The center conditions and bifurcation of limit cycles for a class of fifth degree systems are investigated.Two recursive formulas to compute singular quantities at infinity and at the origin are given.The first nine ...The center conditions and bifurcation of limit cycles for a class of fifth degree systems are investigated.Two recursive formulas to compute singular quantities at infinity and at the origin are given.The first nine singular point quantities at infinity and first seven singular point quantities at the origin for the system are given in order to get center conditions and study bifurcation of limit cycles.Two fifth degree systems are constructed.One allows the appearance of eight limit cycles in the neighborhood of infinity,which is the first example that a polynomial differential system bifurcates eight limit cycles at infinity.The other perturbs six limit cycles at the origin.展开更多
This study describes a multidimensional 3D/lumped parameter（LP） model which contains appropriate inflow/outflow boundary conditions in order to model the entire human arterial trees. A new extensive LP model of the ...This study describes a multidimensional 3D/lumped parameter（LP） model which contains appropriate inflow/outflow boundary conditions in order to model the entire human arterial trees. A new extensive LP model of the entire arterial network（48 arteries） was developed including the effect of vessel diameter tapering and the parameterization of resistance, conductor and inductor variables. A computer aided-design（CAD） algorithm was proposed to effciently handle the coupling of two or more 3D models with the LP model, and substantially lessen the coupling processing time. Realistic boundary conditions and Navier-Stokes equations in healthy and stenosed models of carotid artery bifurcation（CAB） were used to investigate the unsteady Newtonian blood flow velocity distribution in the internal carotid artery（ICA）. The present simulation results agree well with previous experimental and numerical studies. The outcomes of a pure LP model and those of the coupled 3D healthy model were found to be nearly the same in both cases. Concerning the various analyzed 3D zones, the stenosis growth in the ICA was not found as a crucial factor in determining the absorbing boundary conditions.This paper demonstrates the advantages of coupling local and systemic models to comprehend physiological diseases of the cardiovascular system.展开更多
A system of three-unit networks with coupled cells is investigated.The general formula for bifurcation direction of Hopf bifurcation is calculated and the estimate formula of period of the periodic solution is given.
基金Supported by Science Fund of the Education Departmentof Guangxi province( 2 0 0 3) and the NationalNatural Science Foundation of China( 1 0 361 0 0 3)
文摘The center conditions and bifurcation of limit cycles for a class of fifth degree systems are investigated.Two recursive formulas to compute singular quantities at infinity and at the origin are given.The first nine singular point quantities at infinity and first seven singular point quantities at the origin for the system are given in order to get center conditions and study bifurcation of limit cycles.Two fifth degree systems are constructed.One allows the appearance of eight limit cycles in the neighborhood of infinity,which is the first example that a polynomial differential system bifurcates eight limit cycles at infinity.The other perturbs six limit cycles at the origin.
基金the Iranian National Science Foundation (INSF) for the financial support to this project (87040150)
文摘This study describes a multidimensional 3D/lumped parameter（LP） model which contains appropriate inflow/outflow boundary conditions in order to model the entire human arterial trees. A new extensive LP model of the entire arterial network（48 arteries） was developed including the effect of vessel diameter tapering and the parameterization of resistance, conductor and inductor variables. A computer aided-design（CAD） algorithm was proposed to effciently handle the coupling of two or more 3D models with the LP model, and substantially lessen the coupling processing time. Realistic boundary conditions and Navier-Stokes equations in healthy and stenosed models of carotid artery bifurcation（CAB） were used to investigate the unsteady Newtonian blood flow velocity distribution in the internal carotid artery（ICA）. The present simulation results agree well with previous experimental and numerical studies. The outcomes of a pure LP model and those of the coupled 3D healthy model were found to be nearly the same in both cases. Concerning the various analyzed 3D zones, the stenosis growth in the ICA was not found as a crucial factor in determining the absorbing boundary conditions.This paper demonstrates the advantages of coupling local and systemic models to comprehend physiological diseases of the cardiovascular system.
基金This research is supported by the National Natural Science Foundation of China(No.19972058).
文摘A system of three-unit networks with coupled cells is investigated.The general formula for bifurcation direction of Hopf bifurcation is calculated and the estimate formula of period of the periodic solution is given.
