There is growing evidence that ecological interactions are often nonlocal. Correspondingly, increasing attention is paid to mathematical models with nonlocal terms as such models may provide a more realistic description of ecological dynamics. Here we consider a nonlocal prey-predator model where the movement of both species is described by the standard Fickian diffusion, and hence is local, but the

The aim the paper is to study a large class of variational-hemivariational inequalities involving constraints in a Banach space. First, we establish a general existence theorem for this class. Second, we introduce a sequence of penalized problems without constraints. Under the suitable assumptions, we prove that the Kuratowski upper limit with respect to the weak topology of the sets of solutions to

The paper presents numerical and experimental investigations of a novel strongly nonlinear system designed for simultaneously vibration suppression and energy harvesting. Characteristic feature of a system is a magnetic levitation harvester which can recover energy from a pendulum tuned mass damper. A new model of coupling between mechanical and electrical subsystems is proposed. The obtained results

Different types of collective dynamical behavior of the coupled oscillator networks are investigated under heterogeneous environmental coupling. This type of interaction pattern mainly occurs indirectly between two or more dynamical units. By interplaying the diffusive and the environmental coupling, the transition scenarios among several collective states, such as complete synchronization, amplitude

Beyond a pure mathematical interest, q-deformation is promising for the modeling and interpretation of various physical phenomena. In this paper, we numerically investigate the existence and properties of the self-localized soliton solutions of the nonlinear Schrödinger equation (NLSE) with a q-deformed Rosen-Morse potential. By implementing a Petviashvili method (PM), we obtain the self-localized

In this work, we consider two of the most frequently used two-dimensional nonlinear time-fractional anomalous sub-diffusion models for simulating transport phenomena in heterogeneous binary media—a variable-order model and a generalised transport equation based on the Riemann-Liouville fractional operator. Our computational modelling framework uses a second order modified weighted shifted Grünwald-Letnikov

In this work we consider a three-dimensional autonomous system of nonlinear ordinary differential equations, which may be thought of as a generalization of the well-known Hopf–Langford system introduced about forty years ago. This dynamical system turned out to be equivalent to the nonlinear force-free Duffing oscillator. In three special cases, it is found to be completely integrable. To the best

In this paper we study ultimate dynamics of one three-dimensional model for tumor growth under oncolytic virotherapy which describes interactions between cytotoxic T-cells, uninfected tumor cells and infected tumor cells. Using the localization theorem of compact invariant sets we derive ultimate upper bounds for all cell populations and establish the property of the existence of the attracting set

An implicit multiscale method with multiple macroscopic prediction for steady state solutions of gas flow in all flow regimes is presented. The method is based on the finite volume discrete velocity method (DVM) framework. At the cell interface, a numerical flux with construction similar to discrete unified gas-kinetic scheme (DUGKS) is applied to ensure multiscale property and make the scheme free

In this paper, we are concerned with a cross-diffusive evolution system arising from biological transport networks. We study the general regularity properties of solutions to the corresponding Dirichlet-Neumann initial-boundary value problem (DNibvp). By applying the properties of divergence equations and the Dirichlet heat semigroup, we find that DNibvp possesses a globally classical solution which

In the sequel, we extend the Strichartz average approach, for the Laplacian on Sierpiński Simplices, which uses average values of a function over basic sets, following the seminal work of S. Kusuoka and X. Y. Zhou, rather than using pointwise ones as classically done in the literature. Until now, the implementation of the related finite volume method, in the case of Sierpiński Simplices, had not been

Positive and negative nonlinear integrable lattice hierarchies are established starting from a discrete matrix spectral problem with three potential functions, particularly the corresponding Hamiltonian structures are presented respectively with the help of the trace identity, all these facts show that these two hierarchies are integrable in Liouville sense. By using Lax pair we derive infinite number

Delay Sobolev equations (DSEs) are a class of important models in fluid mechanics, thermodynamics and the other related fields. For solving this class of equations, in this paper, linearized compact difference methods (LCDMs) for one- and two-dimensional problems of DSEs are suggested. The solvability and convergence of the methods are analyzed and it is proved under some appropriate conditions that

In this project, we study the periodic Dirichlet boundary value problem for a singularly perturbed reaction-advection-diffusion equation on the segment in case of discontinuous reactive and convective terms. Applying the boundary function method, we construct the asymptotic approximation of the periodic solution with internal transition layer located in the vicinity of a curve of discontinuity of the

Nonlinear mesoscopic materials exhibit anomalous elastic nonlinearity in which fast and slow dynamics effects are mixed up. The former is an instantaneous nonlinear phenomenon due to the explicit strain dependence of velocity and damping. Slow dynamics is a non-equilibrium effect, governed by the dependence of the linear modulus and Q-factor on the dynamic strain level: when excited at constant strain

We investigate the long-term dynamical behavior of the partially viscoelastic wave equation subject to a localized frictional damping, given byutt−Δu+∫0tg(t−s)div(a(x)∇u(s))ds+b(x)g1(ut)=0,inΩ×R+,where g denotes the memory kernel, a(x)∈C1(Ω¯),b(x)∈L∞(Ω) are nonnegative functions satisfying the assumptiona(x)+b(x)≥2δ>0,∀x∈ω0,ω0 is a subset of Ω, and b(x)g1(ut) denotes the frictional damping. Under as

A class of non-linear equations of RAPM (risk-adjusted pricing methodology) model type with a free element, depending on the second derivative with respect to the underlying asset, is studied. This class contains the Jandačka — Ševčovič model of the option pricing with taking into account transactions costs. The equivalence transformations continuous group of the equations class is found and is applied

A class of nonlinear reaction-diffusion-convection equations describing various processes in physics, biology, chemistry etc. is under study in the case of time and two space variables. The group of equivalence transformations is constructed, which is applied for deriving a Lie symmetry classification for the class of such equations by the well-known algorithm. It is proved that the algorithm leads

This paper focuses on improving the conventional discrete velocity method (DVM) into a multiscale scheme in finite volume framework for gas flow in all flow regimes. Unlike the typical multiscale kinetic methodsrepresented by unified gas-kinetic scheme (UGKS) and discrete unified gas-kinetic scheme (DUGKS), which concentrate on the evolution of the distribution function at the cell interface, in the

Many novel chaotic systems have recently been identified and numerically studied. Parametric chaotic sets are a valuable tool for determining and classifying oscillation regimes observed in nonlinear systems. Thus, efficient algorithms for the construction of parametric chaotic sets are of interest. This paper discusses the performance of algorithms used for plotting parametric chaotic sets, considering

We propose and analyze a virus-to-cell and cell-to-cell infections HIV model that includes intracellular time delay and infection-age structure, where infection-age-specific conversion function is considered as the piecewise function related to infection period between initial infection and the formation of productively infected cells. Applying the theory of integrated semigroup and the Hopf bifurcation

Lyapunov exponent is a widely used tool for studying dynamical systems. When calculating Lyapunov exponents for piecewise-smooth systems with time-delayed arguments one faces a lack of continuity in the variational problem. This paper studies how to build a variational equation for the efficient construction of Jacobians along trajectories of a delayed nonsmooth system. Trajectories of a piecewise-smooth

We report on the implementation of a novel total-variation denoising method for diffusion spectrum images (DSI). Our method works on the raw signal obtained from dMRI. From the Stejskal-Tanner equation [6], the signals S(x, sk), 1 ≤ k ≤ K, at a given voxel location x may be considered as samplings of a measure supported on the unit sphere S2∈R3 at locations sk=(θk,ϕk)∈S2 which quantify the ease/difficulty

The main goal of this paper is to understand the formation of hexagonal patterns from the dynamical transition theory point of view. We consider the transitions from a steady state of an abstract nonlinear dissipative system. To shed light on the formation of mixed mode patterns such as the hexagonal pattern, we consider the case where the linearized operator of the system has two critical real eigenvalues

This article investigates the three-dimensional globally modified Navier–Stokes equations with unbounded variable delays. Firstly, we prove the global well-posedness of the solutions, and give the existence of the pullback attractor for the associated process. Then, we construct a family of invariant Borel probability measures, which is supported by the pullback attractor.

In this paper, we present two fixed point results on quasi metric spaces by taking into account a contractive condition that obtained via simulation and Q-functions. Then one of these fixed point results has been applied to guarantee the existence and uniqueness of positive solution of a kind of fractional boundary value problem with Riemann-Liouville fractional derivative.

Mushroom billiards are formed, generically, by a semicircular hat attached to a rectangular stem. The dynamics of mushroom billiards shows a continuous transition from integrability to chaos. However, between those limits the phase space is sharply divided in two components corresponding to regular and chaotic orbits, in contrast to most mixed phase space billiards. In this paper we show that tilting

In this paper, we consider an important kind of fractional partial differential equations, namely multi-term time-fractional mixed sub-diffusion and diffusion-wave equation. The crucial importance of the considered equation is due to the fact that it generalizes some substantial types of fractional differential equations that can be widely used in describing many real-life phenomena, some of these

In this paper we use a phenomenological field theory model to study the first-order phase transition from the lamellar phase to the inverse hexagonal phase in specific lipid bilayers. The model is described by a real scalar field with potential that supports both symmetric and asymmetric phase conformations. We adapt the coordinate and parameters of the model to describe the phase transition, and we

In this paper, we focus on investigating a (2+1)-dimensional generalized breaking soliton (gBS) equation with five model parameters, which contains a lot of important nonlinear partial differential equations (PDEs) as its special cases. Firstly, the integrability features of two special cases of the gBS equation are clarified. Secondly, a general method is established to construct solutions formed

We present localized analytical solutions of the logarithmic nonlinear Schrödinger equation, i.e., the so-called the argument-Schrödinger equation. The Gaussian solitary waveform is shown to be the solution, and we obtain the explicit form in a one-dimensional case when the dynamics evolve under a quadratic potential. The dispersion relation becomes time-dependent due to the logarithmic nonlinearity

In this paper, the generalization of the Particle Swarm Optimization (PSO) algorithm is proposed. The new algorithm involves the adoption of complex-order derivatives (CD). Since the CD produce complex-valued results, conjugate pairs of CD are considered for designing the Complex-Order PSO (CoPSO). First, an extensive sensitivity analysis is carried out for studying the influence of the control parameters

Stochastic resonance (SR) in a harmonic oscillator with parametric bounded noise and external periodic force is investigated. By applying the property of bounded noise and using Cameron-Martin formula, infinite chains of linear differential equations are obtained for the spectral amplification, mean-square displacement, and variance. Multiple stochastic resonances are observed for these characteristics

In this paper, we propose a coupled (2+1)-dimensional modified Korteweg-de Vries (mKdV) system, which admits two kinds of nonlocal reductions. By constructing the Darboux transformation for the considered equation, a variety of exact solutions, such as soliton, soliton-type, kink, kink-type, rational, rogue wave and lump solutions are given explicitly.

Using asymptotic methods we investigate a local in a steady state neighbourhood behavior of solutions in the Fermi–Pasta–Ulam model. Basing on the formalism of the normalization method we got special nonlinear evolution equations. The dynamics of these equations substantially defines the behavior of solutions of original equations. We made the conclusions about the interaction of waves moving in different

The fractional Klein-Kramers equation describes the process of subdiffusion in the presence of an external force field in phase space and incorporates a fractional operator in time of order α, 0 < α < 1. We present a family of finite volume schemes for the fractional Klein-Kramers equation, that includes first or second-order schemes in phase space, and implicit or explicit schemes in time with an

A (2+1)-dimensional fifth-order integrable model, the fifth member of the Kadomtsev-Petviashvilli hierarchy (KP5 equation) is investigated. The Lax pairs and the bilinear form of the system lead to multiple soliton solutions. Applying the velocity resonance conditions to the multiple soliton solutions, various types of soliton molecules (soliton bound states) such as the soliton molecules, breather

The most common problems in nature are about non-conservative non-linearity. Non-conservative non-linear problems can be studied with variational problems of non-standard Lagrangians. Birkhoffian mechanics, as an extension of Hamiltonian mechanics naturally, is a sign that analytical mechanics has entered a new stage of development. Therefore, the study of dynamics based on non-standard Birkhoffians

We present and study an extended Gardner-like family of equations, G(m,n;k):ut+(c+um−c−un)x+(uk)xxx=0,c±>0, n > m > 1, k ≥ 1, endowed with a non-convex convection which may be due to two opposing mechanisms that bound the range of velocities of both solitons and compactons beyond which they dissolve, and kink and/or antikink form. Close to solitons and compactons barrier, there is a narrow strip of

Fractional phase field models have been reported to suitably describe the anomalous two-phase transport in heterogeneous porous media, evolution of structural damage, and image inpainting process. It is commonly different to derive their analytical solutions, and the numerical solution to these fractional models is an attractive work. As one of the popular fractional phase-field models, in this paper

An approximation method of measures in the plane is obtained by combining CT-like (computerized tomography) projections and a one–dimensional fractal approximation technique previously devised by the author. Both methods are based on sampling by orthogonal polynomials and involve operations on Jacobi matrices, to avoid the well known ill conditioning of moment methods.

A novel integrable asymmetric coupling of the Ablowitz-Kaup-Newell-Segur (AKNS) system was generated by the completion process of the integrable coupling. We proved the Liouville integrability of the AKNS integrable coupling by deriving its bi-Hamiltonian structures applying the variational identity. Nextly, we investigated the generalized symmetry and infinitely many conservation laws by Hereman method

The objective of the presented article is to investigate the nonlinear dynamics and vibration of a simply supported fluid conveying pipe coupled with a geometrically nonlinear absorber, as well as the occurrence of the targeted energy transfer phenomena in the system. In addition, given the sensitivity of passive nonlinear absorbers performance to uncertainties in design (e.g., damping coefficient)

We investigate throughout this paper the effect of inhomogeneity on the propagation of solitons in ferromagnetic systems governing the magnetization evolution in a magnetic medium. Indeed we focus our attention on a nonlinear evolution equation derived by M. Saravanan and A. Arnaudon (2018 Phys. Lett. A 382 2638) that takes into account the inhomogeneity we are interested in. The perturbed soliton

Two families of semi-rational solutions to the Mel’nikov equation (ME), which is a known model of the interaction between long and short waves in two dimensions, are reported. These semi-rational solutions describe interaction between lumps and solitons. The first family of semi-rational solutions is derived by employing the KP-hierarchy reduction method. The fundamental (first-order) semi-rational

Gene transcription is a stochastic process with random switching between gene off and on states. In this paper, we established a cycle of gene inactivation consisting of two off states. External signals trigger the random transition from the “ground off” (I1) state to the “excited off” (I2) state, which in turn either jumps forward to the on state or recycles back to I1 state. By integrating inactivation

In this paper, we numerically investigate the space fractional nonlinear damped wave equation. We construct a novel high-accuracy dissipation-preserving finite difference scheme by using the new fourth-order fractional central difference operator. Thanks to the toeplitz-like differentiation matrix, we further raise the computation efficiency of the proposed scheme by fast Fourier transform. Moreover

The quasi-threshold phenomenon in Higgins model with mono-stability driven by Gaussian white noise is investigated. The initial excitation phase is identified as escaping event with a specific trajectory defined as the quasi-threshold. In the limit of weak noise, a group of differential equations governing the optimal exit path, quasi-potential and exponential prefactor are deduced via WKB approximation

In this paper, we consider the following nonlinear k-Hessian system {G(Sk1k(λ(D2z1)))Sk1k(λ(D2z1))=b(|x|)φ(z1,z2),x∈RN,G(Sk1k(λ(D2z2)))Sk1k(λ(D2z2))=h(|x|)ψ(z1,z2),x∈RN,where G is a nonlinear operator. This paper first proves the existence of the entire positive bounded radial solutions, and secondly gives the existence and non-existence conditions of the entire positive blow-up radial solutions. Finally

In this paper, we study a mixed variational problem subject to perturbations, where the noise term is modelled by means of a bilinear form that has to be understood to be “small” in some sense. Indeed, we consider a family of such problems and provide a result that guarantees existence and uniqueness of the solution. Moreover, a stability condition for the solutions yields a Generalized Collage Theorem

This paper studies a contemporary event of the sunken Argentinian submarine ARA San Juan S-42 in November 2017. The submarine’s wreckage was found one year later on the seabed off the southern Atlantic coast of Argentina, with its imploded debris scattered on the seabed at the depth of about 900 meters under sea level. We develop computational mechanics modeling and conduct supercomputer simulations

Enhancing and essentially generalizing previous results on a class of (1+1)-dimensional nonlinear wave and elliptic equations, we apply several new techniques to classify admissible point transformations within this class up to the equivalence generated by its equivalence group. This gives an exhaustive description of its equivalence groupoid. After extending the algebraic method of group classification

In this paper, periodic orbits in the nonlinear dynamical system with a fixed point vortex in a periodic flow are investigated. Under the influence of periodic perturbations in the phase space, an infinite number of nonlinear resonances with elliptic and hyperbolic periodic orbits arise. It is shown that these orbits exist even with completely destroyed resonant islands. In the perturbed system, all

This study addresses the nonlinear forced vibration of a deep curved microbeam with a noncontact actuator. The photostrictive actuator is subjected to an ultraviolet-switching excitation and the governing equations are derived based on the couple stress theory (CST). The von Kármán geometric nonlinearity is utilized to obtain the fundamental equations of thin curved beams in a curvilinear coordinate

We study the synchronization critical coupling in the Kuramoto model of globally coupled oscillators, analyzing natural frequencies distributed according to unimodal functions. Its is shown that asymmetric distributions can lead to a nonmonotonic critical transition when we modify some of their parameters. In particular, we explore the case in which the natural frequencies are given by the log-normal

We explore when the chaos game renders a quasi attractor of an iterated function system (IFS); we emphasize the role of the set in which the chaos game is initialized. For IFS with lower semicontinuous Hutchinson-Barnsley operator we find that these initial points necessarily belong to the largest invariant set of the weak basin of the attractor. Under additional assumptions, namely the attractor is

Capacitor voltage-balancing systems are usually applied to power electronic circuits. The main issue in these systems is equalising the voltage of a large number of capacitors connected to a voltage source in serial or parallel arrangements. A particular application of the capacitor voltage-balancing systems is found in modular multilevel converters (MMC). The voltage balancing of the floating capacitors

We highlight the existence of a topological horseshoe arising from an a–priori stable model of the binary asteroid dynamics. The inspection is numerical and uses correctly aligned windows, as described in a recent paper by A. Gierzkiewicz and P. Zgliczyński, combined with a recent analysis of an associated secular problem.

This work discloses an epidemiological mathematical model to predict an empirical treatment for dogs infected by Pseudomonas aeruginosa. This dangerous pathogen is one of the leading causes of multi-resistant infections and can be transmitted from dogs to humans. Numerical simulations and appropriated codes were developed using Matlab software to gather information concerning long-time dynamics of

Population persistence and extinction are the most important issues in ecosystems. In the past a few decades, various deterministic and stochastic mathematical models with Allee effect have been extensively studied. However, in both population and disease dynamics, the question of how structural transitions caused by internal or external environmental noise emerge has not been fully elucidated. In