A stage-structured predator-prey si model with disease in the prey and impulsive effects

This paper aims to develop a high-dimensional SI model with stage structure for both the prey (pest) and the predator, and then to investigate the dynamics of it. The model can be used for the study of Integrated Pest Management (IPM) which is a combination of constant pulse releasing of animal enemies and diseased pests at two different fixed moments. Firstly, we use analytical techniques for impulsive delay differential equations to obtain the conditions for global attractivity of the ‘pest-free’ periodic solution and permanence of the population model. It shows that the conditions strongly depend on time delay, impulsive release of animal enemies and infective pests. Secondly, we present a pest management strategy in which the pest population is kept under the economic threshold level (ETL) when the pest population is permanent. Finally, numerical analysis is presented to illustrate our main conclusion

Scattering of SH waves by a semi-cylindrical bump in an inhomogeneous half-space

The wave propagation in an inhomogeneous half space with a semi-cylindrical surface bump is investigated by the means of complex function method. With the origin of the coordinate system as the center, the density of the medium changes radially. To solve the Helmholtz equation with variable coefficients caused by the inhomogeneous of the medium, a conformal transformation technique based on the theory of complex variable functions is adopted. Then, by adjusting the inhomogeneous parameters and comparing with the published analytical results, the correctness of the method in this paper is verified. Finally, the displacement amplitudes of typical observation points on the surface and inside are given, and the effects of incident wave angle

Dynamical Analysis of Delayed Plant Disease Models with Continuous or Impulsive Cultural Control Strategies

Delayed plant disease mathematical models including continuous cultural control strategy and impulsive cultural control strategy are presented and investigated. Firstly, we consider continuous cultural control strategy in which continuous replanting of healthy plants is taken. The existence and local stability of disease-free equilibrium and positive equilibrium are studied by analyzing the associated characteristic transcendental equation. And then, plant disease model with impulsive replanting of healthy plants is also considered; the sufficient condition under which the infected plant-free periodic solution is globally attritive is obtained. Moreover, permanence of the system is studied. Some numerical simulations are also given to illustrate our results

Dynamical Analysis of Delayed Plant Disease Models with Continuous or Impulsive Cultural Control Strategies.

Delayed plant disease mathematical models including continuous cultural control strategy and impulsive cultural control strategy are presented and investigated. Firstly, we consider continuous cultural control strategy in which continuous replanting of healthy plants is taken. The existence and local stability of disease-free equilibrium and positive equilibrium are studied by analyzing the associated characteristic transcendental equation. And then, plant disease model with impulsive replanting of healthy plants is also considered; the sufficient condition under which the infected plant-free periodic solution is globally attritive is obtained. Moreover, permanence of the system is studied. Some numerical simulations are also given to illustrate our results

Global dynamics for a new high-dimensional SIR model with distributed delay

In this paper, a new high-dimensional SIR epidemic model with double epidemic hypothesis and delays is proposed, which is a high-dimensional system of impulsive functional differential equations with time delays. The linear chain trick technique is employed to prove the upper boundedness of solutions of the impulsive delay differential equations and scaling method techniques for inequalities and classification method are used to study the permanence of the high-dimensional system. We also prove that the ‘infection-free’ periodic solution of the system is globally attractive when R1<1 and the system is permanent under R2>1. Moreover, numerical simulation for impulsive and delayed system is presented to illustrate our main conclusions which shows that time delays and pulse vaccination have significant effects on the dynamics behaviors of the model. The feature of the present paper is that the double epidemic hypothesis have different forms of delays to more realistically describe the spread of epidemic though which makes the high-dimensional system more complex

Shear horizontal wave propagation in inhomogeneous wedge space

In this paper, a closed-form analytical solution is presented for SH wave propagation in density radial inhomogeneous wedge space. The material parameter of this inhomo- geneous wedge space with arbitrary vertex angle is given in functional form. Based on complex function method, an appropriate mapping function is introduced to transform the governing Helmholtz equation with variable coefficients into a standard one. The wave field expression satisfying zero-stress boundary condition in wedge space is derived. Finally, numerical examples are presented to analysis the influence of different parameters on displacement amplitude

Scattering of plane SH waves by an isosceles trapezoidal hill

This paper presents a theoretical approach to study the surface motion of an isosceles trapezoidal hill impacted by incident SH waves. A rigorous solution has been derived by applying an accurate region-matching technique. The solution region is divided into three parts by an appropriate partitioning method. Based on complex function method and multipolar coordinates, a fractional factor is introduced to construct suitable wave functions which satisfy the governing equation and zero-stress condition on the free surface in each sub-region. According to the continuity condition at the auxiliary boundary, surface displacements are expressed in series of infinite algebraic equations, and the unknown coefficients of the series can be determined by Fourier series expansion technique in complex domain. Numerical results demonstrate the analytical results depend on the following parameters: The slope, the height and the width of the trapezoidal hill, the frequency content of the excitation and the incidence angle

A series solution for SH wave scattering by irregularly shaped surface topographies

This paper proposes a series solution for studying the ground motion of twin-peaks hill, double triangular hills, and hill-canyon composite topography. The propagation medium of SH wave is linearly elastic, isotropic, and homogeneous. A flexible multi-region-matching technique (MRMT) and complex function method are adopted to construct the wave field expression in each sub-region. To solve the unknown coefficients in the wave field expressions, Fourier series expansion method in the complex domain is adopted. Finally, some typical numerical examples are calculated to analyse the influence of the topography shape parameters, wave number, and the incident angle on ground motion