We demonstrate the existence of various types of solitons in the spin-orbit-coupled systems with the fractional dimension based on Lévy random flights, including the systems with or without Zeeman splitting. Specifically, the systems without Zeeman splitting can support families of symmetric solitons, whereas the systems with Zeeman splitting can support families of stable asymmetric solitons. These

In this work, a mathematical model consisting of a compartmentalized coupled nonlinear system of fractional order differential equations describing the transmission dynamics of COVID-19 is studied. The fractional derivative is taken in the Atangana-Baleanu-Caputo sense. The basic dynamic properties of the fractional model such as invariant region, existence of equilibrium points as well as basic reproduction

An issue which is increasingly attracting attention from scientists to engineers, is the robustness of networks which is the ability against perturbations. It is found that both the network topology and network dynamics affect the robustness of networks. In this article, we present the cascading failure model triggered by perturbing a fraction 1−p of nodes on SF networks with three dynamics: the biochemical(B)

The phenomenon of explosive synchronization where asynchronous oscillators abruptly undergo synchronization in complex networks is often considered to be an emergent effect due to correlations imposed on system parameters. However, such correlation constraints avoid flexibility, generality, and applicability. We consider classical Kuramoto oscillators on complete bipartite networks with frequency heterogeneity

In this study, we use Global Sensitivity Analysis (GSA) to rank four non-pharmaceutical interventions (NPIs) in a deterministic compartmental model that might control Covid-19 related deaths in the United States. The NPIs are social distancing, isolation of infected individuals, identifying asymptomatically infected individuals through testing, and the use of face masks. The model uses a fear-based

This paper focuses on the neural adaptive learning synchronization of second-order chaotic systems with guaranteed prescribed performance subject to model uncertainties, external disturbances, and input saturation. First, a neural adaptive state feedback controller is designed. The barrier Lyapunov function (BLF) is utilized to guarantee the output synchronization tracking error always stays within

The present paper deals with the problem of a stochastic predator-prey model with continuous time delay. In the case that the integral kernel is the function ae−at, the persistence in the mean and extinction of this solution are derived by making use of Lyapunov analysis methods. Numerical simulations for a hypothetical set of parameter values are presented to illustrate the analytical findings.

Libration point orbits around collinear points present numerous properties which are worthwhile for space missions. Because orbits around these points are exponentially unstable, station-keeping strategies aim for periodic motion.This paper considers the problem of Lagrangian point stabilisation in the Sun-Jupiter system with non-ideal solar sail and albedo effect. Energy shaping and dissipation injection

One of the most important tools used to create a secure environment for transmitting information is the use of chaotic systems. In the present work, chaotic systems have been improved by using differential equations based on fractional calculations. The structure of the improved system is studied by using various tests. And as an application of the new system, a cryptographic algorithm based on proposed

In this paper we study the equilibrium mechanics problem that originates in a binary tree with infinite levels subjected to loads on its topmost branches. The application of the laws of mechanics to find the equilibrium configuration shows that the functional forms of the vertical and horizontal displacements of its end nodes converge to a Takagi curve and a linear combination of inverses of β-Cantor

In this paper, finite-time stability of fractional delay difference equations with discrete Mittag-Leffler kernel are studied. Firstly, we establish a new generalized Gronwall inequality in sense of Atangana-Baleanu fractional difference sum operator. Then, based on this new generalized Gronwall inequality and the method of steps, finite-time stability criteria of fractional delay difference equations

Cyclicality and instability inherent in the economy can manifest themselves in irregular fluctuations, including chaotic ones, which significantly reduces the accuracy of forecasting the dynamics of the economic system in the long run. We focus on an approach, associated with the identification of a deterministic endogenous mechanism of irregular fluctuations in the economy. Using of a mid-size firm

The present work describes the behavior of solitary and periodic waves in a nonlinear electrical transmission line with linear dispersion. Based on the semidiscrete approximation, we show that the dynamics of modulated wave in the system can be described by an extended cubic-quintic nonlinear Schrödinger equation. Using a simple transformation, we reduce the given equation to a cubic-quintic Duffing

A modified physics-informed neural network is used to predict the dynamics of optical pulses including one-soliton, two-soliton, and rogue wave based on the coupled nonlinear Schrödinger equation in birefringent fibers. At the same time, the elastic collision process of the mixed bright-dark soliton is predicted. Compared the predicted results with the exact solution, the modified physics-informed

Since December 2019, the world has experienced from a virus, known as Covid-19, that is highly transmittable and is now spread worldwide. Many mathematical models and studies have been implemented to work on the infection and transmission risks. Besides the virus's transmission effect, another discussion appears in the community: the fear effect. People who have never heard about coronavirus, face

We consider a family of nonlinear oscillators with quadratic damping, that generalizes the Liénard equation. We show that certain nonlocal transformations preserve autonomous invariant curves of equations from this family. Thus, nonlocal transformations can be used for extending known classification of invariant curves to the whole equivalence class of the corresponding equation, which includes non-polynomial

In the framework of non-autonomous discrete dynamical systems in metric spaces, we propose new equilibrium points, called quasi-fixed points, and prove that they play a role similar to that of fixed points in autonomous discrete dynamical systems. In this way some sufficient conditions for the convergence of iterative schemes of type xk+1=Tkxk in metric spaces are presented, where the maps Tk are contractivities

Here the theory of local fractional differential equations is extended to a more general class of equations akin to usual exact differential equations. In the process, a new notion has been introduced which is termed as α-exact local fractional differential equation. The theory of such equations parallels that for the first order ordinary differential equations. A criterion to check the α-exactness

Considering the sudden change of environmental disturbance, a stochastic susceptible infectious recovered (SIR) model with Markov jump and the limited medical resources is proposed. Firstly, by a bifurcation analysis of the deterministic SIR model, the maximal medical resource tipping point can be detected to adjust and optimize the medical resource allocation. Then, the impact of environmental disturbance

In this paper, a new class of computational techniques for the numerical solution of fractional functional differential equations is discussed. The proposed technique is based on Dickson polynomials with which well-known polynomials such as Fibonacci, Lucas and Chebyshev polynomials are related with some parameters. In general, the proposed combined scheme is improved by the fractional Dickson-Tau

The current paper deals with the parametric modification of Meyer-König-Zeller operators which preserve constant and Korovkin’s other test functions in the form of (x1−x)u, u=1,2 in limit case. The uniform convergence of the newly defined operators is investigated. The rate of convergence is studied by means of the modulus of continuity and by the help of Peetre-K functionals. Also, a Voronovskaya

Numerous anomalous diffusion processes are characterized by crossovers of the scaling exponent in the mean squared displacement at some correlations time. The bi-fractional diffusion equation containing two time-fractional derivatives is a versatile mathematical tool describing specifically retarded subdiffusive transport, in which the scaling exponents acquires a smaller value, i.e., the diffusion

Neurons are often connected, spatially and temporally, in phenomenal ways that promote wave propagation. Therefore, it is essential to analyze the emergent spatiotemporal patterns to understand the working mechanism of brain activity, especially in cortical areas. Here, we present an explicit mathematical analysis, corroborated by numerical results, to identify and investigate the spatiotemporal, non-uniform

Unlike in the standard public goods game (PGG), real-life donors (e.g. to charities) rarely receive any direct benefits from their donation behaviors to a disaster area, but donations are always prevalent. This paper studies why donation behaviors are common and the factors that can influence their propagation. The interactions among individuals are divided into two phases, including all individuals

The Sasa-Satsuma equation on a continuous background describes a nonlinear fiber system with higher-order effects including the third-order dispersion and Kerr dispersion. The Sasa-Satsuma equations describe the simultaneous propagation of two ultrashort pulses in the birefringent or two-mode fiber with the third-order dispersion, self-steepening, and stimulated Raman in scattering effects, and govern

In fluid mechanics, the higher-dimensional and higher-order equations are constructed to describe the propagations of nonlinear waves. In this paper, we investigate the (2+1)-dimensional variable-coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada equation in fluid mechanics. The Nth-order Pfaffian solutions are constructed and proved via the modified Pfaffian technique. The higher-order soliton, first-

The influence of an energetic bistable potential on the entropic vibrational resonance (EVR) is investigated. We demonstrate the existence of vibrational resonance modulated by the high-frequency signal with energetic and entropic barriers, which is termed energetic and entropic vibrational resonance (EEVR). We use different methods, including the numerical simulation of Langevin equation, the numerical

We obtain the exact two and three soliton solutions for higher order NLS equation with variable coefficients using Darboux transformation method with some algebraic manipulations based on constructed Lax Pair. For the first time, switching characteristics of two and three solitons in the attosecond regime via inelastic soliton interactions are discussed through some graphical illustrations. Additionally

The stability of synchronized state is essential for the stable operation and control of power network. This paper focuses on the multiplex oscillatory power network model, and then analyzes the stability of multiplex power network being comprised of Kuramoto oscillators. In specific, we infer the analytical important conditions for synchronous stability in a multiplex oscillatory power network. Furthermore

We introduce a compartmental model SEIAHRV (Susceptible, Exposed, Infected, Asymptomatic, Hospitalized, Recovered, Vaccinated) with age structure for the spread of the SARAS-CoV virus. In order to model current different vaccines we use compartments for individuals vaccinated with one and two doses without vaccine failure and a compartment for vaccinated individual with vaccine failure. The model allows

New travelling wave solutions for a generalised Burgers-Fisher (GBF) equation are obtained. They arise from the solutions of nonlinear second-order equations that can be linearised by a generalised Sundman transformation. The reconstruction problem involves a one-parameter family of first-order equations of Chini type. Firstly we obtain a unified expression of a one-parameter family of exact solutions

Although more than a year has passed since the coronavirus outbreak globally, the Covid-19 pandemic conditions still exist in many countries, including Iran. Predicting the number of future patients and deaths can help governments and policymakers make better decisions to enforce disease control restrictions. In this study, we aim to use a combined multilayer perceptron (MLP) neural network and Markov

The market dynamics produced by simple interactions among rational investors can generate complex phenomena such as bubbles, crashes, and business cycles. One powerful tool to understand those phenomena might be the use of Cellular Automata (CA) models. In this contribution we investigate spatial aggregations effects associated to the propagation of information contagion waves across a network of non-equivalent

Semi-Markov processes established a rich framework for many real-world problems. Semi-Markov processes include Markov processes, Markov chains, renewal processes, Markov renewal processes, Poisson processes, birth and death processes, and etc. Since semi-Markov processes describe more complex mathematical models of various objects, in many cases the obtained mathematical models are investigated numerically

We studied a plankton community composed of phytoplankton (prey) and zooplankton (predators) with herd-taxis. The herd-taxis implies that the zooplankton would not only trend towards the higher density zone of phytoplankton but also has conformity behavior, which leads to the nonlinear cross-diffusion. The stability analysis gives out the conditions for the Hopf stability and the Turing bifurcation

In this article, we present an original method to measure the rate of positional change observed during a soccer match based on the relative spatial distribution of players on the pitch. This is justified as players use their relative position as a key tactical tool to contribute to their team’s objectives. A temporal network representation of the game was used, where nodes are players discretely clustered

Memristor, as a nonlinear electronic component, has good switching characteristics, which makes it has excellent application in the field of artificial intelligence. The study for discontinuous dynamics of memristor-based neural network can best reflect the boundary effect of memristors and the complex nonlinear behaviors of system. In this paper, the non-autonomous FitzHugh-Nagumo neuronal circuit

Assistance and aiding partners exploited by defectors could be essential to avoid being exploited and expanding the payoff. The research on of human behaviors has suggested that organizations and alliances play an important role in promoting cooperation between humans. Therefore, this article studies the evolution of cooperation in spatial public goods games with alliance strategy on square lattice

The aim of this study is to design a singular fractional order pantograph differential model by using the typical form of the Lane-Emden model. The necessary details of the singular-point, fractional order and shape factor of the designed model are also provided. The numerical solutions of the designed model have been presented using the combination of the fractional Meyer wavelet (FMW) neural networks

In this study, we evaluate the performance of a physical unclonable function (PUF) using Al2O3/TiOx based memristors. Through a conduction mechanism analysis, it is confirmed that the distribution of high-resistance state (HRS) is wider than that of low-resistance state (LRS) due to the direct-tunneling gap. Furthermore, cycle-to-cycle variation and random telegraph noise (RTN) characteristics which

Usually, opinion formation models assume that individuals have an opinion about a given topic which can change due to interactions with others. However, individuals can have different opinions on different topics and therefore n-dimensional models are best suited to deal with these cases. While there have been many efforts to develop analytical models for one dimensional opinion models, less attention

This paper analyses the complexity of production, fertilizer-saving level, and emission reduction efforts decisions in a Cournot agricultural products supply chain system. A two-parallel agricultural products supply chain consisting of traditional agricultural producers and green agricultural producers was established. Based on bounded rationality, the decision competition model between the two supply

One of the fundamental topics in sports analytics is the science of success, i.e., the study of the correlation between players’ performances and their success. This is a very challenging task especially in the case of team sports, among which football is a prominent example. This paper is concerned with uncovering a dangerous bias that is present in most of the approaches proposed in the literature

In this article, the global quasi-synchronization of complex-valued recurrent neural networks (CVRNNs) with time-varying delays and interaction terms has been investigated. It is based on the standard Lyapunov stability theory and matrix measure method employed with the nonlinear Lipschitz activation functions. A sufficient condition for global quasi-synchronization of the complex-valued recurrent

Specific biophysical neurons are presented to detect different stimuli, and these external exciting signals are encoded to trigger appropriate firing modes and action potentials for signal propagation between neurons in the network. A thermosensitive neuron can estimate the effect of temperature changes on the excitability and firing modes in nervous system, a photocurrent-dependent neuron can be sensitive

In this paper, the necessary and sufficient conditions are derived for the controllability of Atangana-Baleanu-Caputo (ABC) neutral fractional differential equations (FDEs) with noninstantaneous (NI) impulses. The main controllability result is obtained by using the concept of measure of noncompactness, semigroup, fractional calculus, and K-set contraction principle. An illustration is provided to

This work is devoted to the time fractional differential equations (TFDEs) with the Atangana-Baleanu-Riemann (ABR) fractional derivative and their analytical solutions. We generalize the Nucci’s reduction method to find the exact solutions of such equations. Different general solutions of nonlinear ABR fractional differential equations besides first integrals are discussed in different types such as

In this paper, two-dimensional Legendre wavelets algorithm is applied for the first time to solve a variable order fractional partial differential governing equation of viscoelastic column in the time domain. Firstly, the governing equation of a viscoelastic column is established according to a variable order fractional constitutive model. Secondly, the unknown function is expanded into the elements

One of the priority tasks in studying power grids is to find the conditions of their stable operation. The fundamental requirement is synchronizing all the elements (generators and consumers) of a power grid. However, various disturbances can destroy the synchronization. Moreover, desynchronization occurring in a small part of the grid can lead to severe large-scale power outages (or blackouts) due

Focusing on the unpredictability of person-to-person contacts and the complexity of random variations in nature, this paper will formulate a stochastic SIR epidemic model with nonlinear incidence rate and general stochastic noises. First, we derive a stochastic critical value R0S related to the basic reproduction number R0. Via our new method in constructing suitable Lyapunov function types, we obtain

Bursting is a dynamical behavior that has been widely observed in biological, chemical, and physical systems. It is well-known that the bursting behavior can occur in systems exhibiting distinct fast and slow time scales. Here, we show that bursting can happen in gene regulatory network systems without distinct fast and slow time scales. We perform bifurcation analyses to unravel the mechanisms underlying

Motivated by the dynamics of processive molecular motors in biological transport processes, we study the effect of local irreversible dissociation of two distinct species of particles moving along a bridge lane coupled to the input and output lanes governed by exclusion process. The boundary controlling rates of the particle in the bridge lane are determined self-consistently by the dynamics of the

Stable light bullets and clusters of them are presented in the monostable regime using the mean-field Lugiato–Lefever equation [Gopalakrishnan, Panajotov, Taki, and Tlidi, Phys. Rev. Lett. 126, 153902 (2021)]. It is shown that three-dimensional (3D) dissipative structures occur in a strongly nonlinear regime where modulational instability is subcritical. We provide a detailed analysis on the formation

Light competition, the main force in shaping plant height, is ubiquitous in the plant kingdom. Plant height was commonly treated as a competitive strategy and investigated under the game-theoretic framework. However, how plant heights are shaped by light environment under natural selection has not yet been fully understood. Aiming at revealing the potential mechanism causing the height diversification

This article studies the interesting dynamics of a small neural network with three neurons under electromagnetic radiation. The electromagnetic radiation strength can change the number of the equilibrium points in the neural network, which leads to the diversification of the attractor’s trajectory. Thus, the novel multi-style attractors like one-to-two-spiral attractors and one-to-four-scroll attractors

This paper introduces quaternionic views of multi-level brain activation region intensities in resting-state functional magnetic resonance imaging (rs-fMRI) videos. Quaternions make it possible to explore rs-fMRI brain activation regions in a 4D space in which there are varying brain activation intensities in spiralling activation cycles (each with its own intensity). As a result, there is a natural

In this paper, a fractional-order chaotic circuit with different coupled memristors is established. The dimensionality of the system is reduced by the flux-charge analysis method and the stability of the equilibrium points is analyzed by the fractional-order stability theory. Then, the complex dynamic behaviors, including periodic and chaotic attractors, period doubling bifurcation orbit, coexistence

A new technique has been presented for solving strong nonlinear oscillatory problems. The solution is independent of trigonometric functions, and the determination of unknown coefficients related to the proposed solution is very simple. The method is illustrated by examples. For a large amplitude of oscillation of some nonlinear oscillators, the solution nicely agrees with the corresponding numerical

Chance theory provides us a useful tool to solve an optimal control problem with indeterminacy composing of both uncertainty and randomness. Based on chance theory, this paper studies an optimal control for uncertain random singular systems with multiple time-delays. First, an uncertain random singular system with multiple time-delays is introduced, and then the corresponding optimal control problem