For any C;diffeomorphism on a smooth compact Riemannian manifold that admits an ergodic measure with positive entropy,a lower bound of the Hausdorff dimension for the local stable and unstable sets is given in terms o...For any C;diffeomorphism on a smooth compact Riemannian manifold that admits an ergodic measure with positive entropy,a lower bound of the Hausdorff dimension for the local stable and unstable sets is given in terms of the measure-theoretic entropy and the maximal Lyapunov exponent.The main line of our approach to this result is under the setting of topological dynamical systems,which is also applicable to infinite-dimensional C;dynamical systems.展开更多
Systems of quasilinear first order PDE are studied in the framework of contact manifold. All of the local stable geometric solutions of such systems are classified by using versal deformation and the classification of...Systems of quasilinear first order PDE are studied in the framework of contact manifold. All of the local stable geometric solutions of such systems are classified by using versal deformation and the classification of stable map germs of type ∑1 in singularity theory.展开更多
In this paper,on the basis of the theories and methods of ecology and ordinary differential equations,an ecological model with an impulsive control strategy is established.By using the theories of impulsive equations,...In this paper,on the basis of the theories and methods of ecology and ordinary differential equations,an ecological model with an impulsive control strategy is established.By using the theories of impulsive equations,small amplitude perturbation skills and compar-ison technique,we get the condition which guarantees the global asymptotical stability of the prey-x-eradication and predator-y-eradication periodic solution.It is proved that the system is permanent.Furthermore,numerical simulations are also illustrated which agree well with our theoretical analysis.All these results may be useful in study of the dynamic complexity of ecosystems.展开更多
In this paper, we derive a time-delayed and diffusive echinococcosis transmission model. We first address the well-posedness to the initial-value problem for the model and give the basic reproduction number TO0. In th...In this paper, we derive a time-delayed and diffusive echinococcosis transmission model. We first address the well-posedness to the initial-value problem for the model and give the basic reproduction number TO0. In the case of a bounded spatial domain, we establish the local stability as well as the global stability of the disease-free and disease equilibria of the model. The methods to prove the local and the global stability are to analyze the corresponding characteristic equations and construct Lyapunov functionals, respectively. In the case of an unbounded spatial domain, by applying Schauder＇s fixed point theorem and the limiting arguments, we show that when R0 〉 1, there exists a constant c＊ 〉 0 such that the model admits positive traveling wave solutions connecting the disease-free and endemic equilibrium for c 〉 c＊, and when R0 〉 1 and c 〈 c＊, the model has no positive traveling wave solutions connecting them.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11701394)supported by National Natural Science Foundation of China(Grant Nos.11971455 and 11731003)supported by National Natural Science Foundation of China(Grant Nos.11671279 and 11541003)。
文摘For any C;diffeomorphism on a smooth compact Riemannian manifold that admits an ergodic measure with positive entropy,a lower bound of the Hausdorff dimension for the local stable and unstable sets is given in terms of the measure-theoretic entropy and the maximal Lyapunov exponent.The main line of our approach to this result is under the setting of topological dynamical systems,which is also applicable to infinite-dimensional C;dynamical systems.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 19971035).
文摘Systems of quasilinear first order PDE are studied in the framework of contact manifold. All of the local stable geometric solutions of such systems are classified by using versal deformation and the classification of stable map germs of type ∑1 in singularity theory.
基金Supported by the National Natural Science Foundation of China (Grant No.60804015)National Basic Research Program of China (Grant No.2010CB732501)
文摘In this paper,on the basis of the theories and methods of ecology and ordinary differential equations,an ecological model with an impulsive control strategy is established.By using the theories of impulsive equations,small amplitude perturbation skills and compar-ison technique,we get the condition which guarantees the global asymptotical stability of the prey-x-eradication and predator-y-eradication periodic solution.It is proved that the system is permanent.Furthermore,numerical simulations are also illustrated which agree well with our theoretical analysis.All these results may be useful in study of the dynamic complexity of ecosystems.
文摘In this paper, we derive a time-delayed and diffusive echinococcosis transmission model. We first address the well-posedness to the initial-value problem for the model and give the basic reproduction number TO0. In the case of a bounded spatial domain, we establish the local stability as well as the global stability of the disease-free and disease equilibria of the model. The methods to prove the local and the global stability are to analyze the corresponding characteristic equations and construct Lyapunov functionals, respectively. In the case of an unbounded spatial domain, by applying Schauder＇s fixed point theorem and the limiting arguments, we show that when R0 〉 1, there exists a constant c＊ 〉 0 such that the model admits positive traveling wave solutions connecting the disease-free and endemic equilibrium for c 〉 c＊, and when R0 〉 1 and c 〈 c＊, the model has no positive traveling wave solutions connecting them.
