The authors study bifurcations from a heteroclinic manifold connecting two non-hyperbolic equilibrium P-0 and P-1 for a n-dimensional dynamical system. They show that under some assumptions, each equilibrium P-i split...The authors study bifurcations from a heteroclinic manifold connecting two non-hyperbolic equilibrium P-0 and P-1 for a n-dimensional dynamical system. They show that under some assumptions, each equilibrium P-i splits into two equilibria <(P)over tilde (i)> and P-i(alpha), i = 0, 1, and find the Melnikov vector conditions assuring the existence of a heteroclinic orbit from P-1(alpha) to P-0(alpha) along directions that are tangent to the strong unstable (resp.strong stable) manifold of P-1(alpha) (resp.P-0(alpha)). The exponential trichotomy and the unified and geometrical method are used to prove their results.展开更多
In this paper we obtain a sufficient and necessary condition for a linear system to have exponential trichotomy and obtain that if a linear system has exponential trichotomy with trichotomy constants α and β, then t...In this paper we obtain a sufficient and necessary condition for a linear system to have exponential trichotomy and obtain that if a linear system has exponential trichotomy with trichotomy constants α and β, then the roughness of it is .展开更多
In this paper, we discuss the existence of pseudo-almost automorphic solutions to linear differential equation which has an exponential trichotomy~ and the results also hold for some nonlinear equations with the form ...In this paper, we discuss the existence of pseudo-almost automorphic solutions to linear differential equation which has an exponential trichotomy~ and the results also hold for some nonlinear equations with the form x＇（t） = f（t,x（t）） ＋ λg（t,x（t））, where f,g are pseudo-almost automorphic functions. We prove our main result by the application of Leray-Schauder fixed point theorem.展开更多
文摘The authors study bifurcations from a heteroclinic manifold connecting two non-hyperbolic equilibrium P-0 and P-1 for a n-dimensional dynamical system. They show that under some assumptions, each equilibrium P-i splits into two equilibria <(P)over tilde (i)> and P-i(alpha), i = 0, 1, and find the Melnikov vector conditions assuring the existence of a heteroclinic orbit from P-1(alpha) to P-0(alpha) along directions that are tangent to the strong unstable (resp.strong stable) manifold of P-1(alpha) (resp.P-0(alpha)). The exponential trichotomy and the unified and geometrical method are used to prove their results.
文摘In this paper we obtain a sufficient and necessary condition for a linear system to have exponential trichotomy and obtain that if a linear system has exponential trichotomy with trichotomy constants α and β, then the roughness of it is .
基金supported by the National Natural Science Foundation of China under Grant No.11126070 and 11201309the Natural Science Foundation of SZU(201111)+1 种基金supported the National Natural Science Foundation of China under Grant No.11026168 and 11201046the Fundamental Research Funds for the Central Universities in China(DUT12LK32,DUT13JS02)
文摘In this paper, we discuss the existence of pseudo-almost automorphic solutions to linear differential equation which has an exponential trichotomy~ and the results also hold for some nonlinear equations with the form x＇（t） = f（t,x（t）） ＋ λg（t,x（t））, where f,g are pseudo-almost automorphic functions. We prove our main result by the application of Leray-Schauder fixed point theorem.
