Supercritical Neimark‐Sacker bifurcation of a discrete‐time Nicholson‐Bailey model

We study the local dynamics and supercritical Neimark‐Sacker bifurcation of a discrete‐time Nicholson‐Bailey host‐parasitoid model in the interior of . It is proved that if α>1, then the model has a unique positive equilibrium point , which is locally asymptotically focus, unstable focus and nonhyperbolic under certain parametric condition. Furthermore, it is proved that the model undergoes a supercritical Neimark‐Sacker bifurcation in a small neighborhood of the unique positive equilibrium point , and meanwhile, the stable closed curve appears. From the viewpoint of biology, the stable closed curve corresponds to the period or quasiperiodic oscillations between host and parasitoid populations. Some numerical simulations are presented to verify theoretical results.     

Global existence and asymptotic behavior of classical solutions for a 3D two‐species chemotaxis‐Stokes system with competitive kinetics

This paper considers the 2‐species chemotaxis‐Stokes system with competitive kinetics under homogeneous Neumann boundary conditions in a 3‐dimensional bounded domain with smooth boundary. Both chemotaxis‐fluid systems and 2‐species chemotaxis systems with competitive terms were studied by many mathematicians. However, there have not been rich results on coupled 2‐species–fluid systems. Recently, global existence and asymptotic stability in the above problem with (u·∇)u in the fluid equation were established in the 2‐dimensional case. The purpose of this paper is to give results for global existence, boundedness, and stabilization of solutions to the above system in the 3‐dimensional case when is sufficiently small.     

Global well‐posedness and blow‐up criterion for the periodic quasi‐geostrophic equations in Lei‐Lin‐Gevrey spaces

In this paper we consider a periodic 2‐dimensional quasi‐geostrophic equations with subcritical dissipation. We show the global existence and uniqueness of the solution for small initial data in the Lei‐Lin‐Gevrey spaces . Moreover, we establish an exponential type explosion in finite time of this solution.     

Lagrange‐type basis for multivariate uniform integrable tensor‐product Birkhoff interpolation

Birkhoff interpolation is the most general interpolation scheme. We study the Lagrange‐type basis for uniform integrable tensor‐product Birkhoff interpolation. We prove that the Lagrange‐type basis of multivariate uniform tensor‐product Birkhoff interpolation can be obtained by multiplying corresponding univariate Lagrange‐type basis when the integrable condition is satisfied. This leads to less computational complexity, which drops to from .     

Global stability for the fractional Navier‐Stokes equations in the Fourier‐Herz space

We consider global stability for the fractional incompressible Navier‐Stokes equations in a 3‐D critical Fourier‐Herz space. By introducing a weighted norm space and using Fourier localization technique, the stability of mild solutions with small initial perturbation is established. With the Friedrichs method, the stability of weak solutions is proved under arbitrary large initial perturbation.     

Algebro‐geometric constructions of the Wadati‐Konno‐Ichikawa flows and applications

With the aid of Lenard recursion equations, we derive the Wadati–Konno–Ichikawa hierarchy. Based on the Lax matrix, an algebraic curve of arithmetic genus n is introduced, from which Dubrovin‐type equations and meromorphic function φ are established. The explicit theta function representations of solutions for the entire WKI hierarchy are given according to asymptotic properties of φ and the algebro‐geometric characters of . Copyright © 2015 John Wiley & Sons, Ltd.     

Regular wavelets and Triebel‐Lizorkin type oscillation spaces

In this paper, we apply wavelets to study the Triebel‐Lizorkin type oscillation spaces and identify them with the well‐known Triebel‐Lizorkin‐Morrey spaces. Further, we prove that Calderón‐Zygmund operators are bounded on .     

Multiple sign‐changing solutions for Kirchhoff‐type equations in

In this paper, we study the following Kirchhoff‐type equations where a>0,b⩾0,4<p<2^∗=6, and . Under some suitable conditions, we prove that the equation has three solutions of mountain pass type: one positive, one negative, and sign‐changing. Furthermore, this problem has infinitely many sign‐changing solutions. Copyright © 2017 John Wiley & Sons, Ltd.     

A class of vector‐valued dilation‐and‐modulation frames on the half real line

Vector‐valued frames were first introduced under the name of superframes by Balan in the context of signal multiplexing and by Han and Larson from the mathematical aspect. Since then, the wavelet and Gabor frames in have interested many mathematicians. The space models vector‐valued causal signal spaces because of the time variable being nonnegative. But it admits no nontrivial shift‐invariant system and thus no wavelet or Gabor frame since is not a group by addition (not as ). Observing that is a group by multiplication, we, in this paper, introduce a class of multiplication‐based dilation‐and‐modulation ( ) systems, and investigate the theory of frames in . Since is not closed under the Fourier transform, the Fourier transform does not fit . We introduce the notion of Θ_a transform in , and using Θ_a‐transform matrix method, we characterize frames, Riesz bases, and dual frames in and obtain an explicit expression of duals for an arbitrary given frame. An example theorem is also presented.     

Local well‐posedness and zero‐α limit for the Euler‐α equations

In this paper, we prove the local‐in‐time existence and a blow‐up criterion of solutions in the Besov spaces for the Euler‐α equations of inviscid incompressible fluid flows in . We also establish the convergence rate of the solutions of the Euler‐α equations to the corresponding solutions of the Euler equations as the regularization parameter α approaches 0 in . Copyright © 2016 John Wiley & Sons, Ltd.     

Solutions in Bessel‐potential spaces for wave equations with nonlinear damping

We consider a semilinear wave equation with nonlinear damping in the whole space . Local‐in‐time existence and uniqueness results are obtained in the class of Bessel‐potential spaces . Copyright © 2017 John Wiley & Sons, Ltd.     

Inframonogenic functions and their applications in 3‐dimensional elasticity theory

Solutions of the sandwich equation , where stands for the first‐order differential operator (called Dirac operator) in the Euclidean space , are known as inframonogenic functions. These functions generalize in a natural way the theory of kernels associated with , the nowadays well‐known monogenic functions, and can be viewed also as a refinement of the biharmonic ones. In this paper we deepen study the connections between inframonogenic functions and the solutions of the homogeneous Lamé‐Navier system in . Our findings allow to shed some new light on the structure of the solutions of this fundamental system in 3‐dimensional elasticity theory.     

Finite‐dimensional global attractor for a semi‐discrete fractional nonlinear Schrödinger equation

We consider a semi‐discrete in time Crank–Nicolson scheme to discretize a weakly damped forced nonlinear fractional Schrödinger equation u _t ?i (?Δ)^α u +i |u |²u +γ u =f for considered in the the whole space . We prove that such semi‐discrete equation provides a discrete infinite‐dimensional dynamical system in that possesses a global attractor in . We show also that if the external force is in a suitable weighted Lebesgue space, then this global attractor has a finite fractal dimension. Copyright © 2017 John Wiley & Sons, Ltd.     

Self‐organized criticality of cellular automata model; absorbtion in finite‐time of supercritical region into the critical one

In this work, it is studied the evolution and time behavior of solutions to nonlinear diffusion equation in where , d ≥ 1, and H is the Heaviside function. For d = 1,2,3, this equation describes the dynamics of self‐organizing sandpile process with critical state ρ_c. The main conclusion is that the supercritical region is absorbed in a finite‐time in the critical region . Copyright © 2013 John Wiley & Sons, Ltd.     

Max‐type system of difference equations with positive two‐periodic sequences

This paper deals with the form and the periodicity of the solutions of the max‐type system of difference equations where , and are positive two‐periodic sequences and initial values x₀, x _{? 1}, y₀, y _{? 1} ∈ (0, + ∞ ). Copyright © 2014 John Wiley & Sons, Ltd.     

Involutions in split semi‐quaternions

A map is an involution (resp, anti‐involution) if it is a self‐inverse homomorphism (resp, antihomomorphism) of a field algebra. The main purpose of this paper is to show how split semi‐quaternions can be used to express half‐turn planar rotations in 3‐dimensional Euclidean space and how they can be used to express hyperbolic‐isoclinic rotations in 4‐dimensional semi‐Euclidean space . We present an involution and an anti‐involution map using split semi‐quaternions and give their geometric interpretations as half‐turn planar rotations in . Also, we give the geometric interpretation of nonpure unit split semi‐quaternions, which are in the form p = coshθ + sinhθ i + 0 j + 0 k = coshθ + sinhθ i , as hyperbolic‐isoclinic rotations in .     

Global stability of a discrete virus dynamics model with Holling type‐II infection function

In this paper, we propose a discrete virus dynamics model with Holling type‐II infection function. By constructing Lyapunov function, we prove that if , then the infection‐free equilibrium is globally asymptotically stable; whereas if , then sufficient conditions are established for global stability of the infection equilibrium. Our results generalize some known results studied by other researchers. Copyright © 2015 John Wiley & Sons, Ltd.     

Liouville‐type theorem for the steady compressible Hall‐MHD system

In this paper, we prove a Liouville‐type theorem for the steady compressible Hall‐magnetohydrodynamics system in Π, where Π is whole space or half space . We show that a smooth solution (ρ, u , B ,P) satisfying 1/C₀<ρ<C₀, , and B ∈L^9/2(Π) for some constant C₀>0 is indeed trivial. This generalizes and improves 2 results of Chae.     

Bilinear estimate on tent‐type spaces with application to the well‐posedness of fluid equations

We introduce a class of tent‐type spaces and establish a Poisson extension result of Triebel–Lizorkin spaces . As an application, we get the well‐posedness of Navier–Stokes equations and magnetohydrodynamic equations with initial data in critical Triebel–Lizorkin spaces , . Copyright © 2016 John Wiley & Sons, Ltd.     

Global stability of a multi‐group model with distributed delay and vaccination

A delayed multi‐group SVEIR epidemic model with vaccination and a general incidence function has been formulated and studied in this paper. Mathematical analysis shows that the basic reproduction number plays a key role in the dynamics of the model: the disease‐free equilibrium is globally asymptotically stable when , while the endemic equilibrium exists uniquely and is globally asymptotically stable when . For the proofs, we exploit a graph‐theoretical approach to the method of Lyapunov functionals. Our results show that distributed delay has no impact on the global stability of equilibria, and the results improve and generalize some known results. Copyright © 2016 John Wiley & Sons, Ltd.