In this study, an epidemic model for spreading COVID-19 is presented. This model considers the birth and death rates in the dynamics of spreading COVID-19. The birth and death rates are assumed to be the same, so the population remains constant. The dynamics of the model are explained in two phases. The first is the epidemic phase, which spreads during a season based on the proposed SIR/V model and

In this paper we establish a strong coupled fixed point theorem for a generalized coupling between two subsets of a metric space. These are cyclic generalizations of coupled mappings. Starting from two arbitrary points collected from the two subsets between which the coupling is defined, we construct two iterations each of which converges to the coupled fixed point. Further it is shown that such a

This article offers a review of (chiefly, theoretical) results for self-trapped states (solitons) in two- and three-dimensional (2D and 3D) models of nonlinear dissipative media. The existence of such solitons requires to maintain two stable balances: between nonlinear self-focusing and linear spreading (diffraction and/or dispersion) of the physical fields, and between losses and gain in the medium

This paper theoretically investigates a secondary-encryption optical chaotic communication system scheme based on an optical injection structure with single optical feedback and dual-dispersion optical feedback lasers. In the scheme, a fiber reflector (FR) and Fabry–Perot interferometer (FPI) are selected as the laser feedback cavity and effectively conceals time delay signatures (TDSs) of the generated

Iterative procedures have been proved as a milestone in the generation of fractals. This paper presents a new approach to visualize Mandelbrot and Julia sets for complex polynomials of the form W(z)=zn+mz+r; n≥2 where m,r∈ℂ, and biomorphs for any complex function through a viscosity approximation method which is among the most widely used iterative methods for finding fixed points of non-linear operators

When applied to practical applications, existing chaotic systems exhibit many weaknesses, including discontinuous chaotic intervals and easily predicted chaotic signals. This study proposes an n-dimensional chaotic model (nD-CM) to resolve the weaknesses of existing chaotic systems. nD-CM can produce chaotic maps with any desired dimension utilizing existing 1D chaotic maps as seed chaotic maps. To

Although a large number of studies have verified and explained the controllability of complex networks in real life and nature, there is a deficiency of accurate control strategies based on the proposed theory of network controllability. Here, we propose a new dimension reduction method, which firstly decouples the N-dimensional interdependent system into N independent systems, then re-couples them

We study numerically the spatio-temporal behavior of a two-layer multiplex network of bistable cubic maps when the interlayer coupling is modulated by noise. We refer to this interlayer coupling noise as a multiplexing noise. Various spatio-temporal structures can be established in the uncoupled layers depending on initial conditions. They may represent chimeras of different forms, spatially irregular

We consider coupled weakly birefringent cavities filled-in with nonlinear Kerr material and subject to linearly polarized optical injection. Light propagation in such a system is described by a system of discrete Lugiato–Lefever-type equations for each linear polarization component of the electric field into each cavity, coupled by the cross-phase modulation terms and the neighboring waveguides field

Vegetation patterns in arid and semi-arid ecosystems as a self-organized response to resource scarcity is a well-documented issue. Their formation is often attributed to the symmetry-breaking type of instability. In this contribution, we focus on a regime far from any symmetry-breaking instability and consider a bistable regime involving uniformly vegetated covers and a bare state. We show that vegetation

This paper investigates the analog circuit implementation and adaptive neural backstepping control of a network of four Duffing-type MEMS resonators with mechanical and electrostatic coupling. Firstly, the mathematical model of such network is established by using a series-parallel mode of mechanical and electrostatic coupling between MEMS resonators. Secondly, the dynamic analysis reveals that the

To control uncertain strict-feedback chaotic systems, the adaptive backstepping technique is a popular method, yet this method requires repeatedly differentiating virtual control inputs, which will result in the “explosion of complexity” problem. In this paper, an alternative control method for uncertain strict-feedback chaotic systems without using backstepping technique is presented. We first translate

Tristable system with negative stiffness has attracted extensive attention in the low frequency vibration isolation and vibration energy harvester. As a low frequency vibration isolator, it can achieve high static stiffness and low dynamic stiffness. As a vibration energy harvester, it had a wider bandwidth for resonance than the bistable one. The introduction of negative stiffness may induce subharmonic

Identifying influential nodes in a network is vital for the study of social network structure and to facilitate the dissemination of requisite information. The challenge we address is that, given a complex network, which nodes are more important? How can a group of disseminators be identified and selected to maximize any given field of influence? A series of centrality measures are proposed from different

In this paper, we establish a new local fractional integral identity involving three point by the use of Peano kernel approach. Using this identity we derive some new local fractional integrals inequalities of Maclaurin-type for functions whose local fractional derivatives are generalized convex functions. In order to show the effectiveness of the obtained results, we apply them in numerical integration

Many systems can be transformed into collections containing a large number of networks, such as dynamic networks. Defining metrics on a set of networks leads to analyzing a discrete metric space. In this study, we calculate the generalized correlation dimension of the network space and discuss the relationship between the dimension series and the heterogeneity index. Model-based analysis shows that

We analyze the statistical properties of a temporal point process driven by a confined fractional Brownian motion. The event count distribution and power spectral density of this non-Markovian point process exhibit power-law scaling. We show that a nonlinear Markovian point process can reproduce the same scaling behavior. This result indicates a possible link between nonlinearity and apparent non-Markovian

Background Inter-ictal state is a period between convolutions (seizures). Expert neurologist looks for inter-ictal activity within this period to support the diagnosis of epilepsy. The focus of this work is to automate the process of identification of inter-ictal activity from EEG and to distinguish it from the activity of a controlled patient. Also, we have worked on differentiating between different

This paper introduces the fractal interpolation problem defined over domains with a nonlinear partition. This setting generalizes known methodologies regarding fractal functions and provides a new holistic approach to fractal interpolation. In this context, perturbations of nonlinear partition functions are considered and sufficient conditions for the existence of a unique solution of the underlying

The propagation of electromagnetic solitons in a graphene superlattice device is governed by a modified sine-Gordon equation, referred to as the graphene superlattice equation. Kink-antikink collisions suggest the existence of a quasi-breather solution. Here, a numerical search for static quasi-breathers is undertaken by using a new initial condition obtained by a regular perturbation of the null solution

There is significant literature on Schrödinger differential equation (SDE) solutions, where the fractional derivatives are stated in terms of Caputo derivative (CD). There is hardly any work on analytical and numerical SDE solutions involving conformable fractional derivative (CFD). For the reasons stated above, we are required to solve the SDE in the form of CFD. The main goal of this research is

In this article, we propose two types of discrete fractional cobweb models. We derive the analytical solutions of these models and establish sufficient conditions on the stability of their equilibria. We also provide two examples to demonstrate the applicability of our main results.

This article investigates the existence theory, exact solutions, and the unique solutions of physical problems. In this study the well-known Selkov–Schnakenberg system of coupled nonlinear unidirectional PDEs is analyzed. This is a simple chemical reaction system that admits periodic solutions. The existence of the system is extracted by applying contraction and self-mapping conditions. The new families

In this work, a category of delay distributed-order time fractional fourth-order sub-diffusion equations is investigated. The Chebyshev cardinal polynomials (as a proper class of basis functions) are employed to make an appropriate methodology for these problems. To this end, some matrix relationships regarding the distributed-order fractional differentiation (in the Caputo kind) of these polynomials

This paper can be considered as an introductory review of scale invariance theories illustrated by the study of the equation ∂th=−∂x∂xh1−2ν+∂xxxh, where ν>1/2. The d−dimensionals version of this equation is proposed for ν≥1 to discuss the coarsening of growing interfaces that induce a mound-type structure without slope selection (Golubović, 1997). Firstly, the above equation is investigated in detail

The effects of external digitally synthesized Gaussian noise on the resistive state relaxation time of a ZrO2(Y)-based memristive device when switching from a low resistance state to a high resistance state have been experimentally investigated. A nonmonotonic dependence of the resistive state relaxation time on the external noise intensity is found. This behavior is interpreted as a manifestation

We investigate a discrete-time system derived from the continuous-time Rosenzweig–MacArthur (RM) model using the forward Euler scheme with unit integral step size. First, we analyze the system by varying carrying capacity of the prey species. The system undergoes a Neimark–Sacker bifurcation leading to complex behaviors including quasiperiodicity, periodic windows, period-bubbling, and chaos. We use

In nature, vigilance is a common anti-predator strategy prey individuals employ to protect themselves from a possible attack. It gives them sufficient time to take cover or flee. Yet this seemingly profitable strategy, which lowers the number of successful predatory attacks, has a significant impact on the prey's growth rate. Researchers attribute this to reduced foraging time. In this article, we

In this paper, we investigate the spatial dynamics of a class of spatial fractional predator-prey systems with time delay and Allee effect. Firstly, Hopf bifurcation and Turing bifurcation conditions are obtained by using stability theory and bifurcation theory. Then, the abundant dynamic behaviors of the system are demonstrated by numerical simulation. Finally, numerical results show that time delay

We study bright solitons in the fractional coupler with a spatially periodical modulated nonlinearity. The results show that the linear coupling constant κ, Lévy index α, chemical potential μ and nonlinear intensity g have a significant influence on the amplitude, width and stability of fundamental solitons, dipole solitons and tripole solitons. We investigate the stability of bright solitons by linear

Considering the water waves, people have investigated many systems. In this paper, what we study is a Whitham-Broer-Kaup-like system for the dispersive long waves in the shallow water in an ocean. With respect to the water-wave horizontal velocity and deviation height from the equilibrium of the water, we construct (A) two branches of the hetero-Bäcklund transformations, from that system to a known

In this paper, we formulate a new model of a particular type of influenza virus called AH1N1/09 in the framework of the four classes consisting of susceptible, exposed, infectious and recovered people. For the first time, we here investigate this model with the help of the advanced operators entitled the fractal–fractional operators with two fractal and fractional orders via the power law type kernels

We study the dynamics of the Bianchi IX universe when one of the structure constants tends to zero, i.e. we study the dynamics of the Bianchi VII universe. We prove that there is a surface filled of periodic orbits surrounding an equilibrium point, and that except for another surface filled of equilibria the remainder orbits comes and go to infinity.

The objective of this paper is to locate the embedded solitons with χ(2) and χ(3) nonlinear susceptibilities in presence of multiplicative noise. Itô Calculus was implemented to carry out the analysis of the corresponding stochastic differential equation. The unified Riccati equation expansion method and enhanced Kudryashov’s approach yielded dark, bright and singular solitons. The derived soliton

We aim to introduce a new spectral collocation method for investigating and analyzing nonlinear delay control systems governed by the fractional mixed Volterra–Fredholm integral equations (MVFIEs). The generalized fractional Legendre basis (GFLB) is used as a complete orthogonal basis, and the fractional Legendre–Gaussian nodes are introduced and employed as the fractional collocation points. These

The Galerkin method is presented and applied for getting semi-analytical solutions of quadratic Riccati and Bagley-Torvik differential equations in fractional order. New theorems are proved to minimize the generated residual after invoking the Legendre polynomials as a basis in the Galerkin method. The proposed method is compared with other methods by solving some initial value problems of different

Typical degradation-shock failure processes have been widely investigated in current researches, and the failures caused by their dependence are described as competitive failure processes. This paper explores competitive failure modes for uncertain random fractional systems involving degradation and shock processes. We develop a wear degradation model explicitly by employing uncertain fractional differential

The goal of this research is to determine if it is conceptually sufficient to eliminate infection in a community by utilizing mathematical modelling and simulation techniques when appropriate protective controls are adopted. In this research, we investigate the straightforward interaction transmission method to create a deterministic mathematical formulation of cholera infectious dynamics via the fractal–fractional

Transistor-based chaotic oscillators are known to realize highly diverse dynamics despite having elementary circuit topologies. This work investigates, numerically and experimentally using a ring network, a recently-introduced dual-transistor circuit that generates neural-like spike trains. A multitude of non-trivial effects are observed as a function of the supply voltage and coupling strength, including

In this paper, a three-dimensional nonlinear system with only one equilibrium point is constructed based on the Anishchenko-Astakhov oscillator. The system is analyzed in detail using time-domain waveform plots, phase diagrams, bifurcation diagrams, Lyapunov exponent spectra, basins of attraction, spectral entropy, and C0 complexity (a parameter for dynamic properties). It is found that this system

Fractional derivative and delay are important tools in modeling memory properties in the natural system. This work deals with the stability analysis of a fractional order delay differential equation Dαx(t)=δx(t−τ)−ϵx(t−τ)3−px(t)2+qx(t).We provide linearization of this system in a neighborhood of equilibrium points and propose linearized stability conditions. To discuss the stability of equilibrium

With high-speed communication and information sharing in social networks, the effective immunity to specific false information would markedly reduce the loss brought by the spreading of false information. To date, most studies only focus on the immunity of positive relationships for information spreading between individuals. However, negative relationships also exist in social networks and might have

Understanding the potential promotion mechanism for the formation and maintenance of cooperation is a pivotal issue in the development of human society and the natural world. Evolutionary games provide a forceful theoretical tool to probe into the essence of cooperative behaviors. It is considered that diversity (heterogeneity) is a common attribute of individuals and their interaction environment

In this paper, weighted backward shift operators Tw associated to a Schauder basis of a Banach space are considered. These operators are emblematic in the setting of linear chaos in topological vector spaces. In a constructive way, it is shown the existence of a dense linear subspace having maximal dimension, all of whose nonzero members are simultaneously Tw-hypercyclic for every w belonging to a

The local stability and bifurcation of a circus truss antenna under the influence of the thermal excitation are considered using both analytical and numerical methods. On the basis of the obtained four-dimensional averaged equation with 1:2 internal resonance, a kind of eigenvalues of the bifurcation response equation is investigated. By take advantage of the central manifold theory, nonlinear transformation

This paper studies the issue of high-precision trajectory tracking control for manipulator systems with uncertainty disturbances and develops a fast fixed-time control scheme. First, a new type of (FTSM) surface is constructed by combining inverse trigonometric functions, regardless of the size of the system state, which can obtain a faster convergence velocity and high accuracy. The stabilization

We analyze the existence and characteristics of discrete vortex quantum droplets with intrinsic topological charges S of up to 5 in two-component Bose-Einstein condensates in a deep two-dimensional (2D) optical lattice. The 2D discrete Gross-Pitaevskii equation with a Lee-Huang-Yang (LHY) correction term is used to model the condensate, which incorporates local contact interactions and LHY corrections

Accurately detecting a homoclinic cycle and chaos in a concrete system takes a huge challenge. This paper gives a sufficient condition of coexisting homoclinic cycles (degenerate) with respect to a saddle-focus in a class of three-dimensional piecewise systems with two switching manifolds. Furthermore, by constructing the Poincaré map, it is rigorously shown that chaotic behavior is induced by the

The Speech Emotion Recognition (SER) is a complex task because of the feature selections that reflect the emotion from the human speech. The SER plays a vital role and is very challenging in Human-Computer Interaction (HCI). Traditional methods provide inconsistent feature extraction for emotion recognition. The primary motive of this paper is to improve the accuracy of the classification of eight

Humans try to escape from their mundane lives and look for different experiences. Based on this assumption and story, this paper considers asynchronous public goods games on coevolving networks driven by payoff difference. Starting from a regular square lattice, agents disconnect from neighbors who have similar payoff, and they connect to new agents with different payoff. We measure network cohesion

In this paper, the concept of Lipschitz stability is introduced to impulsive delayed reaction-diffusion neural network models of fractional order. Such networks are an appropriate modeling tool for studying various problems in engineering, biology, neuroscience and medicine. Fractional derivatives of Caputo type are considered in the model. The effects of impulsive perturbations and delays are also

The exponential stabilization of chaotic systems is studied via fuzzy time-triggered intermittent control (FTIC). For the Takagi-Sugeno (T-S) fuzzy model representing a chaotic system, the mathematical description of FTIC is presented initially. Compared with fuzzy intermittent control (FIC), FTIC just needs the information at sampling instants on control time intervals. Compared with fuzzy sampled-data

How to precisely characterize the fractional modeling and physical treatment is an ongoing challenge in fluid mechanics and numerical techniques, especially in nonlinear complex models. A model study is conducted to report fractional time-dependent mixed convection incompressible fluid flow inside a channel. The physical system is under the impacts of viscous dissipation, electrical and magnetic fields

The main aim of this paper is to reveal effects of fractal features on the formation factors associated with different transport processes in scale invariant pore-fracture networks. Accordingly, we explore a class of deterministic infinitely ramified networks associated with pre-fractal standard Sierpinski carpets (including Sierpinski cubes and inverse Menger sponges). The focus is placed on the effects

The resistive switching and synaptic behavior of a fabricated Ti/HfO2/Pt crossbar array device are investigated. The results demonstrated that TiOx layers are created by the movement of oxygen ions during the positive SET process, thereby improving the endurance and multilevel switching behavior of the device. The random properties of SET process were described with the help of stochastic model of

We propose the two-subnet physical information neural network with the weighted loss function (WL-tsPINN) to study the higher-order effects of ultra-short pulses in birefringence fiber transmission and analyze the formation mechanism of vector solitons. We predict the dynamical process of mixed-type single/double soliton and soliton molecules based on the higher-order coupled nonlinear Schrödinger

Motivated by complex transport processes occurring in biological and physical systems, we study a non-conserving totally asymmetric simple exclusion process with a dynamic defect particle. The defect particle may appear or disappear stochastically and slows down the traffic of moving particles while bound to the lattice. We analyze the system in the context of mean-field approach, and investigate the

This paper is devoted to the analysis of a Cournot game, described by a nonlinear mathematical model with four distributed time delays, modelling the behavior of two interacting firms on the market. For each firm, a delay for its own production and one for the production of the competitor are introduced. The analysis of the stability of the four equilibrium points is accomplished. The three equilibria

The piezoelectric ceramic can be activated to produce continuous voltage and it is often used to excite nonlinear circuits, which is tamed as functional circuit to detect the acoustic wave and mechanic forcing. When two piezoelectric devices are combined to couple a nonlinear circuit, any switch between two channels embeds with piezoelectric ceramic will induce distinct mode transition in the output

This paper deals with the investigation of the solution of the time-fractional telegraph equation in higher dimensions with ψ-Hilfer fractional derivatives. By application of the Fourier and ψ-Laplace transforms the solution is derived in closed form in terms of bivariate Mittag-Leffler functions in the Fourier domain and in terms of convolution integrals involving Fox H-functions of two-variables