Based on the differential forms and exterior derivatives of fractional orders, Wu first presented the generalized Tu formula to construct the generalized Hamiltonian structure of the fractional soliton equation. We ap...Based on the differential forms and exterior derivatives of fractional orders, Wu first presented the generalized Tu formula to construct the generalized Hamiltonian structure of the fractional soliton equation. We apply the generalized Tu formula to calculate the fractional Dirac soliton equation hierarchy and its Hamiltonian structure. The method can be generalized to the other fractional soliton hierarchy.展开更多
In this paper, a spatial tri-trophic food chain model with ratio-dependent Michaelis-Menten type functional response under homogeneous Neumann boundary conditions is studied. Conditions for Hopf and Turing bifurcation...In this paper, a spatial tri-trophic food chain model with ratio-dependent Michaelis-Menten type functional response under homogeneous Neumann boundary conditions is studied. Conditions for Hopf and Turing bifurcation are derived. Sufficient conditions for the emergence of spatial patterns are obtained. The results of numerical simulations reveal the formation of labyrinth patterns and the coexistence of spotted and stripe-like patterns.展开更多
This paper presents a robust output feedback control method for uncertain chaotic systems, which comprises a nonlinear inversion-based controller with a fuzzy robust compensator. The proposed controller eliminates the...This paper presents a robust output feedback control method for uncertain chaotic systems, which comprises a nonlinear inversion-based controller with a fuzzy robust compensator. The proposed controller eliminates the unknown nonlinear function by using a fuzzy system, whose inputs are not the state variables but feedback error signals. The underlying stability analysis as well as parameter update law design are carried out by using the Lyapunov-based technique. The proposed method indicates that the nonlinear inversion-based control approach can also be applied to uncertain chaotic systems. Theoretical results are illustrated through two simulation examples.展开更多
This paper deals with the stability analysis to a three-species food chain model with crossdiffusion, the results of which show that there is no Turing instability but crossdiffusion makes the model instability possib...This paper deals with the stability analysis to a three-species food chain model with crossdiffusion, the results of which show that there is no Turing instability but crossdiffusion makes the model instability possible. We then show that the spatial patterns are spotted patterns by using numerical simulations. In order to understand why the spatial patterns happen, the existence of the nonhomogeneous steady states is investigated. Finally, using the Leray-Schauder theory, we demonstrate that cross-diffusion creates nonhomogeneous stationary patterns.展开更多
In this paper we study a class of metrics with some compatible almost complex structures on the tangent bundle TM of a Riemannian manifold (M,g), which are parallel to those in [10]. These metrics generalize the class...In this paper we study a class of metrics with some compatible almost complex structures on the tangent bundle TM of a Riemannian manifold (M,g), which are parallel to those in [10]. These metrics generalize the classical Sasaki metric and Cheeger-Gromoll metric. We prove that the tangent bundle TM endowed with each pair of the above metrics and the corresponding almost complex structures is a locally conformal almost K¨ahler manifold. We also find that, when restricted to the unit tangent sphere bundle, th...展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11271008,61072147,and 11071159 )the Shanghai Leading Academic Discipline Project,China (Grant No. J50101)
文摘Based on the differential forms and exterior derivatives of fractional orders, Wu first presented the generalized Tu formula to construct the generalized Hamiltonian structure of the fractional soliton equation. We apply the generalized Tu formula to calculate the fractional Dirac soliton equation hierarchy and its Hamiltonian structure. The method can be generalized to the other fractional soliton hierarchy.
文摘In this paper, a spatial tri-trophic food chain model with ratio-dependent Michaelis-Menten type functional response under homogeneous Neumann boundary conditions is studied. Conditions for Hopf and Turing bifurcation are derived. Sufficient conditions for the emergence of spatial patterns are obtained. The results of numerical simulations reveal the formation of labyrinth patterns and the coexistence of spotted and stripe-like patterns.
基金Project supported by the Young Talents Natural Science Foundation for Universities of Anhui Province,China(Grant No.2012SQRL179)
文摘This paper presents a robust output feedback control method for uncertain chaotic systems, which comprises a nonlinear inversion-based controller with a fuzzy robust compensator. The proposed controller eliminates the unknown nonlinear function by using a fuzzy system, whose inputs are not the state variables but feedback error signals. The underlying stability analysis as well as parameter update law design are carried out by using the Lyapunov-based technique. The proposed method indicates that the nonlinear inversion-based control approach can also be applied to uncertain chaotic systems. Theoretical results are illustrated through two simulation examples.
文摘This paper deals with the stability analysis to a three-species food chain model with crossdiffusion, the results of which show that there is no Turing instability but crossdiffusion makes the model instability possible. We then show that the spatial patterns are spotted patterns by using numerical simulations. In order to understand why the spatial patterns happen, the existence of the nonhomogeneous steady states is investigated. Finally, using the Leray-Schauder theory, we demonstrate that cross-diffusion creates nonhomogeneous stationary patterns.
基金the National Natural Science Foundation of China (No.10671181)
文摘In this paper we study a class of metrics with some compatible almost complex structures on the tangent bundle TM of a Riemannian manifold (M,g), which are parallel to those in [10]. These metrics generalize the classical Sasaki metric and Cheeger-Gromoll metric. We prove that the tangent bundle TM endowed with each pair of the above metrics and the corresponding almost complex structures is a locally conformal almost K¨ahler manifold. We also find that, when restricted to the unit tangent sphere bundle, th...
