The Hopfbifurcation for the Brusselator ordinary-differential-equation （ODE） model and the corresponding partial-differential-equation （PDE） model are investigated by using the Hopf bifurcation theorem. The stabil...The Hopfbifurcation for the Brusselator ordinary-differential-equation （ODE） model and the corresponding partial-differential-equation （PDE） model are investigated by using the Hopf bifurcation theorem. The stability of the Hopf bifurcation periodic solution is discussed by applying the normal form theory and the center manifold theorem. When parameters satisfy some conditions, the spatial homogenous equilibrium solution and the spatial homogenous periodic solution become unstable. Our results show that if parameters are properly chosen, Hopf bifurcation does not occur for the ODE system, but occurs for the PDE system.展开更多
The general Brusselator system is considered under homogeneous Neumann boundary conditions.The existence results of the Hopf bifurcation to the ordinary differential equation （ODE） and partial differential equation ...The general Brusselator system is considered under homogeneous Neumann boundary conditions.The existence results of the Hopf bifurcation to the ordinary differential equation （ODE） and partial differential equation （PDE） models are obtained.By the center manifold theory and the normal form method,the bifurcation direction and stability of periodic solutions are established.Moreover,some numerical simulations are shown to support the analytical results.At the same time,the positive steady-state solutions and spatially inhomogeneous periodic solutions are graphically shown to supplement the analytical results.展开更多
The competition of waves has remained a hot topic in physics over the past few decades,especially the area of pattern control.Because of improved understanding of various dynamic behaviors,many practical applications ...The competition of waves has remained a hot topic in physics over the past few decades,especially the area of pattern control.Because of improved understanding of various dynamic behaviors,many practical applications have sprung up recently.The prediction of wave competitions is also very important and quite useful in these fields.This paper considers the behaviors of wave competitions in simple,inhomogeneous media which is modeled by Brusselator equations.We present a simple rule to judge the results of wave competitions utilizing the dispersion relation curves and the waves coming from different wave sources.Moreover,this rule can also be used to predict the results of wave propagation.It provides methods of obtaining the desired waves with given frequencies in inhomogeneous media.All our results are concluded and verified by computer simulations.展开更多
基金Project supported by the National Natural Science Foundation of China (No.10771032)the Natural Science Foundation of Jiangsu Province (BK2006088)
文摘The Hopfbifurcation for the Brusselator ordinary-differential-equation （ODE） model and the corresponding partial-differential-equation （PDE） model are investigated by using the Hopf bifurcation theorem. The stability of the Hopf bifurcation periodic solution is discussed by applying the normal form theory and the center manifold theorem. When parameters satisfy some conditions, the spatial homogenous equilibrium solution and the spatial homogenous periodic solution become unstable. Our results show that if parameters are properly chosen, Hopf bifurcation does not occur for the ODE system, but occurs for the PDE system.
基金supported by the National Natural Science Foundation of China (Nos. 10971124 and 11001160)the Natural Science Basic Research Plan in Shaanxi Province of China (Nos. 2011JQ1015 and 2009JQ100)the Doctor Start-up Research Fund of Shaanxi University of Science and Technology (No. BJ10-17)
文摘The general Brusselator system is considered under homogeneous Neumann boundary conditions.The existence results of the Hopf bifurcation to the ordinary differential equation （ODE） and partial differential equation （PDE） models are obtained.By the center manifold theory and the normal form method,the bifurcation direction and stability of periodic solutions are established.Moreover,some numerical simulations are shown to support the analytical results.At the same time,the positive steady-state solutions and spatially inhomogeneous periodic solutions are graphically shown to supplement the analytical results.
基金Supported by National Natural Science Foundation of China under Grant Nos.11105051,11104071,11247272Fundamental Research Funds for Central Universities,Beijing Higher Education Elite Young Teacher ProjectYouth Scholars Program of Beijing Normal University
文摘The competition of waves has remained a hot topic in physics over the past few decades,especially the area of pattern control.Because of improved understanding of various dynamic behaviors,many practical applications have sprung up recently.The prediction of wave competitions is also very important and quite useful in these fields.This paper considers the behaviors of wave competitions in simple,inhomogeneous media which is modeled by Brusselator equations.We present a simple rule to judge the results of wave competitions utilizing the dispersion relation curves and the waves coming from different wave sources.Moreover,this rule can also be used to predict the results of wave propagation.It provides methods of obtaining the desired waves with given frequencies in inhomogeneous media.All our results are concluded and verified by computer simulations.
基金Supported by NSFC(10971124,11001160)the National Science Foundation for Postdoctoral Scientists of China(20090461281)+1 种基金the DrStart-up Scientific Research Foundation of SUST(BJ10-17)the Natural Science Basic Research Planin Shaanxi Province of China(2011JQ1015)
