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On the asymptotic behavior of solutions to time-fractional elliptic equations driven by a multiplicative white noise Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-11-09 Hoang The Tuan
This paper is devoted to study of time-fractional elliptic equations driven by a multiplicative noise. By combining the eigenfunction expansion method for symmetry elliptic operators, the variation of constant formula for strong solutions to scalar stochastic fractional differential equations, Ito's formula and establishing a new weighted norm associated with a Lyapunov–Perron operator defined from
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An adaptive finite element DtN method for the three-dimensional acoustic scattering problem Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-11-18 Gang Bao; Mingming Zhang; Bin Hu; Peijun Li
This paper is concerned with a numerical solution of the acoustic scattering by a bounded impenetrable obstacle in three dimensions. The obstacle scattering problem is formulated as a boundary value problem in a bounded domain by using a Dirichlet-to-Neumann (DtN) operator. An a posteriori error estimate is derived for the finite element method with the truncated DtN operator. The a posteriori error
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A \begin{document}$ C^1 $\end{document} Petrov-Galerkin method and Gauss collocation method for 1D general elliptic problems and superconvergence Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-11-04 Waixiang Cao; Lueling Jia; Zhimin Zhang
In this paper, we present and study $ C^1 $ Petrov-Galerkin and Gauss collocation methods with arbitrary polynomial degree $ k $ ($ \ge 3 $) for one-dimen\-sional elliptic equations. We prove that, the solution and its derivative approximations converge with rate $ 2k-2 $ at all grid points; and the solution approximation is superconvergent at all interior roots of a special Jacobi polynomial of degree
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A spatial food chain model for the Black Sea Anchovy, and its optimal fishery Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-12-07 Mahir Demir; Suzanne Lenhart
We present a spatial food chain model on a bounded domain coupled with optimal control theory to examine harvesting strategies. Motivated by the fishery industry in the Black Sea, the anchovy stock and two more trophic levels are modeled using nonlinear parabolic partial differential equations with logistic growth, movement by diffusion and advection, and Neumann boundary conditions. Necessary conditions
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The motion of weakly interacting localized patterns for reaction-diffusion systems with nonlocal effect Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-11-04 Shin-Ichiro Ei; Hiroshi Ishii
In this paper, we analyze the interaction of localized patterns such as traveling wave solutions for reaction-diffusion systems with nonlocal effect in one space dimension. We consider the case that a nonlocal effect is given by the convolution with a suitable integral kernel. At first, we deduce the equation describing the movement of interacting localized patterns in a mathematically rigorous way
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Predator – Prey/Host – Parasite: A fragile ecoepidemic system under homogeneous infection incidence Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-11-04 Alex P. Farrell; Horst R. Thieme
To underpin the concern that environmental change can flip an ecosystem from stable persistence to sudden total collapse, we consider a class of so-called ecoepidemic models, predator – prey/host – parasite systems, in which a base species is prey to a predator species and host to a micro-parasite species. Our model uses generalized frequency-dependent incidence for the disease transmission and mass
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Computing complete Lyapunov functions for discrete-time dynamical systems Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-11-04 Peter Giesl; Zachary Langhorne; Carlos Argáez; Sigurdur Hafstein
A complete Lyapunov function characterizes the behaviour of a general discrete-time dynamical system. In particular, it divides the state space into the chain-recurrent set where the complete Lyapunov function is constant along trajectories and the part where the flow is gradient-like and the complete Lyapunov function is strictly decreasing along solutions. Moreover, the level sets of a complete Lyapunov
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The dynamics of a two host-two virus system in a chemostat environment Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-10-12 Sze-Bi Hsu; Yu Jin
The coevolution or coexistence of multiple viruses with multiple hosts has been an important issue in viral ecology. This paper is to study the mathematical properties of the solutions of a chemostat model for two host species and two virus species. By virtue of the global dynamics of its submodels and the theories of uniform persistence and Hopf bifurcation, we derive sufficient conditions for the
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Topological phase transition III: Solar surface eruptions and sunspots Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-11-18 Tian Ma; Shouhong Wang
This paper is aimed to provide a new theory for the formation of the solar surface eruptions and sunspots. The key ingredient of the study is the new anti-diffusive effect of heat, based on the recently developed statistical theory of heat by the authors [4]. The anti-diffusive effect of heat states that due to the higher rate of photon absorption and emission of the particles with higher energy levels
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The \begin{document}$ P^* $\end{document} rule in the stochastic Holt-Lawton model of apparent competition Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-12-15 Sebastian J. Schreiber
In 1993, Holt and Lawton introduced a stochastic model of two host species parasitized by a common parasitoid species. We introduce and analyze a generalization of these stochastic difference equations with any number of host species, stochastically varying parasitism rates, stochastically varying host intrinsic fitnesses, and stochastic immigration of parasitoids. Despite the lack of direct, host
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How to detect Wada basins Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-11-04 Alexandre Wagemakers; Alvar Daza; Miguel A. F. Sanjuán
We present a review of the different techniques available to study a special kind of fractal basins of attraction known as Wada basins, which have the intriguing property of having a single boundary separating three or more basins. We expose several approaches to identify this topological property that rely on different, but not exclusive, definitions of the Wada property.
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Ecological and evolutionary dynamics in advective environments: Critical domain size and boundary conditions Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-09-21 Wenrui Hao; King-Yeung Lam; Yuan Lou
We consider the ecological and evolutionary dynamics of a reaction-diffusion-advection model for populations residing in a one-dimensional advective homogeneous environment, with emphasis on the effects of boundary conditions and domain size. We assume that there is a net loss of individuals at the downstream end with rate $ b \geq 0 $, while the no-flux condition is imposed on the upstream end. For
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Modeling multiple taxis: Tumor invasion with phenotypic heterogeneity, haptotaxis, and unilateral interspecies repellence Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-09-21 Niklas Kolbe; Nikolaos Sfakianakis; Christian Stinner; Christina Surulescu; Jonas Lenz
We provide a short review of existing models with multiple taxis performed by (at least) one species and consider a new mathematical model for tumor invasion featuring two mutually exclusive cell phenotypes (migrating and proliferating). The migrating cells perform nonlinear diffusion and two types of taxis in response to non-diffusing cues: away from proliferating cells and up the gradient of surrounding
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Nonlinear dynamics in tumor-immune system interaction models with delays Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-09-21 Shigui Ruan
In this paper, we review some recent results on the nonlinear dynamics of delayed differential equation models describing the interaction between tumor cells and effector cells of the immune system, in which the delays represent times necessary for molecule production, proliferation, differentiation of cells, transport, etc. First we consider a tumor-immune system interaction model with a single delay
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Dynamics of a discrete-time stoichiometric optimal foraging model Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-08-31 Ming Chen; Hao Wang
In this paper, we discretize and analyze a stoichiometric optimal foraging model where the grazer's feeding effort depends on the producer's nutrient quality. We systematically make comparisons of the dynamical behaviors between the discrete-time model and the continuous-time model to study the robustness of model predictions to time discretization. When the maximum growth rate of producer is low,
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Chaotic dynamics in a simple predator-prey model with discrete delay Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-08-31 Guihong Fan; Gail S. K. Wolkowicz
A discrete delay is included to model the time between the capture of the prey and its conversion to viable biomass in the simplest classical Gause type predator-prey model that has equilibrium dynamics without delay. As the delay increases from zero, the coexistence equilibrium undergoes a supercritical Hopf bifurcation, two saddle-node bifurcations of limit cycles, and a cascade of period doublings
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Rich dynamics of a simple delay host-pathogen model of cell-to-cell infection for plant virus Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-08-31 Tin Phan; Bruce Pell; Amy E. Kendig; Elizabeth T. Borer; Yang Kuang
Viral dynamics within plant hosts can be important for understanding plant disease prevalence and impacts. However, few mathematical modeling efforts aim to characterize within-plant viral dynamics. In this paper, we derive a simple system of delay differential equations that describes the spread of infection throughout the plant by barley and cereal yellow dwarf viruses via the cell-to-cell mechanism
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Equilibrium validation in models for pattern formation based on Sobolev embeddings Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-08-31 Evelyn Sander; Thomas Wanner
In the study of equilibrium solutions for partial differential equations there are so many equilibria that one cannot hope to find them all. Therefore one usually concentrates on finding individual branches of equilibrium solutions. On the one hand, a rigorous theoretical understanding of these branches is ideal but not generally tractable. On the other hand, numerical bifurcation searches are useful
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Efficient and accurate sav schemes for the generalized Zakharov systems Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-08-31 Jie Shen; Nan Zheng
We develop in this paper efficient and accurate numerical schemes based on the scalar auxiliary variable (SAV) approach for the generalized Zakharov system and generalized vector Zakharov system. These schemes are second-order in time, linear, unconditionally stable, only require solving linear systems with constant coefficients at each time step, and preserve exactly a modified Hamiltonian. Ample
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Existence and asymptotic results for an intrinsic model of small-strain incompatible elasticity Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-07-27 Samuel Amstutz; Nicolas Van Goethem
A general model of incompatible small-strain elasticity is presented and analyzed, based on the linearized strain and its associated incompatibility tensor field. Strain incompatibility accounts for the presence of dislocations, whose motion is ultimately responsible for the plastic behaviour of solids. The specific functional setting is built up, on which existence results are proved. Our solution
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Higher-order time-stepping schemes for fluid-structure interaction problems Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-07-24 Daniele Boffi; Lucia Gastaldi; Sebastian Wolf
We consider a recently introduced formulation for fluid-structure interaction problems which makes use of a distributed Lagrange multiplier in the spirit of the fictitious domain method. In this paper we focus on time integration methods of second order based on backward differentiation formulae and on the Crank–Nicolson method. We show the stability properties of the resulting method; numerical tests
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Quantitative jacobian determinant bounds for the conductivity equation in high contrast composite media Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-07-24 Yves Capdeboscq; Haun Chen Yang Ong
We consider the conductivity equation in a bounded domain in $ \mathbb{R}^{d} $ with $ d\geq3 $. In this study, the medium corresponds to a very contrasted two phase homogeneous and isotropic material, consisting of a unit matrix phase, and an inclusion with high conductivity. The geometry of the inclusion phase is so that the resulting Jacobian determinant of the gradients of solutions $ DU $ takes
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Uniform stabilization of Boussinesq systems in critical \begin{document}$ \mathbf{L}^q $\end{document}-based Sobolev and Besov spaces by finite dimensional interior localized feedback controls Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-06-15 Irena Lasiecka; Buddhika Priyasad; Roberto Triggiani
We consider the d-dimensional Boussinesq system defined on a sufficiently smooth bounded domain, with homogeneous boundary conditions, and subject to external sources, assumed to cause instability. The initial conditions for both fluid and heat equations are taken of low regularity. We then seek to uniformly stabilize such Boussinesq system in the vicinity of an unstable equilibrium pair, in the critical
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Bifurcations in periodic integrodifference equations in \begin{document}$ C(\Omega) $\end{document} I: Analytical results and applications Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-07-24 Christian Aarset; Christian Pötzsche
We study local bifurcations of periodic solutions to time-periodic (systems of) integrodifference equations over compact habitats. Such infinite-dimensional discrete dynamical systems arise in theoretical ecology as models to describe the spatial dispersal of species having nonoverlapping generations. Our explicit criteria allow us to identify branchings of fold- and crossing curve-type, which include
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Bilinear equations in Hilbert space driven by paths of low regularity Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-07-24 Petr Čoupek; María J. Garrido-Atienza
In the article, some bilinear evolution equations in Hilbert space driven by paths of low regularity are considered and solved explicitly. The driving paths are scalar-valued and continuous, and they are assumed to have a finite $ p $-th variation along a sequence of partitions in the sense given by Cont and Perkowski [Trans. Amer. Math. Soc. Ser. B, 6 (2019) 161–186] ($ p $ being an even positive
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On the role of pharmacometrics in mathematical models for cancer treatments Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-07-03 Urszula Ledzewicz; Heinz Schättler
We review and discuss various aspects that the modeling of pharmacometric properties has on the structure of optimal solutions in mathematical models for cancer treatment. These include (i) the changes in the interpretation of the solutions as pharmacokinetic (PK) models are added, respectively deleted from the modeling and (ii) qualitative changes in the structures of optimal controls that occur as
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Ground state homoclinic orbits for a class of asymptotically periodic second-order Hamiltonian systems Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-06-15 Ying Lv; Yan-Fang Xue; Chun-Lei Tang
In this paper, we consider a class of second-order Hamiltonian systems of the form $ \ddot{u}(t)-L(t) u(t)+\nabla W(t,u(t)) = 0 $
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Dynamic aspects of Sprott BC chaotic system Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-06-15 Marcos C. Mota; Regilene D. S. Oliveira
In this paper we study global dynamic aspects of the quadratic system $ \dot x = yz,\quad \dot y = x-y,\quad \dot z = 1-x(\alpha y+\beta x), $
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A nonuniform anisotropic FEM for elliptic boundary layer optimal control problems Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-06-15 Hongbo Guan; Yong Yang; Huiqing Zhu
In this paper, an anisotropic bilinear finite element method is constructed for the elliptic boundary layer optimal control problems. Supercloseness properties of the numerical state and numerical adjoint state in a $ \epsilon $-norm are established on anisotropic meshes. Moreover, an interpolation type post-processed solution is shown to be superconvergent of order $ O(N^{-2}) $, where the total number
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Existence results for fractional differential equations in presence of upper and lower solutions Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-06-15 Rim Bourguiba; Rosana Rodríguez-López
In this paper, we study some existence results for fractional differential equations subject to some kind of initial conditions. First, we focus on the linear problem and we give an explicit form of solutions by reduction to an integral problem. We analyze some properties of the solutions to the linear problem in terms of its coefficients. Then we provide examples of application of the mentioned properties
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Random attractors for 2D stochastic micropolar fluid flows on unbounded domains Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-06-15 Wenlong Sun; Jiaqi Cheng; Xiaoying Han
The asymptotic behavior of a model for 2D incompressible stochastic micropolar fluid flows with rough noise on a Poincaré domain is investigated. First, the existence and uniqueness of solutions to an evolution equation arising from the underlying stochastic micropolar fluid model is established via the Galerkin method and energy method. Then the existence of a random attractor is studied by using
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Finite element approximation of nonlocal dynamic fracture models Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-06-12 P. K. Jha; R. Lipton
In this work we estimate the convergence rate for time stepping schemes applied to nonlocal dynamic fracture modeling. Here we use the nonlocal formulation given by the bond based peridynamic equation of motion. We begin by establishing the existence of $ H^2 $ peridynamic solutions over any finite time interval. For this model the gradients can become large and steep slopes appear and localize when
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The Poincaré bifurcation of a SD oscillator Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-05-18 Yangjian Sun; Changjian Liu
A van der Pol damped SD oscillator, which was proposed by Ruilan Tian, Qingjie Cao and Shaopu Yang (2010, Nonlinear Dynamics, 59, 19-27), is studied. By improving the criterion function of determining the lowest upper bound of the number of zeros of Abelian Integrals, we show that the number of zeros of Abelian integrals of this SD oscillator is two which is sharp.
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Global well-posedness of non-isothermal inhomogeneous nematic liquid crystal flows Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-05-15 Dongfen Bian; Yao Xiao
In this paper, we consider the initial-boundary value problem to the non-isothermal incompressible liquid crystal system with both variable density and temperature. Global well-posedness of strong solutions is established for initial data being small perturbation around the equilibrium state. As the tools in the proof, we establish the maximal regularities of the linear Stokes equations and parabolic
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Pattern formation in diffusive predator-prey systems with predator-taxis and prey-taxis Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-05-15 Jinfeng Wang; Sainan Wu; Junping Shi
A reaction-diffusion predator-prey system with prey-taxis and predator-taxis describes the spatial interaction and random movement of predator and prey species, as well as the spatial movement of predators pursuing prey and prey evading predators. The spatial pattern formation induced by the prey-taxis and predator-taxis is characterized by the Turing type linear instability of homogeneous state and
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Global existence and exponential decay of strong solutions to the cauchy problem of 3D density-dependent Navier-Stokes equations with vacuum Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-05-15 Yang Liu
This paper deals with the 3D incompressible Navier-Stokes equations with density-dependent viscosity in the whole space. The global well-posedness and exponential decay of strong solutions is established in the vacuum cases, provided the assumption that the bound of density is suitably small, which extends the results of [Nonlinear Anal. Real World Appl., 46:58-81, 2019] to the global one. However
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Convergence to the complex balanced equilibrium for some chemical reaction-diffusion systems with boundary equilibria Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-05-15 Gheorghe Craciun; Jiaxin Jin; Casian Pantea; Adrian Tudorascu
In this paper we study the rate of convergence to the complex balanced equilibrium for some chemical reaction-diffusion systems with boundary equilibria. We first analyze a three-species system with boundary equilibria in some stoichiometric classes, and whose right hand side is bounded above by a quadratic nonlinearity in the positive orthant. We prove similar results on the convergence to the positive
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Bistability of sequestration networks Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-05-15 Xiaoxian Tang; Jie Wang
We solve a conjecture on multiple nondegenerate steady states, and prove bistability for sequestration networks. More specifically, we prove that for any odd number of species, and for any production factor, the fully open extension of a sequestration network admits three nondegenerate positive steady states, two of which are locally asymptotically stable. In addition, we provide a non-empty open set
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Dynamics of the QR-flow for upper Hessenberg real matrices Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-05-15 Joan Carles Tatjer; Arturo Vieiro
We investigate the main phase space properties of the QR-flow when restricted to upper Hessenberg matrices. A complete description of the linear behavior of the equilibrium matrices is given. The main result classifies the possible $ \alpha $- and $ \omega $-limits of the orbits for this system. Furthermore, we characterize the set of initial matrices for which there is convergence towards an equilibrium
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On Milstein-type scheme for SDE driven by Lévy noise with super-linear coefficients Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-05-15 Chaman Kumar
A new explicit Milstein-type scheme for SDE driven by Lévy noise is proposed where both drift and diffusion coefficients are allowed to grow super-linearly. The strong rate of convergence (in $ \mathcal{L}^2 $-sense) is shown to be arbitrarily close to one which is consistent with the corresponding result on the classical Milstein scheme obtained for coefficients satisfying global Lipschitz conditions
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Approximation methods for the distributed order calculus using the convolution quadrature Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-05-15 Baoli Yin; Yang Liu; Hong Li; Zhimin Zhang
In this article we generalize the convolution quadrature (CQ) method, which aims at approximating the fractional calculus, to the case for the distributed order calculus. Our method is a natural expansion that the approximation formulas, convergence results and correction technique reduce to the cases for the CQ method if the weight function $ \mu(\alpha) $ is defined by $ \delta(\alpha-\alpha_0) $
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Diffusive limit to a selection-mutation equation with small mutation formulated on the space of measures Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-05-15 Azmy S. Ackleh; Nicolas Saintier
In this paper we consider a selection-mutation model with an advection term formulated on the space of finite signed measures on $ \mathbb{R}^d $. The selection-mutation kernel is described by a family of measures which allows the study of continuous and discrete kernels under the same setting. We rescale the selection-mutation kernel to obtain a diffusively rescaled selection-mutation model. We prove
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On discrete-time semi-Markov processes Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-05-15 Angelica Pachon; Federico Polito; Costantino Ricciuti
In the last years, several authors studied a class of continuous-time semi-Markov processes obtained by time-changing Markov processes by hitting times of independent subordinators. Such processes are governed by integro-differential convolution equations of generalized fractional type. The aim of this paper is to develop a discrete-time counterpart of such a theory and to show relationships and differences
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Cauchy problem for stochastic non-autonomous evolution equations governed by noncompact evolution families Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-05-15 Pengyu Chen; Yongxiang Li; Xuping Zhang
This paper investigates the Cauchy problem to a class of stochastic non-autonomous evolution equations of parabolic type governed by noncompact evolution families in Hilbert spaces. Combining the theory of evolution families, the fixed point theorem with respect to convex-power condensing operator and a new estimation technique of the measure of noncompactness, we established some new existence results
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Attractors for FitzHugh-Nagumo lattice systems with almost periodic nonlinear parts Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-05-15 Amira M. Boughoufala; Ahmed Y. Abdallah
For FitzHugh-Nagumo lattice dynamical systems (LDSs) many authors studied the existence of global attractors for deterministic systems [4,34,41,43] and the existence of global random attractors for stochastic systems [23,24,27,48,49], where for non-autonomous cases, the nonlinear parts are considered of the form $ f\left( u\right) $. Here we study the existence of the uniform global attractor for a
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On a terminal value problem for a system of parabolic equations with nonlinear-nonlocal diffusion terms Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-05-15 Vo Van Au; Mokhtar Kirane; Nguyen Huy Tuan
We study a terminal value parabolic system with nonlinear-nonlocal diffusions. Firstly, we consider the issue of existence and ill-posed property of a solution. Then we introduce two regularization methods to solve the system in which the diffusion coefficients are globally Lipschitz or locally Lipschitz under some a priori assumptions on the sought solutions. The existence, uniqueness and regularity
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Ergodicity of stochastic damped Ostrovsky equation driven by white noise Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-05-15 Shang Wu; Pengfei Xu; Jianhua Huang; Wei Yan
The current paper is devoted to the stochastic damped Ostrovsky equation driven by white noise. By establishing the uniform estimates for the solution in $ H^1 $ norm, we prove the global well-posedness and the existence of invariant measure for stochastic damped Ostrovsky equation with random initial value. Moreover, we obtain the ergodicity of stochastic damped Ostrovsky equation with deterministic
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Coexistence of competing consumers on a single resource in a hybrid model Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-04-26 Yunfeng Geng; Xiaoying Wang; Frithjof Lutscher
The question of whether and how two competing consumers can coexist on a single limiting resource has a long tradition in ecological theory. We build on a recent seasonal (hybrid) model for one consumer and one resource, and we extend it by introducing a second consumer. Consumers reproduce only once per year, the resource reproduces throughout the"summer" season. When we use linear consumer reproduction
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The Navier-Stokes-Cahn-Hilliard equations for mildly compressible binary fluid mixtures Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-04-26 Andrea Giorgini; Roger Temam; Xuan-Truong Vu
We study the well-posedness for the mildly compressible Navier-Stokes-Cahn-Hilliard system with non-constant viscosity and Landau potential in two and three dimensional domains.
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Global optimization-based dimer method for finding saddle points Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-04-26 Bing Yu; Lei Zhang
Searching saddle points on the potential energy surface is a challenging problem in the rare event. When there exist multiple saddle points, sampling different initial guesses are needed in local search methods in order to find distinct saddle points. In this paper, we present a novel global optimization-based dimer method (GOD) to efficiently search saddle points by coupling ant colony optimization
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Lyapunov exponent and variance in the CLT for products of random matrices related to random Fibonacci sequences Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-04-26 Rajeshwari Majumdar; Phanuel Mariano; Hugo Panzo; Lowen Peng; Anthony Sisti
We consider three matrix models of order 2 with one random entry $ \epsilon $ and the other three entries being deterministic. In the first model, we let $ \epsilon\sim \rm{Bernoulli}\left(\frac{1}{2}\right) $. For this model we develop a new technique to obtain estimates for the top Lyapunov exponent in terms of a multi-level recursion involving Fibonacci-like sequences. This in turn gives a new characterization
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Small time asymptotics for SPDEs with locally monotone coefficients Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-04-26 Shihu Li; Wei Liu; Yingchao Xie
This work aims to prove the small time large deviation principle (LDP) for a class of stochastic partial differential equations (SPDEs) with locally monotone coefficients in generalized variational framework. The main result could be applied to demonstrate the small time LDP for various quasilinear and semilinear SPDEs such as stochastic porous medium equations, stochastic $ p $-Laplace equations,
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A new weak solution to an optimal stopping problem Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-04-26 Cong Qin; Xinfu Chen
In this paper, we propose a new weak solution to an optimal stopping problem in finance and economics. The main advantage of this new definition is that we do not need the Dynamic Programming Principle, which is critical for both classical verification argument and modern viscosity approach. Additionally, the classical methods in differential equations, e.g. penalty method, can be used to derive some
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A continuous-time stochastic model of cell motion in the presence of a chemoattractant Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-04-26 J. C. Dallon; Lynnae C. Despain; Emily J. Evans; Christopher P. Grant
We consider a force-based model for cell motion which models cell forces using Hooke's law and a random outreach from the cell center. In previous work this model was simplified to track the centroid by setting the relaxation time to zero, and a formula for the expected velocity of the centroid was derived. Here we extend that formula to allow for chemotaxis of the cell by allowing the outreach distribution
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Using automatic differentiation to compute periodic orbits of delay differential equations Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-04-26 Joan Gimeno; Àngel Jorba
In this paper we focus on the computation of periodic solutions of Delay Differential Equations (DDEs) with constant delays. The method is based on defining a Poincaré section in a suitable functional space and looking for a fixed point of the flow in this section. This is done by applying a Newton method on a suitable discretisation of the section. To avoid computing and storing large matrices we
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A game-theoretic framework for autonomous vehicles velocity control: Bridging microscopic differential games and macroscopic mean field games Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-04-26 Kuang Huang; Xuan Di; Qiang Du; Xi Chen
This paper proposes an efficient computational framework for longitudinal velocity control of a large number of autonomous vehicles (AVs) and develops a traffic flow theory for AVs. Instead of hypothesizing explicitly how AVs drive, our goal is to design future AVs as rational, utility-optimizing agents that continuously select optimal velocity over a period of planning horizon. With a large number
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Numerical investigation of ensemble methods with block iterative solvers for evolution problems Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-04-26 Lili Ju; Wei Leng; Zhu Wang; Shuai Yuan
The ensemble method has been developed for accelerating a sequence of numerical simulations of evolution problems. Its main idea is, by manipulating the time stepping and grouping discrete problems, to make all members in the same group share a common coefficient matrix. Thus, at each time step, instead of solving a sequence of linear systems each of which contains only one right-hand-side vector,
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Null controllability of one dimensional degenerate parabolic equations with first order terms Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-04-26 J. Carmelo Flores; Luz De Teresa
In this paper we present a null controllability result for a degenerate semilinear parabolic equation with first order terms. The main result is obtained after the proof of a new Carleman inequality for a degenerate linear parabolic equation with first order terms.
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Classical Langevin dynamics derived from quantum mechanics Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-04-26 Håkon Hoel; Anders Szepessy
The classical work by Zwanzig [J. Stat. Phys. 9 (1973) 215-220] derived Langevin dynamics from a Hamiltonian system of a heavy particle coupled to a heat bath. This work extends Zwanzig's model to a quantum system and formulates a more general coupling between a particle system and a heat bath. The main result proves, for a particular heat bath model, that ab initio Langevin molecular dynamics, with
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Ergodic boundary and point control for linear stochastic PDEs driven by a cylindrical Lévy process Discrete Contin. Dyn. Syst. B (IF 1.27) Pub Date : 2020-04-26 Karel Kadlec; Bohdan Maslowski
An ergodic control problem is studied for controlled linear stochastic equations driven by cylindrical Lévy noise with unbounded control operator in a Hilbert space. A family of optimal controls is shown to consist of those asymptotically achieving the feedback form that employs the corresponding Riccati equation. The formula for optimal cost is given. The general results are applied to stochastic