Abstract In this paper, a discrete Leslie-Gower predator-prey system with Michaelis-Menten type harvesting is studied. Conditions on the existence and stability of fixed points are obtained. It shown that can undergo fold bifurcation, flip Neimark-Sacker bifurcation by using center manifold theorem theory. Numerical simulations presented to illustrate main theoretical results. Compared continuo...

The stability and Hopf bifurcation of gene expression models with a mechanism delayed state feedback are considered. An effective algorithm for the calculations on delay stable interval equilibrium point, direction, bifurcating periodic solution is also proposed. τ-decomposition strategy applied to tackle issue local stability, explicit formula provided. In addition, asymptotical behaviors solu...

The formality theorem for Hochschild chains of the algebra of functions on a smooth manifold gives us a version of the trace density map from the zeroth Hochschild homology of a deformation quantization algebra to the zeroth Poisson homology. We propose a version of the algebraic index theorem for a Poisson manifold which is based on this trace density map. 1991 MSC: 19K56, 16E40.

In this paper, we investigate a delayed predator–prey model with prey refuge where the predator population eats according to Beddington–DeAngelis type functional response. Firstly, consider existence of equilibrium points. By analyzing corresponding characteristic equations, local stability trivial equilibrium, predator–extinction balance, and coexistence system are discussed, Hopf bifurcations...

A theory of tubular neighborhoods for strata in manifold stratified spaces is developed. In these topologically stratified spaces, manifold stratified approximate fibrations and teardrops play the role that fibre bundles and mapping cylinders play in smoothly stratified spaces. Applications include a multiparameter isotopy extension theorem, neighborhood germ classification and a topological ve...

In this paper,we deeply research Lagrange interpolation of n-variables and give an application of Cayley-Bacharach theorem for it. We pose the concept of sufficient intersection about s(1 ≤ s ≤ n) algebraic hypersurfaces in n-dimensional complex Euclidean space and discuss the Lagrange interpolation along the algebraic manifold of sufficient intersection. By means of some theorems ( such as Bez...

We use convex decomposition theory to (1) reprove the existence of a universally tight contact structure on every irreducible 3-manifold with nonempty boundary, and (2) prove that every toroidal 3-manifold carries infinitely many nonisotopic, nonisomorphic tight contact structures. It has been known for some time that there are deep connections between the theory of taut foliations and tight co...

In this paper, we give a survey of various sphere theorems in geometry. These include the topological sphere theorem of Berger and Klingenberg as well as the differentiable version obtained by the authors. These theorems employ a variety of methods, including geodesic and minimal surface techniques as well as Hamilton’s Ricci flow. We also obtain here new results concerning complete manifolds w...