We will make a detailed analysis of a class of the Jimbo-Miwa equation, viz., exact or invariant solutions that arise from the symmetries generated by it and the conservation laws of the equation. The equation, it turns out, is rich in its symmetry structure and produces a large class of conservation laws and what we term as ‘approximate’ conservation laws.

In this paper, we consider the pricing problem of forward start options in the presence of stochastic volatility and regime-switching. By making use of the measure transform technique, with the underlying price as a new numeraire, a closed-form pricing formula is derived in which the only unknown term is the so-called forward characteristic function of the underlying price. The analytical expression

Mathematical modelling plays an indispensable role in our understanding of systems and phenomena. However, most mathematical models formulated for systems either have an integer order derivate or posses constant fractional-order derivative. Hence, their performance significantly deteriorates in some conditions. For the first time in the current paper, we develop a model of an economic system with variable-order

In this paper, the follower-leader formation tracking control problem of multiple autonomous underwater vehicles (AUVs) with uncertainties is addressed. A predefined-time sliding-mode reaching law and a predefined-time sliding-mode surface are developed. Then, a novel predefined-time sliding-mode controller (SMC) is proposed. The newly proposed predefined-time SMC extends the recent finite-time and

There are different factors that are the cause of abrupt spread of arbovirus. We modelled the factors (internal & external) that can increase the diffusion of dengue virus and observed their effects. These factors have influenced on the Aedes aegypti (a dengue virus carrier); factors which increase the dengue transmission. Interestingly, there are some factors that can suppress the Aedes aegypti. The

We give sufficient conditions for the unique solvability and maximal regularity of a generalized solution of a second-order differential equation with unbounded diffusion, drift, and potential coefficients. We prove the compactness of the resolvent of the equation and an upper bound for the Kolmogorov widths of the set of solutions. It is assumed that the intermediate coefficient grows quickly and

In this paper, we propose discrete generalized past entropy based on amplitude difference distribution of horizontal visibility graph as a new complexity measure of nonlinear time series. We use amplitude difference distribution instead of degree distribution to extract information from the network constructed from the horizontal visibility graph, and combine amplitude difference distribution with

Mumps is the most common cause of acquired unilateral deafness in children, in which hearing loss occurs at all auditory frequencies. We use a box model to model hearing loss in children caused by the mumps virus, and since the fractional-order derivative retains the effect of system memory, we use the Caputo–Fabrizio fractional derivative in this modeling. In the beginning, we compute the basic reproduction

At the dawn of the year 2020, the world was hit by a significant pandemic COVID-19, that traumatized the entire planet. The infectious spread grew in leaps and bounds and forced the policymakers and governments to move towards lockdown. The lockdown further compelled people to stay under house arrest, which further resulted in an outbreak of emotions on social media platforms. Perceiving people's emotional

The difference of congenital inheritance and acquired development makes the autaptic distribution in different brain regions variant. To investigate the physiological regulation of autaptic structures on the nervous system, the effects of chemical autapses with random distribution on the dynamics of Newman-Watts small-world neuronal networks are systematically analyzed with the help of three network

In this paper we study a logistic-like and Gauss coupled maps to investigate the period-adding phenomenon, where infinite sets of periodicity (p) form a sequence in planar parameter spaces, such that, the periodicity of adjacent elements differ by a same constant (ρ) in the whole sequence (pi+1−pi=ρ). We describe the complete mechanism that form this sequence from a closed domain of isoperiodicity

We construct families of fundamental, dipole, and tripole solitons in the fractional Schrödinger equation (FSE) incorporating self-focusing cubic and defocusing quintic terms modulated by factors cos2x and sin2x, respectively. While the fundamental solitons are similar to those in the model with the uniform nonlinearity, the multipole complexes exist only in the presence of the nonlinear lattice. The

Patterns out of homogeneous equilibrium on monolayer networks have been well-documented. However, it is a challenge to understand patterns on multiplex networks. In this work, we study coupled FitzHugh–Nagumo model on duplex networks consisting of two layers. By numerical investigations, we find that the emergent patterns may be characterized by dominant network modes when the homogeneous equilibrium

We have put an effort to estimate the number of publications related to the modelling aspect of the corona pandemic through the web search with the corona associated keywords. The survey reveals that plenty of epidemiological models outcast the simple population dynamics solution. Most of the future predictions based on these epidemiological models are highly unreliable because of the complexity of

In this paper, we present a two-layer coupled oscillator model, in which the first layer is composed of the nearest neighbor coupled identical oscillator, the second layer is composed of the global coupled identical oscillator, and there is a one-way point-to-point drive from the second layer to the first layer. In this system, the driven layer changes from unsynchronized state to synchronized state

The severe acute respiratory syndrome COVID-19 has been in the center of the ongoing global health crisis in 2020. The high prevalence of mild cases facilitates sub-notification outside hospital environments and the number of those who are or have been infected remains largely unknown, leading to poor estimates of the crude mortality rate of the disease. Here we use a simple model to describe the number

The Coronavirus disease (Covid-19) has been declared a pandemic by World Health Organisation (WHO) and till date caused 585,727 numbers of deaths all over the world. The only way to minimize the number of death is to quarantine the patients tested Corona positive. The quick spread of this disease can be reduced by automatic screening to cover the lack of radiologists. Though the researchers already

Two low-dimensional models for nonlinear dynamo action in Rayleigh-Bénard convection in presence of rigid body rotation about vertical axis are constructed for metallic fluids with finite magnetic Prandtl number (Pm) and small (or zero) thermal Prandtl number (Pr). Dynamo effect is seen for Pm≥0.75 with Pr=0.025 and Taylor number, 0

In this article, we studied the outcomes of environmental transmission for infection dynamics of a debilitating protozoan parasite (Ophryocystis elektroscirrha) that infects monarch butterflies (Danaus plexippus) via new generalised Caputo type fractional derivatives. We solved a non-linear fractional model by using modified version of well known Predictor-Corrector scheme. Existence and uniqueness

In this paper, a tumour-immune model with pulsed treatment of different frequency is proposed. The globally attractive conditions of the tumour-free periodic solution are presented in views of the comparison theorem for impulsive differential equations. Furthermore, the effect of period, dosage and times of drug delivery on the critical threshold is addressed by means of computer simulation, which

In this study, we examine the pricing of vulnerable options under a stochastic volatility model based on the partial differential equation approach. Specifically, we consider a multiscale stochastic volatility model that is assumed to be driven by two diffusions (fast-scale and slow-scale) and use an asymptotic expansion approach to drive the approximate pricing formulas of vulnerable options, which

In this paper, we investigate the multifractal characteristics of the cross-correlations between price and volume in China's first crude oil futures market (INE), and compared the INE market with Brent and WTI market. Multifractal detrended cross-correlation analysis (MF-DCCA) was applied to comprehensively research the multifractal characteristics of the three different crude oil futures markets based

The common Kadomtsev-Petviashivili (KP) system coupled with parity-time symmetry is studied. The bilinear form is introduced to the Alice-Bob Kadomtsev-Petviashivili(AB-KP) system with additional arbitrary constant a. The abundant solutions are discussed for various transformation function f, which are different from common KP system. As a result, a single soliton dependent on parameter a, breather

Automatic language classification is an important contribution to linguistic research. Four statistical features concerning long-range correlations are applied to classify syntactic properties of languages. We calculate Zipf’s exponent, Heaps’ exponent, fractal dimension and entropy, for the Bible translations to one hundred live languages from twenty-eight language families. The Bible has unique concept

In this paper, a reaction-diffusion SIR epidemic model is proposed. It takes into account the individuals mobility, the time periodicity of the infection rate and recovery rate, and the general nonlinear incidence function, which contains a number of classical incidence functions. In our model, due to the introduction of the general nonlinear incidence function, the boundedness of the infected individuals

Electroencephalogram (EEG) signal analysis is one of the mostly studied research areas in biomedical signal processing, and machine learning. Emotion recognition through machine intelligence plays critical role in understanding the brain activities as well as in developing decision-making systems. In this research, an automated EEG based emotion recognition method with a novel fractal pattern feature

A novel fractional nonautonomous system is proposed by introducing fractional order meminductor-memristor based circuit. Four circuit models are presented by different arrangements for the elements and the dynamic behaviors for each circuit are explored. It is observed that the four systems exhibit chaotic and hyperchaotic behaviors which have been verified using Lyapunov exponents. Bifurcation diagrams

Pattern formation processes in non-integer order systems are increasingly becoming the subject of activity considered by many scientists and engineers for scenarios associated with spatial heterogeneity or anomalous diffusion. The major drawback encountered is the computation of the Caputo and Fabrizio fractional operator which leads to non-locality issues or memory problems in time. We formulate efficient

The present paper aims to carry out a new scheme for solving a type of singularly perturbed boundary value problem with a second order delay differential equation. Getting through the solution, we used Reproducing Kernel Hilbert Space (RKHS) method as an efficient approach to obtain the analytical solution for ordinary or partial differential equations that appear in vast areas of science and engineering

This paper proposes and analyzes an adaptive immunity HIV infection model. The model describes the interaction between healthy CD4+T cells, silent (latent) infected cells, active infected cells, free HIV particles, Cytotoxic T lymphocytes (CTLs) and antibodies. The healthy CD4+T cells can be infected when they are contacted by one of the following: (i) free HIV particles, and this is known as virus-to-cell

In this paper, an incompressible orthotropic plate is studied for the bounds of Rayleigh wave speed. A parameter “a” of elastic anisotropy, for all orthotropic materials, is defined. It is found that, for all materials with −4

The most probable response, which acts as a deterministic geometric tool for the response analysis of stochastic systems, offers an attractive alternative to traditional methods for analyzing the P-bifurcation of the stochastic impact system. Specifically, the stochastic impact system perturbed by multiplicative Gaussian white noises is considered to research the P-bifurcations under the most probable

The Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model is one of the standard models of disease spreading. Here we analyse an extended SEIR model that accounts for asymptomatic carriers, believed to play an important role in COVID-19 transmission. For this model we derive a number of analytic results for important quantities such as the peak number of infections, the time taken to

It is well-known that the classical SIR model is unable to make accurate predictions on the course of illnesses such as COVID-19. In this paper, we show that the official data released by the authorities of several countries (Italy, Spain and The USA) regarding the expansion of COVID-19 are compatible with a non-autonomous SIR type model with vital dynamics and non-constant population, calibrated according

Among the few known rigorous results for time-dependent equilibrium correlations, important for understanding transport properties, are the Mazur bound and the Suzuki equality. The Mazur inequality gives a lower bound, on the long-time average of the time-dependent auto-correlation function of observables, in terms of equilibrium correlation functions involving conserved quantities. On the other hand

Nowadays, the number of physical systems that have reported non-Gaussian diffusion emergence in systems whose diffusivity fluctuates is increasing. These systems may present non-Gaussian diffusion associated with a mean square displacement of trace-particles that may be normal or anomalous. To include anomalous diffusion, recent research has investigated superstatistics of scaled Brownian motion (SBM)

In this work, we generalize a (deterministic) mathematical model that anticipates the influence of temperature on dengue transmission incorporating temperature-dependent model parameters. The motivation comes by the epidemiological evidence and several recent studies clearly states fluctuations in temperature, rainfall, and global climate indexes are determinant on the transmission dynamic and epidemic

In this paper, the behavior of gap solitary waves is investigated in a two-dimensional electrical line with nonlinear dispersion. Applying the semidiscrete approximation, we show that the dynamics of modulated wave in the network can be described by an extended nonlinear Schrödinger equation. With the aid of the dynamical systems approach, we examine the fixed points of our model equation and the bifurcations

An immense body of research has focused on chaotic systems, mainly because of their interesting applications in a wide variety of fields. A comprehensive understanding and synchronization of chaotic systems play pivotal roles in practical applications. To this end, the present study investigates a multi-stable fractional-order chaotic system. Firstly, some dynamical features of the system are described

The growing investments and installations of wind farms in the Brazilian Northeast have drawn attention to the region, leading investors and researchers to seek better ways of using the local wind regimen for energy production. In face of the complex behavior of wind speed time series, mixture distribution models have been applied to bimodal databases aiming at achieving the best modeling for series

We investigate the generalized projective synchronization (GPS) problem of fractional-order extended Hindmarsh-Rose (FOEHR) neuronal models with magneto-acoustical stimulation input. The improved neuronal model has advantages in depicting the biological characteristics of neurons and therefore exhibits complex firing behaviors. In addition, we consider the nonlinearity and uncertain parameters of the

Network robustness against sequential attacks is significant for complex networks. However, it is generally assumed that complete information of complex networks is obtained and arbitrary nodes can be removed in previous researches. In this paper, a sequential attack in complex networks is modeled as a partial observable Markov decision process (POMDP). Then a reinforcement learning (RL) approach for

Spontaneous emergence of cell polarity intrinsically lies at the localization of signaling molecules on a particular region of cell membrane. Such a process necessarily contains a positive feedback loop to amplify the localized cluster. To describe the polarizing process and explore different feedback functions involved, deterministic and stochastic models with non-local kinetics are discussed in this

The Wiener polarity index Wp is a topological index that was devised by the chemist Harold Wiener for predicting the boiling points of alkanes. The index Wp for chemical trees (chemical graphs representing alkanes) is defined as the number of unordered pairs of vertices at distance 3. A vertex of a chemical tree with degree at least 3 is called a branching vertex. A segment of a chemical tree T is

A chaotic trajectory in weakly chaotic higher-dimensional Hamiltonian systems may locally present distinct regimes of motion, namely, chaotic, semiordered, or ordered. Such regimes, which are consequences of dynamical traps, are defined by the values of the Finite-Time Lyapunov Exponents (FTLEs) calculated during specific time windows. The Covariant Lyapunov Vectors (CLVs) contain the information about

A fractional compartmental mathematical model for the spread of the COVID-19 disease is proposed. Special focus has been done on the transmissibility of super-spreaders individuals. Numerical simulations are shown for data of Galicia, Spain, and Portugal. For each region, the order of the Caputo derivative takes a different value, that is not close to one, showing the relevance of considering fractional

Life style of people almost in every country has been changed with arrival of corona virus. Under the drastic influence of the virus, mathematicians, statisticians, epidemiologists, microbiologists, environmentalists, health providers, and government officials started searching for strategies including mathematical modeling, lock-down, face masks, isolation, quarantine, and social distancing. With

COVID-19 is a novel coronavirus affecting all the world since December last year. Up to date, the spread of the outbreak continues to complicate our lives, and therefore, several research efforts from many scientific areas are proposed. Among them, mathematical models are an excellent way to understand and predict the epidemic outbreaks evolution to some extent. Due to the COVID-19 may be modeled as

The aim of this study is to model the transmission of COVID-19 and investigate the impact of some control strategies on its spread. We propose an extension of the classical SEIR model, which takes into account the age structure and uses fractional-order derivatives to have a more realistic model. For each age group j the population is divided into seven classes namely susceptible Sj, exposed Ej, infected

We propose an adaptive master-slave coupling scheme to achieve explosive synchronization (ES) in a targeted (slave) layer of a multilayer network of Sakaguchi-Kuramoto (SK) oscillators. The natural frequencies of the oscillators in the networks are drawn from Lorentzian distribution of zero mean. In the absence of inter-layer coupling, the dynamics of the master layer is governed by SK model with local

In this work we analyze predictability and complexity of monthly rainfall temporal series recorded from 1950 to 2012, at 133 gauging stations in Pernambuco state, northeastern Brazil. To this end we use the complexity entropy causality plane (CECP) and Fisher Shannon plane (FS) formed by information quantifiers permutation entropy, permutation statistical complexity, and Fisher information measure

The need to optimize and rationally exploit, both fractally distributed natural resources and civil infrastructures, has led us to study the covering of random fractals with circular tiles of a fixed radius. The study has been carried out for different fractal dimensions and radii of the tiles. From the study it is deduced that the fractal mass enclosed by the circular tiles follows a parabolic fractal

The analysis of infant cry signals is becoming an attractive field of research in biomedical physics and engineering for better understanding of the pathologies and appropriate medial diagnosis. The main purpose of the current study is to characterize infant normal and pathological cry signals by studying their respective oscillations by means of approximate entropy and correlation dimension estimated

2019 novel coronavirus (COVID 19) infections detected as the first official records of the disease in Wuhan, China, affected almost all countries worldwide, including Turkey. Due to the number of infected cases, Turkey is one of the most affected countries in the world. Thus, an examination of the pandemic data of Turkey is a critical issue to understand the shape of the spread of the virus and its

Forecasting the dynamics of flu epidemics could be vital for policy-making concerning the allocation of public health resources. Reliable predictions about disease transmission networks also help fix the benchmark for reconciling diverse aspects to the decision-makers while selecting and implementing a suitable health intervention. To this aim, we propose an SIR/VM epidemic game model to reveal the

During pandemic events, strategies such as social distancing can be fundamental to reduce simultaneous infections and mitigate the disease spreading, which is very relevant to the risk of a healthcare system collapse. Although these strategies can be recommended, or even imposed, their actual implementation may depend on the population perception of the risks associated with a potential infection.

In this paper, the nonlinear modified Gardner (mG) equation is under consideration which represents the super nonlinear proliferation of the ion-acoustic waves and quantum electron-positronion magneto plasmas. The considered model is investigated with the help of Lie group analysis. Lie point symmetries are computed under the invariance criteria of Lie groups and symmetry group for each generator is

Optimal control is always intended for optimization of different systems. In this study, new introduced differential operators called fractal-fractional derivatives have been used to investigate the behavior of one of the attractions of applied mathematics in physics and engineering. A novel version of the optimal control problem (OCP) generated using a dynamic system of type space-time fractal-fractional

The earthquakes statistical analysis are essential for understanding the seismic activity of a region and consequently, in seismic hazard studies. Nowadays, the statistics that describe the relationship between the earthquake magnitude and the total number of quakes in a given region has been dominated by the Gutenberg–Richter (GR) power-law. However, the GR law is only valid from a threshold magnitude