Modern weather and climate prediction models are based on a system of nonlinear partial differential equations called the primitive equations. Lie symmetries of the primitive equations with zero external heating rate are computed and the structure of its maximal Lie invariance algebra, which is infinite-dimensional, is studied. The maximal Lie invariance algebra for the case of a nonzero constant Coriolis

We investigate the stochastic processes obtained as the fractional Riemann-Liouville integral of order α∈(0,1) of Gauss-Markov processes. The general expressions of the mean, variance and covariance functions are given. Due to the central role, for the fractional integral of standard Brownian motion and of the non-stationary/stationary Ornstein-Uhlenbeck processes, the covariance functions are carried

In this paper first we consider eigenvalue problems for the weighted (p,q)-Laplacian and prove the existence of a continuous spectrum and determine its infimum. Then we deal with perturbations of the eigenvalue problem. We consider the case of sublinear and superlinear perturbations.

We consider a general mathematical model which describes the quasistatic contact of a deformable body with an obstacle, the so-called foundation. The material’s behaviour is modeled with a visco-elastic-type constitutive law and the contact is described with a general interface law associated to a version of Coulomb’s law of dry friction. We list the assumptions on the data and provide relevant examples

This paper is devoted to study a new nonlinear system involving a parabolic variational inequality, a history-dependent hemi-variational inequality and a differential equation in Banach spaces. By employing the surjectivity argument and Banach’s fixed point theorem, we derive a unique solvability theorem for such a problem under some mild conditions. Moreover, the main results are applied to obtain

Ordinary differential equation (ODE) models of cancer growth are often used to predict tumor growth and form the basis for more complex models used in personalized medicine. Unfortunately, ODE models provide predictions of the average behaviour of the cell population neglecting the fact that cells are discrete objects subject to discrete events. This kind of stochasticity can dramatically change the

In this paper we reveal a common property of generalized fractional equations used for the description of many physical systems related to non-exponential relaxation and anomalous diffusion. It follows from conjugate pairs of Bernstein functions being Laplace exponents of random processes that participate at subordination of simple processes such as ordinary exponential relaxation or Brownian motion

Compactons are studied in the framework of the Korteweg–de Vries (KdV) equation with the sublinear nonlinearity. Compactons represent localized bell-shaped waves of either polarity which propagate to the same direction as waves of the linear KdV equation. Their amplitude and width are inverse proportional to their speed. The energetic stability of compactons with respect to symmetric compact perturbations

The aim of this paper is to develop an effective finite volume method for numerical simulation of the adiabatic shear bands (ASB) formation processes. A formation of ASB happens at high-speed shear strains of ductile materials. A numerical simulation of such problems using Lagrangian approach is associated with some problems, the main one of which is a mesh distortion at large deformations. We use

This paper focuses on the stabilization problem of complex-valued hybrid stochastic delayed systems via aperiodically intermittent control (AIC). As for AIC in existing literature, strict conditions on the lower bound of control intervals and upper bound of control periods or the maximum proportion of rest intervals are required. In this paper, we relax these constraints by proposing average control

Branched manifold is certainly the finest description of the structure of chaotic attractors, characterizing how the unstable periodic orbits are knotted. Many chaotic attractors produced by strongly dissipative systems were thus topologically described. In spite of this, the different possibilities for the branched manifolds which may be constructed from unimodal maps were never exhaustively listed

In this paper we study an inverse problem governed by a constrained nonlinear elliptic quasi-variational hemivariational inequality. The inequality involves two nondifferentiable functions which directly depend on solutions. We solve the direct problem and obtain the properties of weak closedness and uniform boundedness of solutions, which develops some existing results in literature. Then, using a

Echo State Network (ESN) is often used for time series prediction and chaotic series prediction.But in the training process of ESN model, the reserve pool will involve a large number of calculations, so the reserve pool may have node redundancy, resulting in inaccurate training model. It is very important to select the active nodes in the reserve pool because the predicted nodes are very few compared

In this paper, a novel framework to investigate the effect of external electrical signals on cardiac rhythm dynamics using the extended state observer-based control (ESOBC) is proposed. Heterogeneous coupled oscillator model (HCOM) is adopted for the generation of P, Ta, QRS, and T waves, and the realistic synthetic electrocardiogram (ECG) due to its capacity for simulating cardiac muscles response

This study focuses on characterising numerically the attractor volume in the state space of dynamical systems excited by additive white noise. A definition for stochastic attractors is introduced in terms of probability measure and numerical methodologies are presented to characterise them. The study is limited to investigating the effects of additive noise on fixed point and limit cycle attractors

In recent years, experimental and theoretical studies have shown that size effect is non-negligible in mechanical micro- and nano-structures. As a result, classical continuum theory cannot model these structures. To accurately predict the behavior of micro- and nano-structures, non-classical continuum theories should be used. In this paper, the effect of size on the chaotic region of resonators is

This study deals with the (2+1)-dimensional potential Kadomtsev-Petviashvili (pKP) equation, which is used to describe the dynamics of a wave of small but finite amplitude in two dimensions in diverse areas of physics and applied mathematics. Through symbolic computations with Maple, the resonance multi-stripe solutions in real fields, and multi-stripe complexiton solutions in complex fields are derived

Intermittent androgen deprivation therapy is often used to treat prostate cancer, but there are few mathematical modelling studies of it. To explore the mechanisms of such therapy, we describe intermittent therapy with impulsive differential equations, then we propose a novel mathematical model of intermittent androgen deprivation therapy with white noise. We first studied the model’s basic properties

In most cases, the lump wave will collide with line waves and breather waves in the hybrid solutions for (2+1)-dimensional integrable systems. However, this study introduces a new constraint condition to construct a nonlinear superposition in which the lump wave does not collide with other waves forever. In particular, the soliton molecule consisting of a lump wave, a line wave and any number of breather

With the increase of urban population and the expansion of urban scale, understanding the urban structure could provide intellectual support for urban planning, traffic congestion, and even the spread of diseases. Little research has addressed the relationship between urban structure and human mobility. In this study, the community division method is applied to the itinerary network generated by taxi

The most critical factor for increasing crop production is the successful resistance of pests and pathogens which has massive impacts on global food security. Therefore, Filippov systems have been used to model and grasp control strategies for limited resources in Integrated Pest Management (IPM). Extensive studies have been done on these systems where the evolution is governed by a smooth set of ordinary

The extended BKP-Boussinesq equation is considered to construct abundant breather waves, multi-shocks waves and localized excitation solutions. We first transform the original model to its bilinear form through a logarithmic transformation relation. Then, by setting a simple ansatz as a combinations of exponential and sinusoidal functions to obtain various breather waves solutions. We successfully

Pavlov equation, Conservation law, Multipliers, Divergence theorem, Lie symmetry method

This paper discusses some properties of solutions to fractional neutral delay differential equations. By combining a new weighted norm, the Banach fixed point theorem and an elegant technique for extending solutions, results on existence, uniqueness, and growth rate of global solutions under a mild Lipschitz continuous condition of the vector field are first established. Be means of the Laplace transform

This paper presents the first analytical pricing formulas for volatility swaps and volatility options with discrete sampling under the Black-Scholes model with time varying risk-free interest rate. Despite numerous analytical works on the pricing of variance swaps with discrete sampling under different models of asset prices, an analytical pricing formula for volatility swaps as well as volatility

In this article, with the aid of the Lie algebra A1 composed of second order matrices and Lie algebra A2 composed of third order matrices, some new soliton hierarchies of evolution equations are deduced and the corresponding Hamiltonian structures are also worked out by utilizing the trace identity. Specially, one of the integrable soliton hierarchicy is reduced to the generalized Fokker–Plank equation

The goal of this paper is to present a methodology for the computation of invariant tori in Hamiltonian systems combining flow map methods, parameterization methods, and symplectic geometry. While flow map methods reduce the dimension of the tori to be computed by one (avoiding Poincaré maps), parameterization methods reduce the cost of a single step of the derived Newton-like method to be proportional

In this article, with due attention to a new labeling method for vertices of arbitrary graphs, we investigate the existence results for a novel modeling of the fractional multi-term boundary value problems on each edge of the graph representation of the Glucose molecule. In this direction, we consider a graph with labeled vertices by 0 or 1 inspired by the molecular structure of the Glucose molecule

The DYCAST (Dynamic Crash Analysis of Structures) experiments that started at NASA Langley Research Center during the late 1970s have greatly influenced the methodology and thinking of aircraft crashworthiness and survivability studies, and was continued and refined at other aerospace establishments. Nevertheless, so far most of the existing work has emphasized the impact damage to the aircraft section

Representation of a dynamical system in terms of simplifying modes is a central premise of reduced order modelling and a primary concern of the increasingly popular DMD (dynamic mode decomposition) empirical interpretation of Koopman operator analysis of complex systems. In the spirit of optimal approximation and reduced order modelling the goal of DMD methods and variants are to describe the dynamical

A particular system of two-dimensional Lotka-Volterra maps, Ta:(x′,y′)=(x(a−x−y),xy), unfolding a map originally proposed by Sharkovsky for a=4, is considered. We show the routes to chaos leading to the dynamics of map T4. For map T4 we show that even if the stable set of the origin O includes a set dense in an invariant area, the only homoclinic points of O belong to the x−axis, as well as the cycles

Bone remodeling is regulated by numerous signaling pathways being transforming growth factor-β (TGFβ) and Wnt crucial for coupling bone formation and elimination activities. Bone diseases, such as osteoporosis and bone metastasis, develop when the bone cells cross-talk is corrupted which causes unbalanced bone mass production. In this work, we explore the effects of TGFβ and Wnt in bone dynamics based

Soliton molecules may exist experimentally and theoretically. In this work, we generate some soliton molecules for (2 + 1)–dimensional Sawada–Kotera equation by multiple soliton solutions and a subtle velocity resonance ansatz excited by an observation of bound state behavior of solitons. Asymmetric solitons can be derived by selecting specific parameters of soliton molecules. On the basis of multiple

A lump solution is a rational function solution which is real analytic and decays in all directions of space variables. The equation under consideration in this study is the (2 + 1)-dimensional generalized fifth-order KdV equation which demonstrates long wave movements under the gravity field and in a two-dimensional nonlinear lattice in shallow water. The collisions between lump and other analytic

To accurately predict the time series having limited data with stochastic disturbances and nonlinearity, this paper proposed a composite forecasting model by adaptive data preprocessing and optimized nonlinear grey Bernoulli model. Specifically, improvements in the proposed model lie in the following aspects: firstly, the new-information-based buffer operator is utilized to eliminate stochastic disturbance

Finite element simulations of the temperature-dependent stress-strain response in the elastoplastic region of a material usually involve incremental procedures based on the Newton–Raphson iterative scheme. Although essential to obtaining the correct result, iterations inherently extend the computational time of the simulations. In order to increase the computational effectiveness of such finite element

In reality, environment has the considerable effect on the decision making of individuals. Meanwhile, individuals with different amount of resources could have distinct responses to environmental impacts. In this article, based on spatial multigame model, the mutual effect of environment and resources allocation on cooperation is studied. Firstly, the fitness of individuals in multigame is redefined

The search of high-order periodic orbits has been typically restricted to problems with symmetries that help to reduce the dimension of the search space. Well-known examples include reversible maps with symmetry lines. The present work proposes a new method to compute high-order periodic orbits in twist maps without the use of symmetries. The method is a combination of the parameterization method in

Many social interactions can be modeled by networks, where social actors are represented by vertices and their relations by edges. Researchers, over the years, have used social network analysis (SNA) to study the topological structure of the network and understand relational patterns. More recently, scholars have included in the SNA the actors’ attributes in the search for a better understanding, given

The non-Debye, i.e., non-exponential, behavior characterizes a large plethora of dielectric relaxation phenomena. Attempts to find their theoretical explanation are dominated either by considerations rooted in the stochastic processes methodology or by the so-called fractional dynamics based on equations involving fractional derivatives which mimic the non-local time evolution and as such may be interpreted

This paper proposes a new method to quantify the strength and direction of the information flow, that is, Time-delay multiscale symbolic phase compensated transfer entropy (denoted as SPcTE(τ,s)). We integrate time delay factors and time scale factors into the study of transfer entropy and use compensated transfer entropy to estimate transfer entropy to effectively eliminate the influence of instantaneous

We report the propagation dynamics of necklace beams in the framework of nonlinear fractional Schrödinger equation. The fractional diffraction can be partially compensated by a saturable nonlinearity and their combination leads to the quasi-stable propagation of necklace beams with integer or fractional angular momentum. The expansion of necklace can be slowed down remarkably by the decrease of Lévy

We have investigated synchronized patterns in a network of Thomas oscillators coupled with sinusoidal nonlinear and linear couplings. Patterns like chimera and cluster states are not only observed for many nonlocally coupled oscillators, it is also observed for nearly local coupled network topology in the case of nonlinear coupling. As coupling radius increases, the critical coupling constant for complete

A new transformation v=4(lnf)xx that can formulate a quintic linear equation and a pair of Hirota’s bilinear equations for the (2 + 1)-dimensional Sawada–Kotera (2DSK) Eq. (1) or u=4(lnf)x for 2DSK Eq. (2) is reported firstly, which enables one to obtain a new set of multiple soliton solutions of the 2DSK equation. They are not special cases of the known multiple solitons. The results presented in

Spiral wave chimeras (SWCs), which combine the features of spiral waves and chimera states, are a new type of dynamical patterns emerged in spatiotemporal systems due to the spontaneous symmetry breaking of the system dynamics. In generating SWC, the conventional wisdom is that the dynamical elements should be coupled in a nonlocal fashion. For this reason, it is commonly believed that SWC is excluded

Mass and energy conservative numerical methods are proposed for a general system of N strongly coupled nonlinear Schrödinger equations (N-CNLS). Motivated by the structure preserving properties of composition methods, two basic conservative, first and second order time integrators, are developed as seed schemes for the derivation of high order conservative methods. To avoid solving a global nonlinear

In this paper, we numerically solve a stochastic space-fractional nonlinear wave equation which includes fractional derivative, nonlinear term, damping term and noise term. The energy of system in the continuous case is derived in detail and discrete energy preserving physical characteristic is also proved. We propose a numerical method that uses Crank-Nicolson difference discretization based on second-order

Cross-correlations are ubiquitous in nonstationary multivariable systems. By using detrended cross-correlation (DCCA) technique, recently a new multiple cross-correlation coefficient DMC was proposed to quantity the correlation between multivariate and a target variable. We studied the statistical properties of DMC in detail. More specifically, we first proved that 0≤DMC≤1, and then deduced that the

The nonlinear dynamics of a flexible rotating multi-tethered satellite formation in a Halo orbit with uncertain-but-bounded parameters are examined in this paper via an interval analysis method. In Hill's problem, equations of motion for the focused system are derived with the flexibility and extensibility of tethers involved. Not limited to the system of concern, the developed dynamic model could

This paper proposes an effective diffusion equation method to analyze nuclear magnetic resonance (NMR) relaxation. NMR relaxation is a spin system recovery process, where the evolution of the spin system is affected by the random field due to Hamiltonians, such as dipolar couplings. The evolution of magnetization can be treated as a random walk in phase space described either by a normal or fractional

Installing a tuned mass damper (TMD) is a promising vibration control method in many engineering applications which can suppress excessive vibration of a primary structure by transferring and dissipating vibration energy from the primary structure to the TMD. To overcome some limitations and drawbacks of traditional tuned mass dampers in practice, a bio-inspired X-shaped structure/mechanism is utilized

We first introduce a Lie algebra g˜ which can be used to construct integrable couplings of some isospectral and nonisospectral problems. As two applications of the Lie algebra g˜, the MKdV spectral problem is enlarged to an isospectral problem and the AKNS spectral problem is expanded to a nonisopectral problem. Then, two integrable couplings are obtained by solving an isospectral and a nonisospectral

In this paper, we estimate the domain of attraction of the origin of two interconnected nonlinear systems. For each subsystem we introduce an auxiliary system and assume that the origin is locally robustly asymptotically stable. Then an integral input-to state stable Lyapunov function for each subsystem on a bounded set is constructed via Zubov’s method and the introduced auxiliary system. A local

The purpose of this paper is to open a scientific discussion on possible applications of media described by fractional-order (FO) models (FOMs) in electromagnetic cloaking. A 2-D cloak based on active sources and the surface equivalence theorem is simulated. It employs a medium described by FOM in communication with sources cancelling the scattered field. A perfect electromagnetic active cloak is thereby

An approach to solving coefficient inverse problems for nonlinear reaction-diffusion-advection equations is proposed. As an example, we consider an inverse problem of restoring a coefficient in a nonlinear Burgers-type equation. One of the features of the inverse problem is a use of additional information about the position of a reaction front. Another feature of the approach is a use of asymptotic

In this paper, we consider a new kind of obstacle problem for the elastic membrane. The obstacle is made of a rigid body covered by a soft layer that is deformable and allows penetration. It assigns a reactive normal pressure, which depends on the interpenetration of the membrane and the obstacle, during the contact process. Three equivalent descriptions of the new obstacle problem are derived, namely

In this paper, the profile and stability of alternating wave solution, which arises as a bifurcated periodic solution of equivariant Hopf bifurcation with amazing properties, are investigated for a Stuart-Landau system consisting of three oscillators. The method of multiple scales is used to compute the normal form equation up to fifth order. The Floquet theory is introduced because it is difficult

This paper presents a systematic and rigorous analysis on the convergence rates of the Harmonic balance Method (HB) for general smooth and non-smooth systems. In doing so, the convergence rates of Fourier truncation are established at first for functions with different smoothness, and then, the errors of HB are estimated with the help of a coercive condition and the established results on Fourier truncation

To explore the influence of environmental pollution on the spread of waterborne diseases, we formulate a diffusive waterborne pathogen model with the distinct diffusion rates and spatial heterogeneity. We define the basic reproduction number R0 and show its threshold role: if R0<1, the disease-free steady state is globally asymptotically stable; if R0>1, the model system is uniformly persistent. The

In this paper, some of the scenarios that can occur in the numerical nonlinear non-smooth response of a vibro-impact single-degree-of-freedom system, symmetrically constrained by deformable and dissipative bumpers, were identified and described. The different scenarios, obtained varying selected dimensionless parameters, were investigated identifying homogeneous frequency intervals, characterized by