Search

This paper is concerned with the chaos of discrete dynamical systems. A new concept of heteroclinic cycles connecting expanding periodic points is raised, and by a novel method, we prove an invariant subsystem is topologically conjugate to the one-side symbolic system. Thus, heteroclinic cycles imply chaos in the sense of Devaney. In addition, if a continuous differential map h has heteroclinic cycles in ℝ n , then g has heteroclinic cycles with h − g C 1 being sufficiently small. The results demonstrate C 1 structural stability of heteroclinic cycles. In the end, two examples are given to illustrate our theoretical results and applications. [ABSTRACT FROM AUTHOR]

In this paper, we consider a hybrid network model of delayed predator-prey Gompertz systems with impulsive diffusion between two patches, in which the patches represent nodes of the network such that the prey population interacts locally in each patch and diffusion occurs along the edges connecting the nodes. Using the discrete dynamical system determined by the stroboscopic map which has a globally stable positive fixed point, we obtain the global attractive condition of predator-extinction periodic solution for the network system. Furthermore, by employing the theory of delay functional and impulsive differential equation, we obtain sufficient condition with time delay for the permanence of the network. [ABSTRACT FROM AUTHOR]

This paper introduces a new Cournot duopoly game and gives an applied study for price discrimination in a market by dynamic methods. One of two oligopolies has two different prices for a homogeneous product, while the other charges one kind of price. It is found that there is only one stable equilibrium for the discrete dynamic system, and a corresponding stable condition is given. Using a discriminative price is not always beneficial to a firm in equilibrium. If both oligopolies carry out price discrimination, the market's average price is lower than when only one oligopoly does it. The results are verified by numerical simulations. [ABSTRACT FROM AUTHOR]