Sanling Yuan - Academia.edu (original) (raw)

Papers by Sanling Yuan

Journal of Mathematical Chemistry

A model of competition between two species in a turbidostat with delayed feedback control is inve... more A model of competition between two species in a turbidostat with delayed feedback control is investigated. By choosing the delay in the measurement of the optical sensor to the turbidity of the fluid as a bifurcation parameter, we show that Hopf bifurcations can occur as the delay crosses some critical values. The direction and stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem. Computer simulations illustrate the results.

Nonlinear Dynamics, 2010

The properties of Hopf bifurcations induced by the coupling time delay in a pair of identical tri... more The properties of Hopf bifurcations induced by the coupling time delay in a pair of identical tri-neuron network loops are investigated. Using center manifold reduction and normal-form theorem of retarded differential equations, explicit conditions ensuring the stability and direction of the Hopf bifurcation are given. Numerical simulations are used to illustrate our theoretical results.

Chaos Solitons & Fractals, 2004

We have considered a chemostat model with two distributed delays in a recent paper [Chaos, Solito... more We have considered a chemostat model with two distributed delays in a recent paper [Chaos, Solitons & Fractals 2004;20:995-1004], where, using the average time delay corresponding to the growth response as a bifurcation parameter, it is proven that the model undergoes Hopf bifurcations for two weak kernels. This article is a sequel to the previous work. The direction and stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem.

Applied Mathematical Modelling, 2007

In this paper, we consider a regulated logistic growth model. We first consider the linear stabil... more In this paper, we consider a regulated logistic growth model. We first consider the linear stability and the existence of a Hopf bifurcation. We show that Hopf bifurcations occur as the delay s passes through critical values. Then, using the normal form theory and center manifold reduction, we derive the explicit algorithm determining the direction of Hopf bifurcations and the stability of the bifurcating periodic solutions. Finally, numerical simulation results are given to support the theoretical predictions.

Nonlinear Analysis-real World Applications, 2006

In this paper, a predator-prey system with a discrete delay and a distributed delay is investigat... more In this paper, a predator-prey system with a discrete delay and a distributed delay is investigated. We first consider the stability of the positive equilibrium and the existence of local Hopf bifurcations. In succession, using the normal form theory and center manifold argument, we derive the explicit formulas determining stability, direction and other properties of bifurcating periodic solutions. Finally, several numerical simulations for supporting the theoretical analysis are also given. ᭧

Journal of Mathematical Chemistry

A model of competition between two species in a turbidostat with delayed feedback control is inve... more A model of competition between two species in a turbidostat with delayed feedback control is investigated. By choosing the delay in the measurement of the optical sensor to the turbidity of the fluid as a bifurcation parameter, we show that Hopf bifurcations can occur as the delay crosses some critical values. The direction and stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem. Computer simulations illustrate the results.

Nonlinear Dynamics, 2010

The properties of Hopf bifurcations induced by the coupling time delay in a pair of identical tri... more The properties of Hopf bifurcations induced by the coupling time delay in a pair of identical tri-neuron network loops are investigated. Using center manifold reduction and normal-form theorem of retarded differential equations, explicit conditions ensuring the stability and direction of the Hopf bifurcation are given. Numerical simulations are used to illustrate our theoretical results.

Nonlinear Analysis-real World Applications, 2010

Chaos Solitons & Fractals, 2004

We have considered a chemostat model with two distributed delays in a recent paper [Chaos, Solito... more We have considered a chemostat model with two distributed delays in a recent paper [Chaos, Solitons & Fractals 2004;20:995-1004], where, using the average time delay corresponding to the growth response as a bifurcation parameter, it is proven that the model undergoes Hopf bifurcations for two weak kernels. This article is a sequel to the previous work. The direction and stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem.

Journal of Mathematical Analysis and Applications, 2009

... j = 2 1 r 2 cos( j ) + sin( j ) r 2 2 + 2 + r 2 1 cos( j ) + r 2 sin( j ) r ... j (x, y, ), d... more ... j = 2 1 r 2 cos( j ) + sin( j ) r 2 2 + 2 + r 2 1 cos( j ) + r 2 sin( j ) r ... j (x, y, ), d dt y = AQ 1 y + summationdisplay 1 j! f 2 j (x, y, ), jgreaterorequalslant2 88 S. Yuan, Y. Song / J. Math. ... 1 j! f 2 j (x, y, ) are homogeneous polynomials in (x, y, ) of degree j with coe cients in C 2 ,ker , respectively ...

Applied Mathematical Modelling, 2007

In this paper, we consider a regulated logistic growth model. We first consider the linear stabil... more In this paper, we consider a regulated logistic growth model. We first consider the linear stability and the existence of a Hopf bifurcation. We show that Hopf bifurcations occur as the delay s passes through critical values. Then, using the normal form theory and center manifold reduction, we derive the explicit algorithm determining the direction of Hopf bifurcations and the stability of the bifurcating periodic solutions. Finally, numerical simulation results are given to support the theoretical predictions.

Applied Mathematical Modelling, 2009

In this paper, the delayed Leslie-Gower predator-prey system is investigated. By choosing the del... more In this paper, the delayed Leslie-Gower predator-prey system is investigated. By choosing the delay as a bifurcation parameter, we show that Hopf bifurcations can occur as the delay crosses some critical values. By deriving the equation describing the flow on the center manifold, we can determine the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions. In addition, special attention is paid to the global continuation of local Hopf bifurcations. Using a global Hopf bifurcation result of Wu [J. Wu, Symmetric functional differential equations neural networks with memory, Trans. Am. Math. Soc. 350 (1998) 4799-4838] for functional differential equations, we may show the global existence of periodic solutions.

Nonlinear Analysis-real World Applications, 2006

In this paper, a predator-prey system with a discrete delay and a distributed delay is investigat... more In this paper, a predator-prey system with a discrete delay and a distributed delay is investigated. We first consider the stability of the positive equilibrium and the existence of local Hopf bifurcations. In succession, using the normal form theory and center manifold argument, we derive the explicit formulas determining stability, direction and other properties of bifurcating periodic solutions. Finally, several numerical simulations for supporting the theoretical analysis are also given. ᭧

Chaos Solitons & Fractals, 2004

Beretta and Takeuchi [Differ. Equat. Dyn. Syst. 2 (1994) 19] proposed and studied a chemostat-typ... more Beretta and Takeuchi [Differ. Equat. Dyn. Syst. 2 (1994) 19] proposed and studied a chemostat-type model with two distributed delays. For this model, He et al. [SIAM J. Math. Anal. 29 (1998) 681] showed that the positive equilibrium can be globally asymptotically stable if the mean delays are sufficiently small. In this paper, using the average time delay as a

Nonlinear Analysis-real World Applications, 2010

Journal of Mathematical Analysis and Applications, 2009

... j = 2 1 r 2 cos( j ) + sin( j ) r 2 2 + 2 + r 2 1 cos( j ) + r 2 sin( j ) r ... j (x, y, ), d... more ... j = 2 1 r 2 cos( j ) + sin( j ) r 2 2 + 2 + r 2 1 cos( j ) + r 2 sin( j ) r ... j (x, y, ), d dt y = AQ 1 y + summationdisplay 1 j! f 2 j (x, y, ), jgreaterorequalslant2 88 S. Yuan, Y. Song / J. Math. ... 1 j! f 2 j (x, y, ) are homogeneous polynomials in (x, y, ) of degree j with coe cients in C 2 ,ker , respectively ...

Applied Mathematical Modelling, 2009

In this paper, the delayed Leslie-Gower predator-prey system is investigated. By choosing the del... more In this paper, the delayed Leslie-Gower predator-prey system is investigated. By choosing the delay as a bifurcation parameter, we show that Hopf bifurcations can occur as the delay crosses some critical values. By deriving the equation describing the flow on the center manifold, we can determine the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions. In addition, special attention is paid to the global continuation of local Hopf bifurcations. Using a global Hopf bifurcation result of Wu [J. Wu, Symmetric functional differential equations neural networks with memory, Trans. Am. Math. Soc. 350 (1998) 4799-4838] for functional differential equations, we may show the global existence of periodic solutions.

Chaos Solitons & Fractals, 2004

Beretta and Takeuchi [Differ. Equat. Dyn. Syst. 2 (1994) 19] proposed and studied a chemostat-typ... more Beretta and Takeuchi [Differ. Equat. Dyn. Syst. 2 (1994) 19] proposed and studied a chemostat-type model with two distributed delays. For this model, He et al. [SIAM J. Math. Anal. 29 (1998) 681] showed that the positive equilibrium can be globally asymptotically stable if the mean delays are sufficiently small. In this paper, using the average time delay as a

Journal of Mathematical Chemistry

A model of competition between two species in a turbidostat with delayed feedback control is inve... more A model of competition between two species in a turbidostat with delayed feedback control is investigated. By choosing the delay in the measurement of the optical sensor to the turbidity of the fluid as a bifurcation parameter, we show that Hopf bifurcations can occur as the delay crosses some critical values. The direction and stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem. Computer simulations illustrate the results.

Nonlinear Dynamics, 2010

The properties of Hopf bifurcations induced by the coupling time delay in a pair of identical tri... more The properties of Hopf bifurcations induced by the coupling time delay in a pair of identical tri-neuron network loops are investigated. Using center manifold reduction and normal-form theorem of retarded differential equations, explicit conditions ensuring the stability and direction of the Hopf bifurcation are given. Numerical simulations are used to illustrate our theoretical results.

Chaos Solitons & Fractals, 2004

We have considered a chemostat model with two distributed delays in a recent paper [Chaos, Solito... more We have considered a chemostat model with two distributed delays in a recent paper [Chaos, Solitons & Fractals 2004;20:995-1004], where, using the average time delay corresponding to the growth response as a bifurcation parameter, it is proven that the model undergoes Hopf bifurcations for two weak kernels. This article is a sequel to the previous work. The direction and stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem.

Applied Mathematical Modelling, 2007

In this paper, we consider a regulated logistic growth model. We first consider the linear stabil... more In this paper, we consider a regulated logistic growth model. We first consider the linear stability and the existence of a Hopf bifurcation. We show that Hopf bifurcations occur as the delay s passes through critical values. Then, using the normal form theory and center manifold reduction, we derive the explicit algorithm determining the direction of Hopf bifurcations and the stability of the bifurcating periodic solutions. Finally, numerical simulation results are given to support the theoretical predictions.

Nonlinear Analysis-real World Applications, 2006

In this paper, a predator-prey system with a discrete delay and a distributed delay is investigat... more In this paper, a predator-prey system with a discrete delay and a distributed delay is investigated. We first consider the stability of the positive equilibrium and the existence of local Hopf bifurcations. In succession, using the normal form theory and center manifold argument, we derive the explicit formulas determining stability, direction and other properties of bifurcating periodic solutions. Finally, several numerical simulations for supporting the theoretical analysis are also given. ᭧

Journal of Mathematical Chemistry

A model of competition between two species in a turbidostat with delayed feedback control is inve... more A model of competition between two species in a turbidostat with delayed feedback control is investigated. By choosing the delay in the measurement of the optical sensor to the turbidity of the fluid as a bifurcation parameter, we show that Hopf bifurcations can occur as the delay crosses some critical values. The direction and stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem. Computer simulations illustrate the results.

Nonlinear Dynamics, 2010

The properties of Hopf bifurcations induced by the coupling time delay in a pair of identical tri... more The properties of Hopf bifurcations induced by the coupling time delay in a pair of identical tri-neuron network loops are investigated. Using center manifold reduction and normal-form theorem of retarded differential equations, explicit conditions ensuring the stability and direction of the Hopf bifurcation are given. Numerical simulations are used to illustrate our theoretical results.

Nonlinear Analysis-real World Applications, 2010

Chaos Solitons & Fractals, 2004

We have considered a chemostat model with two distributed delays in a recent paper [Chaos, Solito... more We have considered a chemostat model with two distributed delays in a recent paper [Chaos, Solitons & Fractals 2004;20:995-1004], where, using the average time delay corresponding to the growth response as a bifurcation parameter, it is proven that the model undergoes Hopf bifurcations for two weak kernels. This article is a sequel to the previous work. The direction and stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem.

Journal of Mathematical Analysis and Applications, 2009

... j = 2 1 r 2 cos( j ) + sin( j ) r 2 2 + 2 + r 2 1 cos( j ) + r 2 sin( j ) r ... j (x, y, ), d... more ... j = 2 1 r 2 cos( j ) + sin( j ) r 2 2 + 2 + r 2 1 cos( j ) + r 2 sin( j ) r ... j (x, y, ), d dt y = AQ 1 y + summationdisplay 1 j! f 2 j (x, y, ), jgreaterorequalslant2 88 S. Yuan, Y. Song / J. Math. ... 1 j! f 2 j (x, y, ) are homogeneous polynomials in (x, y, ) of degree j with coe cients in C 2 ,ker , respectively ...

Applied Mathematical Modelling, 2007

In this paper, we consider a regulated logistic growth model. We first consider the linear stabil... more In this paper, we consider a regulated logistic growth model. We first consider the linear stability and the existence of a Hopf bifurcation. We show that Hopf bifurcations occur as the delay s passes through critical values. Then, using the normal form theory and center manifold reduction, we derive the explicit algorithm determining the direction of Hopf bifurcations and the stability of the bifurcating periodic solutions. Finally, numerical simulation results are given to support the theoretical predictions.

Applied Mathematical Modelling, 2009

In this paper, the delayed Leslie-Gower predator-prey system is investigated. By choosing the del... more In this paper, the delayed Leslie-Gower predator-prey system is investigated. By choosing the delay as a bifurcation parameter, we show that Hopf bifurcations can occur as the delay crosses some critical values. By deriving the equation describing the flow on the center manifold, we can determine the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions. In addition, special attention is paid to the global continuation of local Hopf bifurcations. Using a global Hopf bifurcation result of Wu [J. Wu, Symmetric functional differential equations neural networks with memory, Trans. Am. Math. Soc. 350 (1998) 4799-4838] for functional differential equations, we may show the global existence of periodic solutions.

Nonlinear Analysis-real World Applications, 2006

In this paper, a predator-prey system with a discrete delay and a distributed delay is investigat... more In this paper, a predator-prey system with a discrete delay and a distributed delay is investigated. We first consider the stability of the positive equilibrium and the existence of local Hopf bifurcations. In succession, using the normal form theory and center manifold argument, we derive the explicit formulas determining stability, direction and other properties of bifurcating periodic solutions. Finally, several numerical simulations for supporting the theoretical analysis are also given. ᭧

Chaos Solitons & Fractals, 2004

Beretta and Takeuchi [Differ. Equat. Dyn. Syst. 2 (1994) 19] proposed and studied a chemostat-typ... more Beretta and Takeuchi [Differ. Equat. Dyn. Syst. 2 (1994) 19] proposed and studied a chemostat-type model with two distributed delays. For this model, He et al. [SIAM J. Math. Anal. 29 (1998) 681] showed that the positive equilibrium can be globally asymptotically stable if the mean delays are sufficiently small. In this paper, using the average time delay as a

Nonlinear Analysis-real World Applications, 2010

Journal of Mathematical Analysis and Applications, 2009

... j = 2 1 r 2 cos( j ) + sin( j ) r 2 2 + 2 + r 2 1 cos( j ) + r 2 sin( j ) r ... j (x, y, ), d... more ... j = 2 1 r 2 cos( j ) + sin( j ) r 2 2 + 2 + r 2 1 cos( j ) + r 2 sin( j ) r ... j (x, y, ), d dt y = AQ 1 y + summationdisplay 1 j! f 2 j (x, y, ), jgreaterorequalslant2 88 S. Yuan, Y. Song / J. Math. ... 1 j! f 2 j (x, y, ) are homogeneous polynomials in (x, y, ) of degree j with coe cients in C 2 ,ker , respectively ...

Applied Mathematical Modelling, 2009

In this paper, the delayed Leslie-Gower predator-prey system is investigated. By choosing the del... more In this paper, the delayed Leslie-Gower predator-prey system is investigated. By choosing the delay as a bifurcation parameter, we show that Hopf bifurcations can occur as the delay crosses some critical values. By deriving the equation describing the flow on the center manifold, we can determine the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions. In addition, special attention is paid to the global continuation of local Hopf bifurcations. Using a global Hopf bifurcation result of Wu [J. Wu, Symmetric functional differential equations neural networks with memory, Trans. Am. Math. Soc. 350 (1998) 4799-4838] for functional differential equations, we may show the global existence of periodic solutions.

Chaos Solitons & Fractals, 2004

Beretta and Takeuchi [Differ. Equat. Dyn. Syst. 2 (1994) 19] proposed and studied a chemostat-typ... more Beretta and Takeuchi [Differ. Equat. Dyn. Syst. 2 (1994) 19] proposed and studied a chemostat-type model with two distributed delays. For this model, He et al. [SIAM J. Math. Anal. 29 (1998) 681] showed that the positive equilibrium can be globally asymptotically stable if the mean delays are sufficiently small. In this paper, using the average time delay as a