Periodic Orbits and Invariant Tori from a Semistable Limit Cycle in the Fast Dynamics

IntroductionIn the paper,the bifurcations of periodic or-bits and invariant tori of the following system wasstudied:x。=f(x,y) εh(t,x,y,ε)∈R2y。=εg(t,x,y,ε)∈R,0≤ε1(1)where h(t,x,y,ε)and g(t,x,y,ε)are T-periodicin t.For simplicity,the functions f,g and h areassumed to be sufficiently smooth in their argu-ments throughout this paper.In Ref.[1],Wiggins and Holmes called thesystems of form Eq.(1)as slowly varying oscilla-tors and pointed out that the systems taking theform occur as mo…     

Periodic Solutions of Periodic Delay Predator—Prey System with Nonmonotonic Functional Response

By using the continuation theorem of coincidence degree theory, sufficient conditions are obtained for the existence of positive periodic solutions of a delayed predator-prey system with nonmonotonic functional response in a periodic environment.     

Asymptotical Properties for Parabolic Systems of Neutral Type

Asymptotical properties for the solutions of neutral parabolic systems with Robin boundary conditions were analyzed by rising the inequality analysis. The oscillations problems for the neutral parabolic systems were considered and some oscillation criteria for the systems were established.