This paper deals with a class of quadratic Hamiltonian systems with quadratic perturbation. The authors prove that if the first order Melnikov function M1 (h) 0 and the second order Melnikov function M2(h) 0, then the origin of the Hamiltonian system with small perturbation is a center.
This paper deals with the questio n of global stability of the positive locally asymptotically stable equilibrium in a class of predator\|prey system of Gause\|typ e with Holling Ⅲ functional response. The Dulac’s criterion is applied and lia punov functions are constructed to establish the global stability.
Feng Jian\|wen, Zen Xian\|wu College of Mathematics and Computer Sicence, Wuhan University, Wuhan 430072,China
A theorem of Block and Franke is improved on the existence of periodic points for a map of a circle to itself and a proof which seems more understandable is given.
