The influence of distributed delay coupling on Turing pattern in reaction diffusion system was investigated. Numerical-simulation results proved that the distributed delay of the coupling can significantly influence t...The influence of distributed delay coupling on Turing pattern in reaction diffusion system was investigated. Numerical-simulation results proved that the distributed delay of the coupling can significantly influence the spatiotemporal property,even the stable dynamic of the system.The local distributed coupling can spatially orient the pattern at an appropriate coupling strength.展开更多
An analysis of the solute dispersion in the liquid flowing through a pipe by means of Aris–Barton's ‘method of moments', under the joint effect of some finite yield stress and irreversible absorption into th...An analysis of the solute dispersion in the liquid flowing through a pipe by means of Aris–Barton's ‘method of moments', under the joint effect of some finite yield stress and irreversible absorption into the wall is presented in this paper. The liquid is considered as a three-layer liquid where the center region is Casson liquid surrounded by Newtonian liquid layer. A significant change from previous modelling exercises in the study of hydrodynamic dispersion, different molecular diffusivity has been considered for the different region yet to be constant. For all time period, finite difference implicit scheme has been adopted to solve the integral moment equation arising from the unsteady convective diffusion equation. The purpose of the study is to find the dependency of solute transport coefficients on absorption parameter, yield stress, viscosity ratio, peripheral layer variation and in addition with various diffusivity coefficients in different liquid layers. This kind of study may be useful for understanding the dispersion process in the blood flow analysis.展开更多
In this paper methods of differential inequalities and Liapunov functionals for proving the global stability of constant equilibria of reaction-diffusion systems are given, and examples for showing how to use these me...In this paper methods of differential inequalities and Liapunov functionals for proving the global stability of constant equilibria of reaction-diffusion systems are given, and examples for showing how to use these methods are also given.展开更多
This paper is concerned with the existence of entire solutions of some reaction-diffusion systems. We first consider Belousov-Zhabotinskii reaction model. Then we study a general model. Using the comparing argument an...This paper is concerned with the existence of entire solutions of some reaction-diffusion systems. We first consider Belousov-Zhabotinskii reaction model. Then we study a general model. Using the comparing argument and sub-super-solutions method, we obtain the existence of entire solutions which behave as two wavefronts coming from the both sides of x-axis, where an entire solution is meant by a classical solution defined for all space and time variables. At last, we give some examples to explain our results for the general models.展开更多
Modeling and simulation of infectious diseases help to predict the likely outcome of an epidemic. In this paper, a spatial susceptible-infective-susceptible （SIS） type of epidemiological disease model with self- and...Modeling and simulation of infectious diseases help to predict the likely outcome of an epidemic. In this paper, a spatial susceptible-infective-susceptible （SIS） type of epidemiological disease model with self- and cross-diffusion are investigated. We study the effect of diffusion on the stability of the endemic equilibrium with disease-induced mortality and nonlinear incidence rate, In the absence of diffusion the stationary solution stays stable but becomes unstable with respect to diffusion and that Turing instability takes place. We show that a standard （self-diffusion） system may be either stable or unstable, cross-diffusion response can stabilize an unstable standard system or decrease a ＂ihlring space （the space which the emergence of spatial patterns is holding） compared to the ~lhlring space with self-diffusion, i.e. the cross-diffusion response is an important factor that should not be ignored when pattern emerges. Numerical simulations are provided to illustrate and extend the theoretical results.展开更多
In the one-dimensional space, traveling wave solutions of parabolic differential equations have been widely studied and well characterized. Recently, the mathematical study on higher-dimensional traveling fronts has a...In the one-dimensional space, traveling wave solutions of parabolic differential equations have been widely studied and well characterized. Recently, the mathematical study on higher-dimensional traveling fronts has attracted a lot of attention and many new types of nonplanar traveling waves have been observed for scalar reaction-diffusion equations with various nonlinearities. In this paper, by using the comparison argument and constructing appropriate super- and subsolutions, we study the existence, uniqueness and stability of three- dimensional traveling fronts of pyramidal shape for monotone bistable systems of reaction-diffusion equations in R3. The pyramidal traveling fronts are characterized as either a combination of planar traveling fronts on the lateral surfaces or a combination of two-dimensional V-form waves on the edges of the pyramid. In particular, our results are applicable to some important models in biology, such as Lotk,u-Volterra competition-diffusion systems with or without spatio-temporal delays, and reaction-diffusion systems of multiple obligate mutualists.展开更多
In this study, we investigate two-dimensional patterns generated by chemotaxis reaction-diffusion systems. We numerically examine the Keller-Segel models with the volume-filling aggregation term and the receptor aggre...In this study, we investigate two-dimensional patterns generated by chemotaxis reaction-diffusion systems. We numerically examine the Keller-Segel models with the volume-filling aggregation term and the receptor aggregation term in two dimensions. Spotted, striped and reversed spotted patterns are obtained as stable motionless equi- librium patterns. The relative stability of these patterns is studied numerically on the basis of the derived free energy. The intuitive understanding of these generated patterns and the relation with three-dimensional patterns are also discussed.展开更多
文摘The influence of distributed delay coupling on Turing pattern in reaction diffusion system was investigated. Numerical-simulation results proved that the distributed delay of the coupling can significantly influence the spatiotemporal property,even the stable dynamic of the system.The local distributed coupling can spatially orient the pattern at an appropriate coupling strength.
文摘An analysis of the solute dispersion in the liquid flowing through a pipe by means of Aris–Barton's ‘method of moments', under the joint effect of some finite yield stress and irreversible absorption into the wall is presented in this paper. The liquid is considered as a three-layer liquid where the center region is Casson liquid surrounded by Newtonian liquid layer. A significant change from previous modelling exercises in the study of hydrodynamic dispersion, different molecular diffusivity has been considered for the different region yet to be constant. For all time period, finite difference implicit scheme has been adopted to solve the integral moment equation arising from the unsteady convective diffusion equation. The purpose of the study is to find the dependency of solute transport coefficients on absorption parameter, yield stress, viscosity ratio, peripheral layer variation and in addition with various diffusivity coefficients in different liquid layers. This kind of study may be useful for understanding the dispersion process in the blood flow analysis.
基金This research is supportedby the National Natural Science Foundation of China(No. 19971004 and19331043).
文摘In this paper methods of differential inequalities and Liapunov functionals for proving the global stability of constant equilibria of reaction-diffusion systems are given, and examples for showing how to use these methods are also given.
文摘This paper is concerned with the existence of entire solutions of some reaction-diffusion systems. We first consider Belousov-Zhabotinskii reaction model. Then we study a general model. Using the comparing argument and sub-super-solutions method, we obtain the existence of entire solutions which behave as two wavefronts coming from the both sides of x-axis, where an entire solution is meant by a classical solution defined for all space and time variables. At last, we give some examples to explain our results for the general models.
文摘Modeling and simulation of infectious diseases help to predict the likely outcome of an epidemic. In this paper, a spatial susceptible-infective-susceptible （SIS） type of epidemiological disease model with self- and cross-diffusion are investigated. We study the effect of diffusion on the stability of the endemic equilibrium with disease-induced mortality and nonlinear incidence rate, In the absence of diffusion the stationary solution stays stable but becomes unstable with respect to diffusion and that Turing instability takes place. We show that a standard （self-diffusion） system may be either stable or unstable, cross-diffusion response can stabilize an unstable standard system or decrease a ＂ihlring space （the space which the emergence of spatial patterns is holding） compared to the ~lhlring space with self-diffusion, i.e. the cross-diffusion response is an important factor that should not be ignored when pattern emerges. Numerical simulations are provided to illustrate and extend the theoretical results.
基金supported by National Natural Science Foundation of China (Grant Nos. 11371179 and 11271172)National Science Foundation of USA (Grant No. DMS-1412454)
文摘In the one-dimensional space, traveling wave solutions of parabolic differential equations have been widely studied and well characterized. Recently, the mathematical study on higher-dimensional traveling fronts has attracted a lot of attention and many new types of nonplanar traveling waves have been observed for scalar reaction-diffusion equations with various nonlinearities. In this paper, by using the comparison argument and constructing appropriate super- and subsolutions, we study the existence, uniqueness and stability of three- dimensional traveling fronts of pyramidal shape for monotone bistable systems of reaction-diffusion equations in R3. The pyramidal traveling fronts are characterized as either a combination of planar traveling fronts on the lateral surfaces or a combination of two-dimensional V-form waves on the edges of the pyramid. In particular, our results are applicable to some important models in biology, such as Lotk,u-Volterra competition-diffusion systems with or without spatio-temporal delays, and reaction-diffusion systems of multiple obligate mutualists.
文摘In this study, we investigate two-dimensional patterns generated by chemotaxis reaction-diffusion systems. We numerically examine the Keller-Segel models with the volume-filling aggregation term and the receptor aggregation term in two dimensions. Spotted, striped and reversed spotted patterns are obtained as stable motionless equi- librium patterns. The relative stability of these patterns is studied numerically on the basis of the derived free energy. The intuitive understanding of these generated patterns and the relation with three-dimensional patterns are also discussed.
