Due to the great importance of the outward current carried by K+ions and the inward one by Na+ and Ca2+ions in 3-D Chay neuron model, the dynamical behaviors associated with the maximal conductances of K+ions channel and mixed Na+-Ca2+ions channel are explored for better demonstrating dynamical effects on the electrical activities in this paper. By utilizing some common dynamical exploring methods

In this paper the fractional version of the proposed integer order chaotic ecological system is studied. Here chaos has been observed in the competitive ecological model due to linear and nonlinear interactions among various species considering shortage of food resources. The system being important constituent of the food supply chain is analyzed using tools of dynamics viz. Lyapunov dynamics, bifurcation

This paper derives results for the stabilizing and synchronizing controller for a generalized class of nonlinear systems connected in chain configuration. The proposed procedure utilizes contraction based backstepping approach blended with Gershgorin theorem instead of Lyapunov stability based backstepping technique for designing controllers for such systems. A systematic step by step strategy is adopted

While the world has experience with many different types of infectious diseases, the current crisis related to the spread of COVID-19 has challenged epidemiologists and public health experts alike, leading to a rapid search for, and development of, new and innovative solutions to combat its spread. The transmission of this virus has infected more than 18.92 million people as of August 6, 2020, with

The present problem deals with the effect of the radiation pressure on the topology of the basins of convergence in the restricted problem of four bodies in two different configurations: (I) the equilateral four-body configuration (II) the collinear four-body problem. We have illustrated the basins of convergence linked to the in-plane as well as out-of-plane libration points by applying the Newton-Raphson

Dynamical stabilization of an inverted pendulum through vertical movement of the pivot is a well-known counter intuitive phenomenon in classical mechanics. This system is also known as Kapitza pendulum and the stability can be explained with the aid of effective potential. We explore the effect of many body interaction for such a system. Our numerical analysis shows that interaction between pendula

Non-transitive dominance and the resulting cyclic loop of three or more competing species provide a fundamental mechanism to explain biodiversity in biological and ecological systems. Both Lotka-Volterra and May-Leonard type model approaches agree that heterogeneity of invasion rates within this loop does not hazard the coexistence of competing species. While the resulting abundances of species become

The transmission of influenza has been explained by analyzing a diffusive epidemic model. The Operating splitting based on finite difference (OSBFD), explicit formula based on meshless method (EFBMM), Operator splitting based on meshless method (OSBMM) are applied to obtain numerical solutions of equations under varied initial distribution of dense population. The specific role of diffusion and distribution

In this work, we study an integral boundary-value problem for a singularly perturbed linear system of integrodifferential equations, which has the phenomena of initial jumps. An analytical formula and asymptotic estimations of the solution and its derivatives are obtained. It is established that the solution of the boundary-value problem at the left point of the segment has the phenomenon of an initial

In this paper, we analyze a stochastic coronavirus (COVID-19) epidemic model which is perturbed by both white noise and telegraph noise incorporating general incidence rate. Firstly, we investigate the existence and uniqueness of a global positive solution. Then, we establish the stochastic threshold for the extinction and the persistence of the disease. The data from Indian states, are used to confirm

Herein, the numerical investigation is carried out to study the flow and heat transfer analysis through a hybrid nanofluid flow over a porous medium. The governing partial differential equations are transformed into ordinary differential equations with the help of similarity transformations. The resulting ODEs are solved by a numerical technique using RKF-45 Method. Through graphs, the impacts of pertinent

In this work, a stochastic fractional advection diffusion model with multiplicative noise is studied numerically. The Galerkin finite element method in space and finite difference in time are used, where the fractional derivative is in Caputo sense. The error analysis is investigated via Galerkin finite element method. In terms of the Mittag Leffler function, the mild solution is obtained. For the

In the present paper, a biological population model of fractional order (FBPM) with one carrying capacity has been examined with the help of reproducing kernel Hilbert space method (RKHSM). This important fractional model arises in many applications in computational biology. It is worth noting that, the considered FBPM is used to provide the changes that is made on the densities of the predator and

The coronavirus COVID-19 is affecting 213 countries and territories around the world. Iran was one of the first affected countries by this virus. Isfahan, as the third most populated province of Iran, experienced a noticeable epidemic. The prediction of epidemic size, peak value, and peak time can help policymakers in correct decisions. In this study, deep learning is selected as a powerful tool for

Without any vaccine or medical intervention to cure the infected individual from COVID-19, the non-pharmaceutical intervention become the most reasonable intervention against the spread of COVID-19. In this paper, we proposed a deterministic model governed by a system of nonlinear differential equations which consider the intervention of media campaign to increase human awareness, and rapid testing

In this paper, we deliberate two classes of initial value problems for nonlinear fractional differential equations under a version weighted generalized of Caputo fractional derivative given by Jarad et al. (2020a) [25]. We get a formula for the solution through the equivalent fractional integral equations to the proposed problems. The existence and uniqueness of positive solutions have been obtained

In this paper, a fractional viscoelastic model is proposed to describe the physical behaviour of polymeric material. The material parameters in the model are characterized by the experimental data obtained in the dynamical mechanical analysis. The proposed model is integrated into the fractional governing equation of polymethyl methacrylate (PMMA) above its glass transition temperature. The numerical

The transition from extremely brittle to very ductile behaviours of creeping materials is discussed, where analogies with power-law hardening materials are pointed out. Considering Norton's Law as a viscous constitutive law, it is possible to define a generalized stress-intensity factor Kc ―characterizing the intermediate asymptotic behaviour under steady-state creep conditions― with physical dimensions

This manuscript is mainly focusing on the approximate controllability of fractional differential evolution inclusions of order 1 < r < 2 with infinite delay. We study our primary outcomes by using the theoretical concepts about fractional calculus, cosine, and sine function of operators and Dhage’s fixed point theorem. Initially, we prove the approximate controllability for the fractional evolution

Recent years have seen an increasing body of research into the evaluation of the team-level technical-tactical performance in association football using match events data. However, most studies used mono-dimensional approach and modeled the influence of each performance aspects on match result in isolation, which limited the interpretability of the results. The study was aimed to apply a state-of-the-art

The ground states of a harmonically trapped spin-1 Bose–Einstein condensate (BEC) with SU(3) spin-orbit coupling (SOC) affected by the external rotation are investigated. The two-dimensional density, phase and magnetization distributions of the ground states under different parameter conditions are calculated numerically. It is found that a new kind of ground-states with clover-type structure in the

Chaotic hash functions are a prospective branch of modern cryptography. Being compared with traditional hashing algorithms, an approach based on deterministic chaos allows achieving diffusion and confusion with less computational costs. Most of the recently proposed chaotic hash functions use piecewise maps. Cryptosystems based on such maps are not vulnerable to attack by the reconstruction of phase

Two fractional Swartzendruber models applying the Atangana-Baleanu (A-B) derivative are proposed to describe non-Darcy flow in porous media. The analytical solutions of models are obtained by using Laplace transform. Fitting curves with the experimental data display the proposed models are suitable to describe non-Darcy flow problems in low and high permeability media. In addition, sensitivity analysis

The time-varying electromagnetic field in the media could be formed when there is a fluctuation in the concentration of charged ions across the membrane of neurons. The electrical activities of neurons will be affected by the electromagnetic field. In this paper, the effect of positive and negative field coupling on the wave propagation in the regular network is discussed. The mechanism for how the

This paper aims to study the transition to order from chaos using a mathematical model of coupled non-identical oscillators. In the course of our analysis, we adopt a different control parameter other than the conventional parameters: coupling strength and frequency-mismatch, generally used in literature to obtain the aforementioned transition. Both the interacting oscillators become periodic, and

To obtain a more secure colour image cryptosystem without complex construction, this paper presents a general simple colour image encryption model with a very high level of security, and that is based on two nearby orbits of chaotic systems. First, the initial value of a one-dimensional (1D) chaotic map is obtained using plaintext. Then, we obtain two nearby orbits of 1D chaotic maps to generate three

The present investigation deals with a generic oxygen-plankton model with constant time delays using the combinations of analytical and numerical methods. First, a two-component delayed model: the interaction between the concentration of dissolved oxygen and the density of the phytoplankton is examined in terms of the local stability and Hopf bifurcation analysis around the positive steady state. Then

In this paper, we discuss the quasi-synchronization of delayed heterogeneous dynamic neural networks based on impulsive control. The main difference of this paper with previous works on quasi-synchronization is that both proportional delay and distributed delay are considered. By establishing a novel impulsive delay inequality, combining Lyapunov theory and the concept of average impulsive interval

In this study, we consider the thermo-physical properties of Newtonian boundary layer fluid flow near a heated rotating disk. The viscosity is assumed to vary inversely as a linear function of temperature while thermal and concentration diffusion coefficients vary directly as linear functions of temperature and concentration. Temperature dependent viscosity and conductivity are adopted to analyze the

Comparative studies of structural and electrophysical properties were performed for Ba0.8Sr0.2TiO3 (BSTO) films with the thickness of 100 nm, 120 nm and 350 nm. The surface morphology, the domain structure and local polarization switches were explored in the ferroelectric phase whereas high-frequency capacitance–voltage characteristics were measured in the paraelectric phase at 121°С. It was shown

We consider the nonlinear fourth-order partial differential equation that can be used for describing solitary waves in nonlinear optics. The Cauchy problem for this equation is not solved by the inverse scattering transform. However we demonstrate that nonlinear ordinary differential equation for description of the wave packet envelope possesses the Painlevé property and is integrable. The Lax pair

A tumor is most dangerous disease of medical science which is a mass or lumps of tissue that’s formed by an accumulation of abnormal cells. A famous fractional tumor-immune model is interpreting the dynamics of tumor and effector cells. In this work, we provide a comparative and chaotic study of tumor and effector cells through fractional tumor-immune dynamical model. A new arbitrary operator based

In order to improve the engineering feasibility of the memristive cellular neural network, a new memristor model with the smooth characteristic curve is designed. Based on the new memristor model, a new four-dimensional chaotic memristive cellular neural network (CNN) system is constructed, and its chaotic dynamic behaviors are analyzed. It can be applied to the secure communication based on the chaos

Colloquially known as coronavirus, the Severe Acute Respiratory Syndrome CoronaVirus 2 (SARS-CoV-2), that causes CoronaVirus Disease 2019 (COVID-19), has become a matter of grave concern for every country around the world. The rapid growth of the pandemic has wreaked havoc and prompted the need for immediate reactions to curb the effects. To manage the problems, many research in a variety of area of

Knock-in options are a type of barrier options which are path-dependent and get activated if the prices of underlying assets reach predetermined levels. This paper studies knock-in options in an uncertain market where the stock price follows a geometric process and the interest rate is dynamic. Pricing formulas of the knock-in call options and put options are derived by means of α-paths of uncertain

In this article, we study approximate analytic solutions for one of the famous models in biomathematics, namely the nonlinear fractional mathematical smoking model. When alpha=1, we deduce the analytical solution using the Reduced differential transforms method (RDTM) for the nonlinear ordinary mathematical smoking model. The disease-free equilibrium point, the stability of the equilibrium point, and

This paper presents an image encryption algorithm based on Tent-Dynamics Coupled Map Lattices (TDCML) system and diffusion of Household. All aspects of the TDCML spatiotemporal chaotic system proposed in this paper meet the cryptographic characteristics and are suitable for studying image encryption. The specific image encryption algorithm first generates chaotic sequences according to the TDCML system

This manuscript is mainly focusing on approximate controllability for fractional differential evolution equations of order 1 < r < 2 in Hilbert spaces. We consider a class of control systems governed by the fractional differential evolution equations. By using the results on fractional calculus, cosine and sine functions of operators, and Schauder’s fixed point theorem, a new set of sufficient conditions

The influence of Gaussian colored noises on the stability of tumor-immune responses to chemotherapy system is analyzed. By means of the unified colored noise approximation of multidimensional stochastic dynamic system, the system is changed into the stochastic system with Gaussian white noises. I derive the analytic formula of the maximum Lyapunov exponent of system as a function of intensities and

The Fractional-order model of fin problem in the presence of a temperature-dependent rate of internal heat generation in fin material has been studied in the proposed paper. Fractional-order Legendre functions (F-OLFs) with the Galerkin approach has been used to compute the result of the proposed fin problem. The exact solution is also calculated in a particular case of our fractional-order fin problem

We present an analytically tractable scheme to solve the mean transition path shape and mean transition path time of one-dimensional stochastic systems driven by Poisson white noise. We obtain the Fokker-Planck operator satisfied by the mean transition path shape. Based on the non-Gaussian property of Poisson white noise, a perturbation technique is introduced to solve the associated Fokker-Planck

The dynamic bifurcation analysis of the nonlinear oscillation of a simple fluidelastic structure is presented. This structure is a cantilever beam in a flow, and it behaves as a nonlinear system without potential energy. The structure demonstrates complex flutter behaviour that varies with the controlled flow velocity. We observe the flutter behaviour in a flow experiment, and the motion is characterised

Number of well-known contagious diseases exist around the world that mainly include HIV, Hepatitis B, influenzas etc., among these, a recently contested coronavirus (COVID-19) is a serious class of such transmissible syndromes. Abundant scientific evidence the wild animals are believed to be the primary hosts of the virus. Majority of such cases are considered to be human-to-human transmission, while

We propose a Susceptible–Infected–Recovered (SIR) modified model for Coronavirus disease – 2019 (COVID-19) spread to estimate the efficacy of lockdown measures introduced during the pandemic. As input data, we used COVID-19 epidemiological information collected in fifteen European countries either in private surveys or using official statistics. Thirteen countries implemented lockdown measures, two

We correct some numerical results of [Chaos Solitons Fractals 135 (2020), 109846], by providing the correct numbers and plots. The conclusions of the paper remain, however, the same. In particular, the numerical simulations show the suitability of the proposed COVID-19 model for the outbreak that occurred in Wuhan, China. This time all our computer codes are provided, in order to make all computations

This paper focuses on the design and analysis of an efficient numerical method based on the novel implicit finite difference scheme for the solution of the dynamics of reaction-diffusion models. The work replaces the integer first order derivative in time with the Caputo fractional derivative operator. The dynamics of activator-inhibitor as encountered in chemistry, physics and engineering processes

We show that via the complete discrimination system for polynomial method, the bifurcation, critical condition and topological properties of the nonlinear dynamics can be seen very easily. Concrete example of perturbed Gardner’s equation with high order dispersion also verifies our conclusion. The results indicate that the complete discrimination system for polynomial method can not only be used to

Nonlinear second-order ordinary differential equations are common in various fields of science, such as physics, mechanics and biology. Here we provide a new family of integrable second-order ordinary differential equations by considering the general case of a linearization problem via certain nonlocal transformations. In addition, we show that each equation from the linearizable family admits a transcendental

The effects of noise on any electronic system is a crucial aspect for the delineation of the proper functioning of circuits. Different and consolidated models have been proposed for classical electronic circuital elements but the effect of noise sourcing on memristive devices still lacks a wide and rich experimental description. Despite the larger use of Gaussian white noise in the stimulation of memristive

In this manuscript, we solve a model of the novel coronavirus (Covid-19) epidemic by using Corrector-predictor scheme. For the considered system exemplifying the model of Covid-19, the solution is established within the frame of the new generalized Caputo type fractional derivative. The existence and uniqueness analysis of the given initial value problem are established by the help of some important

In this work, a new compartmental mathematical model of COVID-19 pandemic has been proposed incorporating imperfect quarantine and disrespectful behavior of the citizens towards lockdown policies, which are evident in most of the developing countries. An integer derivative model has been proposed initially and then the formula for calculating basic reproductive number R0 of the model has been presented

This work introduces a new markovian stochastic model that can be described as a non-homogeneous Pure Birth process. We propose a functional form of birth rate that depends on the number of individuals in the population and on the elapsed time, allowing us to model a contagion effect. Thus, we model the early stages of an epidemic. The number of individuals then becomes the infectious cases and the

In this paper, we formulated a general model of COVID-19 model transmission using biological features of the disease and control strategies based on the isolation of exposed people, confinement (lock-downs) of the human population, testing people living risks area, wearing of masks and respect of hygienic rules. We provide a theoretical study of the model. We derive the basic reproduction number R0

In this paper, a susceptible-infected-removed (SIR) model has been used to track the evolution of the spread of COVID-19 in four countries of interest. In particular, the epidemic model, that depends on some basic characteristics, has been applied to model the evolution of the disease in Italy, India, South Korea and Iran. The economic, social and health consequences of the spread of the virus have

Epidemiological models of COVID-19 transmission assume that recovered individuals have a fully protected immunity. To date, there is no definite answer about whether people who recover from COVID-19 can be reinfected with the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). In the absence of a clear answer about the risk of reinfection, it is instructive to consider the possible scenarios

The COVID-19 is a severe respiratory disease caused by a devastating coronavirus family (2019-nCoV) has become a pandemic across the globe. It is an infectious virus and transmits by inhalation or contact with droplet nuclei produced during sneezing, coughing, and speaking by infected people. Airborne transmission of COVID-19 is also possible in a confined place in the immediate environment of the

This paper studies the stability and L1-gain problems for impulsive positive switched systems (IPSS) consisting of both unstable and stable subsystems, and proposes a mode-dependent impulsive control (MDIC) method for the first time. By means of a piecewise linear co-positive Lyapunov function (PLCLF) and using average dwell time (ADT) approach, some sufficient criteria for global exponential stability

Non-equilibrium phase transition is always one of the most important issue for complexity science, since it can reveal physical mechanisms of abundant physical phenomena. Exploring applications of non-equilibrium phase transitions in basic paradigm models of complexity science is vital for better comprehending essences of real physical processes. Among these processes, totally asymmetric simple exclusion

This article concerns the global exponential quasi-synchronization issue of conformable fractional-order complex dynamical networks (FCDNs) by periodically intermittent pinning control. We first establish two conformable fractional-order differential inequality, which are useful to deal with the global exponential quasi-synchronization of conformable FCDNs, and then by the obtained inequalities, the

The COVID-19 pandemic is an emerging respiratory infectious disease, also known as coronavirus 2019. It appears in November 2019 in Hubei province (in China), and more specifically in the city of Wuhan, then spreads in the whole world. As the number of cases increases with unprecedented speed, many parts of the world are facing a shortage of resources and testing. Faced with this problem, physicians