ISSN:

1531-3492

eISSN:

1553-524X

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## Discrete and Continuous Dynamical Systems - B

February 2022 , Volume 27 , Issue 2

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*+*[Abstract](1148)

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**Abstract:**

The transmission of production-limiting disease in farm, such as Neosporosis and Johne's disease, has brought a huge loss worldwide due to reproductive failure. This paper aims to provide a modeling framework for controlling the disease and investigating the spread dynamics of *Neospora caninum*-infected dairy as a case study. In particular, a dynamic model for production-limiting disease transmission in the farm is proposed. It incorporates the vertical and horizontal transmission routes and two vaccines. The threshold parameter, basic reproduction number *Neospora caninum*-infected dairy in Switzerland, sensitivity analysis of all involved parameters with respect to the basic reproduction number

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**Abstract:**

The paper is concerned with a class of nonlinear time-varying retarded integro-differential equations (RIDEs). By the Lyapunov–Krasovski$ \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{ı} $ functional method, two new results with weaker conditions related to uniform stability (US), uniform asymptotic stability (UAS), integrability, boundedness, and boundedness at infinity of solutions of the RIDEs are given. For illustrative purposes, two examples are provided. The study of the results of this paper shows that the given theorems are not only applicable to time-varying linear RIDEs, but also applicable to time-varying nonlinear RIDEs.

*+*[Abstract](1177)

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**Abstract:**

In this paper, the global exponential stability and periodicity are investigated for impulsive neural network models with Lipschitz continuous activation functions and generalized piecewise constant delay. The sufficient conditions for the existence and uniqueness of periodic solutions of the model are established by applying fixed point theorem and the successive approximations method. By constructing suitable differential inequalities with generalized piecewise constant delay, some sufficient conditions for the global exponential stability of the model are obtained. The methods, which does not make use of Lyapunov functional, is simple and valid for the periodicity and stability analysis of impulsive neural network models with variable and/or deviating arguments. The results extend some previous results. Typical numerical examples with simulations are utilized to illustrate the validity and improvement in less conservatism of the theoretical results. This paper ends with a brief conclusion.

*+*[Abstract](987)

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**Abstract:**

We structure a phytoplankton zooplankton interaction system by incorporating (i) Monod-Haldane type functional response function; (ii) two delays accounting, respectively, for the gestation delay

*+*[Abstract](935)

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**Abstract:**

In this paper, we formulate a multi-group *SIR* epidemic model with the consideration of proportionate mixing patterns between groups and group-specific fractional-dose vaccination to evaluate the effects of fractionated dosing strategies on disease control and prevention in a heterogeneously mixing population. The basic reproduction number

*+*[Abstract](950)

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**Abstract:**

In this paper we discuss the weak pullback mean random attractors for stochastic Ginzburg-Landau equations defined in Bochner spaces. We prove the existence and uniqueness of weak pullback mean random attractors for the stochastic Ginzburg-Landau equations with nonlinear diffusion terms. We also establish the existence and uniqueness of such attractors for the deterministic Ginzburg-Landau equations with random initial data. In this case, the periodicity of the weak pullback mean random attractors is also proved whenever the external forcing terms are periodic in time.

*+*[Abstract](994)

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**Abstract:**

In 1996, Edward Lorenz introduced a system of ordinary differential equations that describes a scalar quantity evolving on a circular array of sites, undergoing forcing, dissipation, and rotation invariant advection. Lorenz constructed the system as a test problem for numerical weather prediction. Since then, the system has also found use as a test case in data assimilation. Mathematically, this is a dynamical system with a single bifurcation parameter (rescaled forcing) that undergoes multiple bifurcations and exhibits chaotic behavior for large forcing. In this paper, the main characteristics of the advection term in the model are identified and used to describe and classify possible generalizations of the system. A graphical method to study the bifurcation behavior of constant solutions is introduced, and it is shown how to use the rotation invariance to compute normal forms of the system analytically. Problems with site-dependent forcing, dissipation, or advection are considered and basic existence and stability results are proved for these extensions. We address some related topics in the appendices, wherein the Lorenz '96 system in Fourier space is considered, explicit solutions for some advection-only systems are found, and it is demonstrated how to use advection-only systems to assess numerical schemes.

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**Abstract:**

Reaction networks can be regarded as finite oriented graphs embedded in Euclidean space. *Single-target networks* are reaction networks with an arbitrarily set of source vertices, but *only one* sink vertex. We completely characterize the dynamics of all mass-action systems generated by single-target networks, as follows: either *(i)* the system is globally stable for all choice of rate constants (in fact, is dynamically equivalent to a detailed-balanced system with a single linkage class), or *(ii)* the system has no positive steady states for any choice of rate constants and all trajectories must converge to the boundary of the positive orthant or to infinity. Moreover, we show that global stability occurs if and only if the target vertex of the network is in the relative interior of the convex hull of the source vertices.

*+*[Abstract](1201)

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**Abstract:**

In this paper, the input-to-state stability (ISS), stochastic-ISS (SISS) and integral-ISS (iISS) for mild solutions of infinite-dimensional stochastic nonlinear systems (IDSNS) are investigated, respectively. By constructing a class of Yosida strong solution approximating systems for IDSNS and using the infinite-dimensional version Itô's formula, Lyapunov-based sufficient criteria are derived for ensuring ISS-type properties of IDSNS, which extend the existing corresponding results of infinite-dimensional deterministic systems. Moreover, two examples are presented to demonstrate the main results.

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**Abstract:**

In this paper, we investigate a reaction-diffusion-advection two-species competition system with a free boundary in heterogeneous environment. The primary aim is to study the impact of small advection terms and heterogeneous environment, which is on two species' dynamics via a free boundary. The function

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**Abstract:**

Stability problem on perturbations near the hydrostatic balance is one of the important issues for Boussinesq equations. This paper focuses on the asymptotic stability and large-time behavior problem of perturbations of the 2D fractional Boussinesq equations with only fractional velocity dissipation or fractional thermal diffusivity. Since the linear portion of the Boussinesq equations plays a crucial role in the stability properties, we firstly study the linearized fractional Boussinesq equations with only fractional velocity dissipation or fractional thermal diffusivity and complete the following work: 1) assessing the stability and obtaining the precise large-time asymptotic behavior for solutions to the linearized system satisfied the perturbation; 2) understanding the spectral property of the linearization; 3) showing the

*+*[Abstract](1013)

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**Abstract:**

In this paper we establish a comparison approach to study stabilization of stochastic differential equations driven by

*+*[Abstract](1581)

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**Abstract:**

In this paper, we consider the time fractional diffusion equation with Caputo fractional derivative. Due to the singularity of the solution at the initial moment, it is difficult to achieve an ideal convergence order on uniform meshes. Therefore, in order to improve the convergence order, we discrete the Caputo time fractional derivative by a new

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**Abstract:**

This paper concerns the mathematical analysis of quasi-periodic travelling wave solutions for beam equations with damping on 3-dimensional rectangular tori. Provided that the generators of the rectangular torus satisfy certain relationships, by excluding some values of two model parameters, we establish the existence of small amplitude quasi-periodic travelling wave solutions with three frequencies. Moreover, it can be shown that such solutions are either continuations of rotating wave solutions, or continuations of quasi-periodic travelling wave solutions with two frequencies, and that the set of two model parameters is dense in the positive quadrant.

*+*[Abstract](939)

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**Abstract:**

Randomly drawn

*+*[Abstract](849)

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**Abstract:**

This paper considers consumer-resource systems with Holling II functional response. In the system, the consumer can move between a source and a sink patch. By applying dynamical systems theory, we give a rigorous analysis on persistence of the system. Then we show local/global stability of equilibria and prove Hopf bifurcation by the Kuznetsov Theorem. It is shown that dispersal in the system could lead to results reversing those without dispersal. Varying a dispersal rate can change species' interaction outcomes from coexistence in periodic oscillation, to persistence at a steady state, to extinction of the predator, and even to extinction of both species. By explicit expressions of stable equilibria, we prove that dispersal can make the consumer reach overall abundance larger than if non-dispersing, and there exists an optimal dispersal rate that maximizes the abundance. Asymmetry in dispersal can also lead to those results. It is proven that the overall abundance is a ridge-like function (surface) of dispersal rates, which extends both previous theory and experimental observation. These results are biologically important in protecting endangered species.

*+*[Abstract](1019)

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**Abstract:**

In this paper, we study the energy equality for weak solutions to the 3D homogeneous incompressible magnetohydrodynamic equations with viscosity and magnetic diffusion in a bounded domain. Two types of regularity conditions are imposed on weak solutions to ensure the energy equality. For the first type, some global integrability condition for the velocity

*+*[Abstract](909)

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**Abstract:**

This paper will prove the normal deviation of the synchronization of stochastic coupled system. According to the relationship between the stationary solution and the general solution, the martingale method is used to prove the normal deviation of the fixed initial value of the multi-scale system, thereby obtaining the normal deviation of the stationary solution. At the same time, with the relationship between the synchronized system and the multi-scale system, the normal deviation of the synchronization is obtained.

*+*[Abstract](878)

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**Abstract:**

In this paper we consider an

*+*[Abstract](972)

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**Abstract:**

In this paper we are concerned with the approximate controllability of a multidimensional semilinear reaction-diffusion equation governed by a multiplicative control, which is locally distributed in the reaction term. For a given initial state we provide sufficient conditions on the desirable state to be approximately reached within an arbitrarily small time interval. Our approaches are based on linear semigroup theory and some results on uniform approximation with smooth functions.

*+*[Abstract](844)

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**Abstract:**

Feller kernels are a concise means to formalize individual structural transitions in a structured discrete-time population model. An iteroparous populations (in which generations overlap) is considered where different kernels model the structural transitions for neonates and for older individuals. Other Feller kernels are used to model competition between individuals. The spectral radius of a suitable Feller kernel is established as basic turnover number that acts as threshold between population extinction and population persistence. If the basic turnover number exceeds one, the population shows various degrees of persistence that depend on the irreducibility and other properties of the transition kernels.

*+*[Abstract](1111)

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**Abstract:**

In this paper, by using the eigenvalue theory, the sub-supersolution method and the fixed point theory, we prove the existence, multiplicity, uniqueness, asymptotic behavior and approximation of positive solutions for singular multiparameter *p*-Laplacian elliptic systems on nonlinearities with separate variables or without separate variables. Various nonexistence results of positive solutions are also studied.

*+*[Abstract](941)

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**Abstract:**

The original Hegselmann-Krause (HK) model consists of a set of

*+*[Abstract](2007)

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**Abstract:**

In this article, Turing instability and the formations of spatial patterns for a general two-component reaction-diffusion system defined on 2D bounded domain, are investigated. By analyzing characteristic equation at positive constant steady states and further selecting diffusion rate

*+*[Abstract](1118)

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**Abstract:**

In this work, two fully novel finite difference schemes for two-dimensional time-fractional mixed diffusion and diffusion-wave equation (TFMDDWEs) are presented. Firstly, a Hermite and Newton quadratic interpolation polynomial have been used for time discretization and central quotient has used in spatial direction. The H2N2 finite difference is constructed. Secondly, in order to increase computational efficiency, the sum-of-exponential is used to approximate the kernel function in the fractional-order operator. The fast H2N2 finite difference is obtained. Thirdly, the stability and convergence of two schemes are studied by energy method. When the tolerance error

2020
Impact Factor: 1.327

5 Year Impact Factor: 1.492

2020 CiteScore: 2.2

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