues, we study the interaction between the water agency and farmers through a leader–follower differential game in which both agents are perfect foresight. Since the farmers have to pay a tax on individual withdrawals imposed by the water

We consider a virtual element method in space for the nonlinear Ginzburg–Landau equation, while a linearized time-variable-step second order backward differentiation formula (BDF2) is adopted in time. The error splitting approach is used to prove the unconditional optimal error estimate of the derived scheme under the mild restriction on the ratio of adjacent time-steps ratios (similarly proposed in

We analyze the spatial–temporal dynamics of cultural vibrancy in the Swedish sub-region of Skaraborg. Our database consists of 4170 geo-localized cultural activities and facilities, mapped between October 2013 and March 2014. We make use of the TWC methodology for the dynamic simulation of the evolution of geo-localized activity starting from an observed distribution of events, and of the AutoCM ANN

Trend filtering is a regression problem to estimate underlying trends in time series data. It is necessary to investigate data in various disciplines. We propose a trend filtering method by adaptive piecewise polynomials. More specifically, we adjust the location and the number of breakpoints or knots to obtain a better fitting to given data. The numerical results on synthetic and real data sets show

Financial and economic crises are not always the same. It is important to understand why some episodes of crisis generate prolonged and systemic recessions. Developing the Financial Instability Hypothesis, Hyman Minsky introduced the idea that in periods of stability, financial actors tend to increase their risk exposure, moving from a stable hedge-dominated structure to an unstable one, characterized

We are concerned with the Cauchy problem of two-dimensional (2D) full compressible magnetohydrodynamic (MHD) equations in the whole plane with zero density at infinity. By spatial weighted energy method, we derive the local existence and uniqueness of strong solutions provided that the initial density and the initial magnetic field decay not too slowly at infinity. In particular, vacuum states at both

An acoustic wave asymmetric propagation is implemented by a conical granular chain here. The chain size is gradually changed interacting via Hertzian contacts. Theoretical modeling and numerical analysis are conducted to investigate the diode-like propagation behavior. Results show that the chain blocks/allows the low-frequency acoustic wave, which depend on different configurations and driving amplitudes

In this work a fractional-step DG-FE method for the time-dependent generalized Boussinesq equations is proposed and analysed. The scheme is composed of two steps. In the first step the original problem is reduced into several scalar elliptic equations. An intermediate velocity and temperature are solved simultaneously. Then in the second step, the incompressibility constraint is enforced and velocity

Zika virus is an arbovirus transmitted by mosquitoes, which can cause low fever, mild skin rash and eye swelling. In severe cases, it may cause neurological and autoimmune complications, such as microcephaly. Climate factors and weather, especially temperature, have a strong effect on the transmission dynamics of vector-borne diseases, such as Dengue, West Nile virus, Schistosomiasis, and Zika. To

In this paper, we propose a deep learning method to solve high-dimensional optimal multiple stopping problems. We represent the policies of multiple stopping problems by the composition of functions. Using the new representation, we approximate the optimal stopping policy recursively with simulation samples. We also derive lower and upper bounds and confidence intervals for the values. Finally, we

In this paper, we are concerned with the species interaction model with the ratio-dependent Holling III functional response and strong Allee effect. To explore nonhomogeneous solutions of the model, we consider the existence and non-existence of non-constant steady states and temporal bifurcation. Then we show the boundedness of the global positive solutions for the parabolic system and present the

This paper is a study of a nonlinear dynamical system with 3/2 degrees of freedom consisting of a point vortex and an unsteady background flow. This background flow consists of two parts, a steady and a (quasi)periodic with two sinusoidal components with different frequencies and amplitudes. The considered system with a separatrix loop in the phase portrait is the simplest model of chaotic scattering

Due to the continuous interference of environmental white noise, the dynamical behaviors of a stochastic SIQR epidemic model with mean-reverting Ornstein–Uhlenbeck process and standard incidence are considered. Several conclusions can be verified after dimensionality reduction. We study the existence and uniqueness of positive solution by construct a nonnegative Lyapunov function at first. Then, a

This paper is concerned with a diffusive HIV infection model with space-dependent parameters, different infection stages and different classes of antiretroviral drugs, in which the cells are assumed to be comparatively immobile and the viruses obey Fickian diffusion in a continuous bounded domain with a smooth boundary. The aim of this paper is twofold: first, to investigate the combined effect of

The adoption of prophylaxis attitudes, such as social isolation and use of face masks, to mitigate epidemic outbreaks strongly depends on the support of the population. In this work, we investigate a susceptible–infected–recovered (SIR) epidemic model, in which the epidemiological perception of the environment can adapt the behavior of susceptible individuals towards preventive behavior. Two rules

As its dual, observability, the controllability of controllable systems actuated in different ways can be quantified by coefficients which can be computed either by a numerical approach or a symbolic one. If the interpretation of observability coefficients is rather straightforward, this is not the case for controllability. This paper, after proposing slight but important adjustments to the computation

Recently, much research has been conducted on fractional-order differential calculus to generalise existing mathematical models or propose new ones to describe different phenomena. Fractional models are not as well researched as the classical models, and it is recommended that they should be compared to the classical well-established models. However, questions arise about the relationships between

This study addresses the resilient finite-time distributed event-triggered (ET) consensus control of multi-agent systems (MASs) with multiple cyber-attacks, such as replay, deception, and denial-of-service (DoS) attacks. For the first attempt, a model is proposed for multiple cyber-attacks on MASs under DoS, deception, and replay attacks, that occur stochastically in a unified framework. Furthermore

In this work, the distributed-order time fractional version of the Schrödinger problem is defined by replacing the first order derivative in the classical problem with this kind of fractional derivative. The Caputo fractional derivative is employed in defining the used distributed fractional derivative. The orthonormal piecewise Jacobi functions as a novel family of basis functions are defined. A new

In this study, by using the perturbation series approach, a global solution to the implosion problem is obtained for a quasi-linear hyperbolic system of partial differential equations (PDEs) describing a problem of strong converging cylindrical shock waves collapsing at the axis of symmetry in a Van der Waals dusty gas under the effect of axial magnetic field. This global solution provides the results

This article develops a small-scale evolutionary agent-based model to investigate the interplay between heterogeneous agents, institutions and technological change. By acknowledging the concept of behavioural dispositions, we differentiate between changers, neutrals, and deniers. The composition of the population is endogenously determined taking into account that reasoning is context-dependent. As

Solar energy projects contribute to smart city goals by reducing pollution and assisting cities to become self-sustaining. However, these projects, characterised by their sequential nature, require a huge amount of irreversible investment, especially in the case of large-scale photovoltaic projects (MW). This aspect could make solar projects unattractive for potential investors. To mitigate the risks

This paper studies the dynamic characteristics of a nonlinear monopoly model involving two boundedly rational monopolists with different information and knowledge on the market demand. The ℓ-monopolist knows only the actual values of output and the profit in the immediate past two periods, whereas the k-monopolist knows the marginal revenue but lacks computational ability to solve the profit maximization

The paper considers a stochastic version of the conceptual map-based Chialvo model of neural activity. Firstly, we focus on the parametric zone where this model exhibits mono- and bistability with coexistence of equilibria and oscillatory spiking attractors forming closed invariant curves. Stochastic effects of excitement and generation of bursting are studied both numerically and analytically by confidence

The algorithm for the detection of lag synchronization from time series data is presented in this paper. Multi-variate time series data are re-organized into a sequence of perfect matrices of delayed Lagrange differences and mapped into a two-dimensional pattern of discriminants. The minimization of this pattern yields a discrete sequence of time lags with a high resolution in time. The proposed technique

The time discretization of stochastic fractional wave equation is studied by using difference methods. Firstly, we use the rectangular formula to obtain a low-order time discretization, and its strong convergence order is less than 1 in the sense of mean squared L2-norm. Meanwhile, by modifying the low order method with trapezoidal rule, the convergence rate is improved at expenses of requiring some

Based on the direct method proposed by A. Nakamura, we present a numerical process to derive N-periodic wave solutions of integrable equations. In particular, we investigate numerical 3-periodic wave solutions of the shallow water wave equation, modified generalized Vakhnenko equation, (2+1)-dimensional BKP equation and a (2+1)-dimensional Boussinesq equation. Numerical experiments are conducted using

Physiological experiments have shown that inhibitory interneurons can induce and maintain epileptiform activities, and different interneuron subtypes may be responsible for different types of seizures. Here we aim to link these electrophysiological experimental phenomena with theoretical dynamic mechanisms based on an improved Liley mean field model. Fascinatingly, the number of synapses between inhibitory

The release of Wolbachia-infected mosquitoes into the wild mosquitoes population is an excellent biological control strategy which can be effective against mosquito-borne infections. In this work, we propose a dengue transmission model that incorporates releasing Wolbachia into the wild mosquito population and vaccinating human population. We analyze the basic reproduction number, the existence and

Excitable media are prevalent models for describing interesting effects in physical, chemical, and biological systems such as pattern formation, chaos, and wave propagation. In this manuscript, we propose a spatially extended variant of the FitzHugh–Nagumo model that exhibits new effects. In this excitable medium, waves of new kinds propagate. We show that the time evolution of the medium state at

In this paper, we study the bifurcation of periodic orbits for high-dimensional piecewise smooth near integrable systems defined in three regions separated by two switching manifolds. We assume that the unperturbed system has a family of periodic orbits which cross two switching manifolds transversely. The expression of Melnikov function is derived based on the first integral. And the conditions of

In this paper, we propose a non-autonomous reaction–diffusion SIR infectious disease model with nonlinear incidence, taking fully into account the effects of periodic environmental factors as well as population dynamics on disease transmission in space, and investigate the existence of periodic traveling wave solutions satisfying boundary conditions. Specifically, we first define the basic reproductive

Brown planthopper Nilaparvata lugens is a serious rice damaging pest and can transmit rice ragged stunt virus. A new biological control method for Nilaparvata lugens by using Wolbachia wStri has been successful in the laboratory. No matter using the strategy of population replacement or the strategy of population suppression to release Nilaparvata lugens infected with wStri, theoretical analysis shows

This work presents a method that analyzes the global stabilization of fractional-order uncertain nonlinear feedback systems classes with fractional-order proportional–integral–derivative (PID) controllers. Two theorems are provided to necessary conditions for global convergence to any desired setpoints by designing controllers. The first theorem addresses a class of second-order time-varying systems

In this manuscript, the Lie point symmetries, conservation laws, and traveling wave reductions have all been derived. Also, new forms of soliton solutions of generalized q-deformed equation via means of unified method has been extracted. Implementing this approach the results of governing model are obtained as rational and polynomial functions. The unified technique is used to analyze solitary solutions

Given a smooth m-manifold M, a smooth Lagrangian L:TM→R and endpoints x0,xT∈M, we look for an extremal x:[0,T]→M of the action ∫0TL(x(t),ẋ(t))dt satisfying x(0)=x0 and x(T)=xT. When interpolating between endpoints, this amounts to a 2-point boundary value problem for the Euler–Lagrange equation. Single or multiple shooting is one of the most popular methods to solve boundary value problems, but the

A canonical mass–spring model of electrostatically actuated Micro-Electro-Mechanical System (MEMS) is studied. We investigate the existence and bifurcations of the periodic solution by means of the continuation theorem of Mańasevich and Mawhin with techniques of a priori estimate and bifurcation theory. The main results answer the open problem proposed by P. Torres in the known literature. It also