With analytical and numerical methods, dynamic response of a composite laminated buckled beam with a lumped mass and an axial excitation is investigated in this paper. The dynamic equation of the first mode for this model, which is a perturbation of a Hamilton system with both quadratic and cubic nonlinearities as well as external and parametric excitations, is obtained with the Galerkin method. The

Electrocardiogram (ECG), as a biological signal that contains important information about the cardiac activities of heart, exhibits chaotic characteristics. Since a clean ECG signal is of vital importance in the diagnosis and analysis of heart diseases, we address the task of extracting ECG for a set of noisy observations. Based on the phase space similarity of ECG, we propose an objective called similarity

In this article, we investigate the existence of solutions for Hadamard type two dimensional fractional functional integral equations on [1,b]×[1,c]. We use the concept of measure of non-compactness and Darbo’s fixed point theorem as the main tool to prove our results. Also, with the help of an example, we discuss the validity of our result.

The aim of this study is to establish a precise illustration of the structure of the nonconstant steady state for a Holling-II predator–prey reaction–diffusion system, with prey-taxis. We treat the nonlinear prey-taxis as a bifurcation parameter to discuss the global bifurcation of the system. Furthermore, the prey-taxis term, under a rather natural condition, offers nonconstant steady states. In the

Barrier-lookback option stands for a class of exotic options involving both high risky and high payback properties that are popular for many investors, which expresses that the lookback option comes into effect or becomes invalid depending on whether the underlying asset reaches the predetermined barrier level. This paper aims at investigating the pricing formulas for barrier-lookback option in uncertain

We investigate the finite time blow-up and global existence of sign-changing solutions to the Cauchy problem for the inhomogeneous semilinear parabolic system with space-time forcing terms{ut−Δu=|v|p+tσw1(x),x∈RN,t>0,vt−Δv=|u|q+tγw2(x),x∈RN,t>0,(u(0,x),v(0,x))=(u0(x),v0(x)),x∈RN,where N≥1, p,q>1, σ,γ>−1, σ,γ≠0, w1,w2≢0, and u0,v0∈C0(RN). For the finite time blow-up, two cases are discussed under the

Discrete fractional calculus (DFC) is continuously spreading in the engineering practice, neural networks, chaotic maps, and image encryption, which is appropriately assumed for discrete-time modelling in continuum problems. First, we start with a novel discrete ℏ-proportional fractional sum defined on the time scale ℏZ so as to give the premise to the more broad and complex structures, for example

Noise and time-delays are ubiquitous in physical and biological systems. In this paper, the multiple time-delays coupled FitzHugh-Nagumo (FHN) models is employed to investigate the synchronization mode transition. The orbital projection method is used to study the difference of membrane potential between two FHN neurons in the phase plane, and a measure of anti-phase is defined to characterize the

We analyze the chaotic dynamics of a one-dimensional discrete nonlinear Schrödinger equation. This nonintegrable model, ubiquitous in several fields of physics, describes the behavior of an array of coupled complex oscillators with a local nonlinear potential. We explore the Lyapunov spectrum for different values of the energy density, finding that the maximal value of the Kolmogorov-Sinai entropy

The present work is devoted to giving new insights into the extended Malkus-Robbins (EMR) dynamo. Firstly, based on differential geometry method, i.e. Kosambi-Cartan-Chern (KCC) theory, the paper investigates the Jacobi stability of the equilibrium and periodic orbit by the eigenvalues of the deviation curvature tensor. The deviation vector is applied to analyze the trajectory behaviors near the equilibrium

In this paper we study the lateral instability in a discharge channel using a continuum model. We observe analogies with the onset of Kelvin-Helmholz instability in fluids. In strong electric fields, lateral long wave length perturbations can grow while small wave length perturbations diminish during the discharge evolution. We perform numerical simulations and carry out asymptotic analysis of the

We derive the time-dependent probability distribution for the number of infected individuals at a given time in a stochastic Susceptible-Infected-Susceptible (SIS) epidemic model. The mean, variance, skewness, and kurtosis of the distribution are obtained as a function of time. We study the effect of noise intensity on the distribution and later derive and analyze the effect of changes in the transmission

A novel stochastic chemostat model with two complementary nutrients and flocculation effect is considered in this paper. Firstly, the well-posedness of the stochastic chemostat model is considered. Then, by constructing appropriate stochastic Lyapunov functions, some sufficient conditions for the existence of an ergodic stationary distribution and persistence of the stochastic model are given. The

We propose a mixed strategy named multi-biased random walk on complex networks, i.e., a walker simultaneously adopts different biased random walks with respective proportions. An analytical expression of mean first passage time is derived to quantify the expected time required to find a given target. The global mean first passage time of our strategy turns out to obey a convex function with respect

This paper primarily focuses on LQ optimal control problem of fractional-order discrete-time systems based on uncertainty theory that is a significant tool to model belief degree. First, an equivalent LQ problem, which is integer-order one, is presented by expanding the state variables with the unchanging control variables. This equivalent problem is then solved by dynamic programming approach. Accordingly

We investigate a class of time-fractal-fractional Stochastic differential equation with the Atangana’s fractal-fractional differential operator in Caputo sense with power law type kernel. The upper growth bound of the random solution to the equation is estimated, and the result shows that the second moment of the solution grows exponentially at most at a precise rate. The existence and uniqueness result

The main attention of this work focus on finding rogue wave solutions. Here, we analytically derived multi-order rogue wave solutions for the generalized (3+1)-dimensional Kadomtsev–Petviashvili equation, through its bilinear form and symbolic computation. First, second and third order rogue waves have been systematically analyzed and the numerical simulations are exhibited to look into their dynamical

Recently, four new strains of SARS-COV-2 were reported in different countries which are mutants and considered as 70% more dangerous than the existing covid-19 virus. In this paper, hybrid mathematical models of new strains and co-infection in Caputo, Caputo-Fabrizio, and Atangana-Baleanu are presented. The idea behind this co-infection modeling is that, as per medical reports, both dengue and covid-19

Some properties of cylindrical/spherical dust acoustic solitary waves have been studied in collisionless dusty plasma with variable charges under the influence of polarization force by reductive perturbation method. It is shown that the collisionless damping due to dust charge fluctuation causes the dust acoustic wave propagation to be described by the nonplanar damped Korteweg de Vries equation. By

Developing a grey prediction model with high nonlinear prediction accuracy is an important issue in grey system theory. A new grey prediction model was developed that was the first to combine the idea of twin support vector regression with Hausdorff derivative operator. The new model is a non-linear data-driven model. An improved salp swarm algorithm is used to determine parameters of the model. Two

We can construct passing networks when we regard a player as a node and a pass as a link in football games. Thus, we can analyze the networks by using tools developed in network science. Among various metrics characterizing a network, centrality metrics have often been used to identify key players in a passing network. However, a tolerance to players being marked or passes being blocked in a passing

Water waves, one of the most common phenomena in nature, play an important role in the marine/offshore engineering, hydraulic engineering, energy development, mechanical engineering, etc. Hereby, for the shallow water waves near an ocean beach or in a lake, we study a Boussinesq-Burgers system. With respect to the water-wave horizontal velocity and height deviating from the equilibrium position of

Obesity has become a serious problem in both developed and developing countries. In this work, we analyse the obesity model that involves three operators Caputo, Atangana–Baleanu in Caputo sense and fractal-fractional derivatives. The existence and uniqueness of the solution have been examined. The various numerical schemes have been presented for each operator. Many numerical analysis are carried

We introduce an exactly integrable version of the well-known leaky integrate-and-fire (LIF) model, with continuous membrane potential at the spiking event, the c-LIF. We investigate the dynamical regimes of a fully connected network of excitatory c-LIF neurons in the presence of short-term synaptic plasticity. By varying the coupling strength among neurons, we show that a complex chaotic dynamics arises

The gist behind this study is to extend the classical computer virus model into fractal fractional model and subsequently to solve the model by Atangana-Toufik method. This method solve nonlinear model under consideration very efficiently. We use the Mittag-Leffler kernels on the proposed model. Atangana-Baleanu integral operator is used to solve the set of fractal-fractional expressions. In this model

A novel coronavirus disease (COVID-19) appeared in Wuhan, China in December 2019 and spread around the world at a rapid pace, taking the form of pandemic. There was an urgent need to look for the remedy and control this deadly disease. A new strain of coronavirus called Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) was considered to be responsible for COVID-19. Novel coronavirus (SARS-CoV-2)

We propose a refined version of the stochastic SEIR model for epidemic of the new corona virus SARS-Cov-2, causing the COVID-19 disease, taking into account the spread of the virus due to the regular infected individuals (transmission coefficient β), hospitalized individuals (transmission coefficient lβ, l>0) and superspreaders (transmission coefficient β′). The model is constructed from the corresponding

Carbon dioxide is the crucial factor leading to global warming, which has brought great negative effects on economic development and human life. Accurate prediction of carbon dioxide emissions is of great significance for the evaluation of China's current low-carbon environmental protection policy. However, the traditional forecasting models only consider the regularity of historical data, and seldom

This paper introduces two new one-dimensional chaotic systems. They can be considered as an improvement of Logistic map, Sine map and Tent map. One is the chaotic system composed of Sine and Tent maps (STCS), the other is Logistic-Logistic chaotic system (L-LCS). Based on the two, an image encryption algorithm using dynamic row scrambling and Zigzag transformation is proposed. Firstly, the image is

In recent years, complex networks have been used as new tools to study patterns in earthquake data. Although various methods have been developed to construct earthquake networks, there is still a long way to use this approach as a complete framework for analyzing seismicity. This research develops novel methods for building earthquake networks and investigates the patterns that they could reveal. The

In this work, a tritrophic food chain model has been proposed by incorporating Ivlev-like nonmonotonic functional response, where prey is equipped with defense ability. We have performed a detailed dynamical study and pattern formation analysis to obtain complex dynamics of the proposed system. Stability and bifurcation analysis have been performed in the model system. Persistence and permanence are

In this work, some novel analytic traveling wave solutions including the cnoidal and solitary wave solutions of the planar Extended Kawahara equation are deduced. Four different analytical methods (the Jacobian elliptic function, Weierrtrass elliptic function, the traditional tanh method and the sech-square) are devoted for solving this equation. By means of the Jacobian elliptic function ansatz, the

This paper recovers stationary optical soliton solutions when chromatic dispersion, in addition to self–phase modulation, is rendered to be nonlinear. The extended trial function algorithm recovers stationary soliton solutions for eleven forms of nonlinear refractive index structures of optical fibers. The technical criteria for the existence of such stationary solitons are also presented.

The Modified Operational Matrix method (MOMM) has proved to be a reliable and efficient algorithm for solving fractional delay equations. However, no convergence results are known in the literature. The aim of this paper is to derive the MOMM and to show its efficiency. Numerical examples are studied to illustrate the efficiency of the proposed method.

Adaptive modified projective function synchronization of non-linear distributive fractional order complex dynamical networks (DFCDN) is addressed in this paper. Firstly, we have created a model for DFCDN with model uncertainty, external disturbances and uncertain parameters. Based on the Laplace and inverse Laplace transform property of distributive order fractional differential equations and Lyapunov

Pandemic COVID-19 which has infected more than 35,027,546 people and death more than 1,034,837 people in 235 countries as on October 05, 2020 has created a chaos across the globe. In this paper, we develop a compartmental epidemic model to understand the spreading behaviour of the disease in human population with a special case of Bhilwara, a desert town in India where successful control measures TTT

Modern industrial requirements are continuously demanding better performance, smaller clearance, higher rotational speed and higher load from hydraulic generating set, under this circumstance, vibration mitigation is of considerable importance for safe and efficient functioning of rotor-bearing system. The overall goal of this research is to reveal the mechanism for unexpected nonlinear vibration induced

A ring of the FitzHugh–Nagumo (FHN) oscillators coupled via memristive elements is studied. The impact of the memristive element initial states on the travelling wave characteristics is established for the self-oscillatory and excitable dynamics of the individual oscillators. It is shown that the initial state effect is especially evident in the excitable regime. In such a case the initial distribution

The mechanism of compound bursting behaviors of a forced Mathieu-van der Pol-Duffing system is explored. Four compound bursting types and one typical relaxation oscillation, i.e., compound “Homoclinic/Homoclinic” bursting, compound “fold/fold-cycle” bursting, compound “subHopf/fold-cycle” bursting via “fold/fold” hysteresis loop, compound “supHopf/supHopf” bursting via “fold/fold” hysteresis loop and

This targeted work deals with the forward and inverse approaches to handle fractional radon diffusion problems in an uncertain environment. In general, fractional differential equations may model certain problems more efficiently than differential equations of integer order. As such, this work proposes Mittage-Leffler function method to handle fuzzy fractional radon transport mechanism. Further, inverse

In a three-dimensional (3D) dissipative medium described by the higher-order (3+1)-dimensional cubic-quintic-septic complex Ginzburg-Landau [(3+1)D CQS-CGL] equation with the viscous (spectral-filtering) term, self steepening, Raman effect, dispersion terms up to six, diffraction and cubic-quintic-septic nonlinearities, we demonstrate that necklace ring beams with initial spherical shape carrying integer

We explore numerically inter-layer synchronization of spatiotemporal patterns in a heterogeneous bilayer network of nonlocally coupled Rössler oscillators. Both layers exhibit phase chimera regimes with similar cluster structures, but there is a mean frequency mismatch between the layers. We show that an entrainment of the mean frequency in the interacting layers is observed already for sufficiently

In this article, exponential synchronization between fractional order chaotic systems has been studied by using exponential stability theorem. The stability analysis has been done with help of an existing lemma, which is given for Lyapunov function for fractional order system. The fractional order complex chaotic systems viz., Lorenz and Lu systems are considered to illustrate the exponential synchronization

Identifying important nodes in networks is essential to analysing their structure and understanding their dynamical processes. In addition, myriad real systems are time-varying and can be represented as temporal networks. Motivated by classic gravity in physics, we propose a temporal gravity model to identify important nodes in temporal networks. In gravity, the attraction between two objects depends

In this paper, using the monotone iterative technique, we discuss a new approximate method for solving multi-point boundary value problems of p-Laplacian fractional differential equations with singularities, which are of great importance in the fluid dynamics field. To do this, first, a sequence of auxiliary problems that release the nonlinear source terms contained in the equations from the singularities

Bioeactors with various configuration are used for the biodegradation of industrial and municipal wastes. In this article we study dynamic performance of a nonlinear bioreactor model for the aerobic biodegradation of wastes. The proposed model accounts for oxygen transfer, cells decay, Contois growth kinetics for cells decay, while the biomass yield coefficient is assumed to depend on the substrate

In this paper, we present a new type of Gronwall inequality and discuss some particular cases. We apply these results to investigate the uniqueness and δ-Ulam–Hyers–Rassias stability of mild solutions of a fractional differential equation with non-instantaneous impulses in a Pδ-normed Banach space. In this sense, we present an example, in order to elucidate one of the results discussed.

The major objective of this work is to investigate sufficient conditions of existence and uniqueness of positive solutions for a finite system of ψ-Hilfer fractional differential equations. The gained results are obtained by building the upper and lower control functions of the nonlinear expression with the help of fixed point theorems such as Banach and Schauder. Furthermore, we establish various

In this paper, we are interested in the existence and multiplicity of solutions for a class of fractional Hamiltonian systems. Our approach is based on the direct method of minimization and with the help of Nehari manifold.

Memory effect of time fractional Schrödinger equation plays a significant role in evolution of a single quantum state and quantum entanglement. We investigate the time fractional evolution of a single quantum state and entangled state respectively. Comparing to the results of standard Schrödinger equation, we find that the influence of memory action is unstable, which will change over time until the

Current methods of fractal analysis rely on capturing approximations of an images’ fractal dimension by distributing iteratively smaller boxes over the image, counting the set of box and fractal, and using linear regression estimators to estimate the slope of the set count line. To minimize the estimation error in those methods, our aim in this study was to derive a generalized fractal feature that

In this paper, we study a portfolio selection problem under safety first expected utility model with distortion (SFEUD model) where the underlying probability scale is transformed by a nonlinear distortion function. By employing the quantile formulation and the relaxation method, we obtain the general form of optimal solution to the problem, and the necessary and sufficient condition for existing such

Based on the non-separation method, the finite-time projective synchronization of fractional-order quaternion-valued memristive networks with discontinuous activation functions is investigated in this paper. Firstly, the sign function related to quaternion is introduced and some properties concerning it are developed. Secondly, two different quaternion-valued controllers are designed by feat of the

Prevention of crops from pest has always been a serious cause of concern throughout the world, especially in agricultural countries as it contributes majorly to the economy of these countries. Keeping in mind this issue, we have formulated a mathematical model of Eggplant fruit and shoot borer which has been controlled through biological control. The dynamical analysis of the system has been discussed

In this article, we define a new class of convexity called generalized (h−m)-convexity, which generalizes h-convexity and m-convexity on fractal set Rα (0<α≤1). Some properties of this new class are discussed. Using local fractional integrals and generalized (h−m)-convexity, we generalized Hermite–Hadamard (H–H) and Fejér–Hermite–Hadamard (Fejér–H–H) types inequalities. We also obtained a new result

The linear quadratic differential game plays an important role in many fields. It is well known that the saddle point of linear quadratic differential game is given in a feedback form with a solution of Riccati differential equation. However, the control-related Riccati differential equation cannot be solved analytically in many cases. Then the optimal controls may be difficult to be implemented in

The current paper deals with the investigation of a fractional order model describing the dynamics of hepatitis B infectious disease. The derivatives are taken in the sense of Caputo-Fabrizio operator. Using the Banach fixed point theory approach, we study the existence and uniqueness of the concerned solution. The semi-analytical solution of the system is investigated with the aid of Laplace Adomian

A dynamic Cournot duopoly model with isoelastic demand function and knowledge spillover effects is established, in which the goals of two enterprises are relative profit maximization. Since these two enterprises only have incomplete information of the market, then it is assumed that the enterprises are boundedly rational, and they need to adjust their production decision in next period according to