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Large time behavior of solutions to a quasilinear attraction–repulsion chemotaxis system with logistic source
Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Xiao He, Miaoqing Tian, Sining ZhengAbstractThis paper studies the quasilinear attraction–repulsion chemotaxis system with a logistic source ut=∇⋅(D(u)∇u)−∇⋅(Φ(u)∇v)+∇⋅(Ψ(u)∇w)+f(u), τ1vt=Δv+αu−βv, τ2wt=Δw+γu−δw, under homogeneous Neumann boundary conditions in a bounded domain Ω⊂RN (N≥1), where τ1,τ2∈{0,1}, D,Φ,Ψ∈C2([0,+∞)) nonnegative with D(s)≥(s+1)p for s≥0, Φ(s)≤χsq, ξsr≤Ψ(s)≤ζsr for s≥s0>0, f(s)≤μs(1−sk) for s>0, f(0)≥0. In a previous paper o...
Source: Nonlinear Analysis: Real World Applications - January 21, 2020 Category: Research Source Type: research

The anisotropic regularity criteria for 3D Navier–Stokes equations involving one velocity component
Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Chenyin QianAbstractThe anisotropic regularity criterion for the Navier–Stokes equations in terms of the one component of the velocity gradient (∂iuj,1≤i,j≤3) is investigated. It is an improvement of results of Qian (2016) and is also a complement of the results of Guo et al. (2018) for i=j. Besides, the consistent regularity criterion without distinguishing i=j and i≠j is also obtained. Finally, the regularity result based on the fractional derivatives for one component of the velocity field Dhαu3 with α∈[0...
Source: Nonlinear Analysis: Real World Applications - January 21, 2020 Category: Research Source Type: research

Complicated oscillations and non-resonant double Hopf bifurcation of multiple feedback delayed control system of the gut microbiota
Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Lijun Pei, Yameng Chen, Shuo WangAbstractIn this paper, we consider the complex dynamics of a novel mathematical model for a feedback control system of the gut microbiota, which was proposed by Dong, et al. The main work of the present paper is to study the effect of antibiotics injection on the gut microbiota through some dynamical methods, such as double Hopf bifurcation analysis and so on. We first use DDE-BIFTOOL to find the non-resonant double Hopf bifurcation points of the system, and draw the bifurcation diagram wit...
Source: Nonlinear Analysis: Real World Applications - January 21, 2020 Category: Research Source Type: research

Editorial Board
Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): (Source: Nonlinear Analysis: Real World Applications)
Source: Nonlinear Analysis: Real World Applications - January 15, 2020 Category: Research Source Type: research

Miridae control using sex-pheromone traps. Modeling, analysis and simulations
Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): M. Djoukwe Tapi, L. Bagny-Beilhe, Y. DumontAbstractCocoa mirid, Sahlbergella singularis, is known to be one of the major pests of cocoa in West Africa. In this paper, we consider a biological control method, based on mating disrupting, using artificial sex pheromones, and trapping, to limit the impact of mirids in plots. We develop and study a piece-wise smooth delayed dynamical system. Based on previous results, a theoretical analysis is provided in order to derive all possible dynamics of the system. We show that two mai...
Source: Nonlinear Analysis: Real World Applications - January 8, 2020 Category: Research Source Type: research

Global existence and asymptotic stability in a predator–prey chemotaxis model
Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Shengmao Fu, Liangying MiaoAbstractIn this paper, we consider the global behavior of the fully parabolic predator–prey chemotaxis model u1t=d1Δu1+χ∇⋅(u1∇v)+μ1u1(1−u1−e1u2),x∈Ω,t>0,u2t=d2Δu2−ξ∇⋅(u2∇v)+μ2u2(1+e2u1−u2),x∈Ω,t>0,vt=d3Δv+αu1+βu2−γv,x∈Ω,t>0,∂u1∂ν=∂u2∂ν=∂v∂ν=0,x∈∂Ω,t>0,u1(x,0)=u1,0(x),u2(x,0)=u2,0(x),v(x,0)=v0(x),x∈Ωin a smooth bounded domain Ω⊂Rn, where d1,d2,d3,χ,ξ,μ1,μ2,e1,e2,β,γ are positive constants, α∈R. It is proved that if n≤2...
Source: Nonlinear Analysis: Real World Applications - January 7, 2020 Category: Research Source Type: research

Trajectory statistical solutions for the 3D Navier–Stokes equations: The trajectory attractor approach
Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Caidi Zhao, Yanjiao Li, Zhongchun SongAbstractIn this article, we construct the trajectory statistical solution for the 3D incompressible Navier–Stokes equations via the natural translation semigroup and trajectory attractor. In our construction, the trajectory statistical solution is an invariant space–time probability measure which is carried by the trajectory attractor of the natural translation semigroup defined on the trajectory space, and the trajectory statistical solution possesses the invariant property under th...
Source: Nonlinear Analysis: Real World Applications - December 27, 2019 Category: Research Source Type: research

A global mathematical model of malaria transmission dynamics with structured mosquito population and temperature variations
Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Bakary Traoré, Ousmane Koutou, Boureima SangaréAbstractIn this paper, a mathematical model of malaria transmission which takes into account the four distinct mosquito metamorphic stages is presented. The model is formulated thanks to the coupling of two sub-models, namely the model of mosquito population and the model of malaria parasite transmission due to the interaction between mosquitoes and humans. Moreover, considering that climate factors have a great impact on the mosquito life cycle and parasite survival in mosqui...
Source: Nonlinear Analysis: Real World Applications - December 27, 2019 Category: Research Source Type: research

Existence of a time periodic solution for the compressible Euler equation with a time periodic outer force
Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Naoki TsugeAbstractWe are concerned with a time periodic supersonic flow through a bounded interval. This motion is described by the compressible Euler equation with a time periodic outer force. Our goal in this paper is to prove the existence of a time periodic solution. Although this is a fundamental problem for other equations, it has not been received much attention for the system of conservation laws until now.When we prove the existence of the time periodic solution, we face with two problems. One is to prove that init...
Source: Nonlinear Analysis: Real World Applications - December 25, 2019 Category: Research Source Type: research

Global dynamics of nonautonomous Hindmarsh–Rose equations
Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Chi Phan, Yuncheng YouAbstractGlobal dynamics of nonautonomous diffusive Hindmarsh–Rose equations on a three-dimensional bounded domain in neurodynamics is investigated. The existence of a pullback attractor is proved through uniform estimates showing the pullback dissipative property and the pullback asymptotical compactness. Then the existence of pullback exponential attractor is also established by proving the smoothing Lipschitz continuity in a long run of the solution process. (Source: Nonlinear Analysis: Real World Applications)
Source: Nonlinear Analysis: Real World Applications - December 25, 2019 Category: Research Source Type: research

Spatial-temporal risk index and transmission of a nonlocal dengue model
Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Min Zhu, Zhigui Lin, Lai ZhangAbstractThe nonlocal incidence and free boundaries are introduced into a classic SIR-SI model describing the transmission dynamics of dengue fever, where the nonlocal incidence allows for interactions of susceptible population at a given location with infected mosquitoes in the whole area, and free boundaries represent the expanding front of the area contaminated by dengue virus. We derive a spatial–temporal risk index in terms of the basic reproduction number, which depends on the nonlocal in...
Source: Nonlinear Analysis: Real World Applications - December 24, 2019 Category: Research Source Type: research

The dynamics of a zooplankton–fish system in aquatic habitats
Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Yu Jin, Feng-Bin WangAbstractDiel vertical migration is a common movement pattern of zooplankton in marine and freshwater habitats. In this paper, we use a temporally periodic reaction–diffusion–advection system to describe the dynamics of zooplankton and fish in aquatic habitats. Zooplankton live in both the surface water and the deep water, while fish only live in the surface water. Zooplankton undertake diel vertical migration to avoid predation by fish during the day and to consume sufficient food in the surface wate...
Source: Nonlinear Analysis: Real World Applications - December 21, 2019 Category: Research Source Type: research

Erratum to “On the Cauchy problem for a model equation for shallow water waves of moderate amplitude” [Nonlinear Anal. RWA 14 (5) (2013) 2022–2026]
Publication date: Available online 12 December 2019Source: Nonlinear Analysis: Real World ApplicationsAuthor(s): N. Duruk MutlubaşAbstractThe local well-posedness for a nonlinear equation modeling the evolution of the free surface for waves of moderate amplitude in the shallow water regime was proved in Duruk Mutlubaş (2013). In this paper, we correct the mistake made in the proof of the main result and give the appropriate assumptions and corresponding results. (Source: Nonlinear Analysis: Real World Applications)
Source: Nonlinear Analysis: Real World Applications - December 14, 2019 Category: Research Source Type: research

Continuity of periodic solutions of the Landesman–Lazer equation in external forces
Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Yaru Dou, Gang MengAbstractIn this paper we study the continuity of periodic solutions of the Landesman–Lazer equations in coefficient functions. It will be proved that these periodic solutions are not only continuous in coefficient functions with respect to the usual Lp topologies, but also with respect to the weak topologies of the Lp spaces. The continuity results of this paper are the basis to study some quantities defined from solutions in a quantitative way. (Source: Nonlinear Analysis: Real World Applications)
Source: Nonlinear Analysis: Real World Applications - December 11, 2019 Category: Research Source Type: research

Large time behavior for the support of momentum density of the Holm–Staley b-family equation with weakly dissipative term
Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Lu Cao, Zaihong Jiang, Mingxuan ZhuAbstractIn this paper, we study the Holm–Staley b-family equation with weakly dissipative term. Firstly, we show the infinite propagation speed that if the initial datum u0(x) has a compact support, the corresponding solution u(x,t) does not have a compact x-support any longer in its lifespan. Then, we obtain the large time behavior of the support of momentum density with the initial data compact supported. (Source: Nonlinear Analysis: Real World Applications)
Source: Nonlinear Analysis: Real World Applications - December 8, 2019 Category: Research Source Type: research