1 Introduction
In recent years, there are a lot of work on holomorphic vector bundles on non-algebraicManifolds. The main problem is to determine which continuous complex vector bundle carry-ing a holomorphic structur...1 Introduction
In recent years, there are a lot of work on holomorphic vector bundles on non-algebraicManifolds. The main problem is to determine which continuous complex vector bundle carry-ing a holomorphic structure or further a holomorphic filtrable structure and the correspondingclassification[1,2,7].展开更多
In this paper, regarding the time delay as a bifurcation parameter, the stability and Hopf bifurcation of the model of competition between two species in a turbidostat with Beddington-DeAngelis functional response and...In this paper, regarding the time delay as a bifurcation parameter, the stability and Hopf bifurcation of the model of competition between two species in a turbidostat with Beddington-DeAngelis functional response and discrete delay are studied. The Hopf bifurcations can be shown when the delay crosses the critical value. Furthermore, based on the normal form and the center manifold theorem, the type, stability and other properties of the bifurcating periodic solutions are determined. Finally, some numerical simulations are given to illustrate the results.展开更多
In this paper, two sunflower equations are considered. Using delay T as a parameter and applying the global Hopf bifurcation theorem, we investigate the existence of global Hopf bifurcation for the sunflower equation....In this paper, two sunflower equations are considered. Using delay T as a parameter and applying the global Hopf bifurcation theorem, we investigate the existence of global Hopf bifurcation for the sunflower equation. Furthermore, we analyze the local Hopf bifurcation of the modified equation with nonlinear relation about stem＇s increase, including the occurrence, the bifurcation direction, the stability and the approximation expression of the bifurcating periodic solution using the theory of normal form and center manifold. Finally, the obtained results of these two equations are compared, which finds that the result about the period of their bifurcating periodic solutions is obviously different, while the bifurcation direction and stability are identical.展开更多
This paper presents a definition of residue formulas for the Euler class ot eohomology-oriented sphere fibrations ε. If the base of ε is a topological manifold, a Hopf index theorem can be obtained and, for the smoo...This paper presents a definition of residue formulas for the Euler class ot eohomology-oriented sphere fibrations ε. If the base of ε is a topological manifold, a Hopf index theorem can be obtained and, for the smooth category, a generalization of a residue formula is derived for real vector bundles given in [2].展开更多
In this paper, the dynamics of mathematical model for infection of thymus gland by HIV-1 is analyzed by applying some perturbation through two different types of delays such as in terms of Hopf bifurcation analysis. F...In this paper, the dynamics of mathematical model for infection of thymus gland by HIV-1 is analyzed by applying some perturbation through two different types of delays such as in terms of Hopf bifurcation analysis. Further, the conditions for the existence of Hopf bifurcation are derived by evaluating the characteristic equation. The direction of Hopf bifurcation and stability of bifurcating periodic solutions are determined by employing the center manifold theorem and normal form method. Finally, some of the numerical simulations are carried out to validate the derived theoretical results and main conclusions are included.展开更多
A mathematical model describing the dynamics of toxin producing phytoplankton- zooplankton interaction with instantaneous nutrient recycling is proposed. We have explored the dynamics of plankton ecosystem with multip...A mathematical model describing the dynamics of toxin producing phytoplankton- zooplankton interaction with instantaneous nutrient recycling is proposed. We have explored the dynamics of plankton ecosystem with multiple delays; one due to gestation period in the growth of phytoplankton population and second due to the delay in toxin liberated by TPP. It is established that a sequence of Hopf bifurcations occurs at the interior equilibrium as the delay increases through its critical value. The direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determined using the theory of normal form and center manifold. Meanwhile, effect of toxin on the stability of delayed plankton system is also established numerically. Finally, numerical simulations are carried out to support and supplement the analytical findings.展开更多
In this paper, a time-delayed predator-prey system is considered. The existence of Hopf bifurcations at the positive equilibrium is established by analyzing the distribution of the characteristic values. An explicit a...In this paper, a time-delayed predator-prey system is considered. The existence of Hopf bifurcations at the positive equilibrium is established by analyzing the distribution of the characteristic values. An explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by using the normal form and the center manifold theory. Numerical simulations to support the analytical conclusions are carried out.展开更多
In this paper, we study dynamics in a predator-prey model with delay, in which predator can be infected, with particular attention focused on nonresonant double Hopf bifurca- tion. By using center manifold reduction m...In this paper, we study dynamics in a predator-prey model with delay, in which predator can be infected, with particular attention focused on nonresonant double Hopf bifurca- tion. By using center manifold reduction methods, we obtain the equivalent normal forms near a double Hopf critical point in this system. Moreover, bifurcations are classified in a two-dimensional parameter space near the critical point. Numerical simulations are presented to demonstrate the applicability of the theoretical results.展开更多
基金Foundation item:The research was supported by 973 Project Foundation of China and the Outstanding Youth Science Grant of NSFC(grant No.19825102)
文摘1 Introduction
In recent years, there are a lot of work on holomorphic vector bundles on non-algebraicManifolds. The main problem is to determine which continuous complex vector bundle carry-ing a holomorphic structure or further a holomorphic filtrable structure and the correspondingclassification[1,2,7].
基金Acknowledgments The authors would like to thank the editors and the anonymous referees for their helpful suggestions and comments which led to the improvement of our original manuscript. This work is supported by the National Natural Science Foundation of China （Grant Nos. 11561022, 11261017）, the China Postdoctoral Science Foundation （Grant No. 2014M562008）.
文摘In this paper, regarding the time delay as a bifurcation parameter, the stability and Hopf bifurcation of the model of competition between two species in a turbidostat with Beddington-DeAngelis functional response and discrete delay are studied. The Hopf bifurcations can be shown when the delay crosses the critical value. Furthermore, based on the normal form and the center manifold theorem, the type, stability and other properties of the bifurcating periodic solutions are determined. Finally, some numerical simulations are given to illustrate the results.
文摘In this paper, two sunflower equations are considered. Using delay T as a parameter and applying the global Hopf bifurcation theorem, we investigate the existence of global Hopf bifurcation for the sunflower equation. Furthermore, we analyze the local Hopf bifurcation of the modified equation with nonlinear relation about stem＇s increase, including the occurrence, the bifurcation direction, the stability and the approximation expression of the bifurcating periodic solution using the theory of normal form and center manifold. Finally, the obtained results of these two equations are compared, which finds that the result about the period of their bifurcating periodic solutions is obviously different, while the bifurcation direction and stability are identical.
基金Project supported by the DGICYT Grant (No. MTM2007-60016)the Junta de Andalucía Grant(No. P07-FQM-2863)
文摘This paper presents a definition of residue formulas for the Euler class ot eohomology-oriented sphere fibrations ε. If the base of ε is a topological manifold, a Hopf index theorem can be obtained and, for the smooth category, a generalization of a residue formula is derived for real vector bundles given in [2].
文摘In this paper, the dynamics of mathematical model for infection of thymus gland by HIV-1 is analyzed by applying some perturbation through two different types of delays such as in terms of Hopf bifurcation analysis. Further, the conditions for the existence of Hopf bifurcation are derived by evaluating the characteristic equation. The direction of Hopf bifurcation and stability of bifurcating periodic solutions are determined by employing the center manifold theorem and normal form method. Finally, some of the numerical simulations are carried out to validate the derived theoretical results and main conclusions are included.
文摘A mathematical model describing the dynamics of toxin producing phytoplankton- zooplankton interaction with instantaneous nutrient recycling is proposed. We have explored the dynamics of plankton ecosystem with multiple delays; one due to gestation period in the growth of phytoplankton population and second due to the delay in toxin liberated by TPP. It is established that a sequence of Hopf bifurcations occurs at the interior equilibrium as the delay increases through its critical value. The direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determined using the theory of normal form and center manifold. Meanwhile, effect of toxin on the stability of delayed plankton system is also established numerically. Finally, numerical simulations are carried out to support and supplement the analytical findings.
文摘In this paper, a time-delayed predator-prey system is considered. The existence of Hopf bifurcations at the positive equilibrium is established by analyzing the distribution of the characteristic values. An explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by using the normal form and the center manifold theory. Numerical simulations to support the analytical conclusions are carried out.
文摘In this paper, we study dynamics in a predator-prey model with delay, in which predator can be infected, with particular attention focused on nonresonant double Hopf bifurca- tion. By using center manifold reduction methods, we obtain the equivalent normal forms near a double Hopf critical point in this system. Moreover, bifurcations are classified in a two-dimensional parameter space near the critical point. Numerical simulations are presented to demonstrate the applicability of the theoretical results.
