aDepartment of Mathematics, Shandong University, Jinan, Shandong 250100, PR China
bDepartment of Applied Mathematics, The University of Western Ontario, London, Ont., Canada N6A 5B7
Abstract:
This paper is concerned with chaos induced by strictly turbulent maps in noncompact sets of complete metric spaces. Two criteria of chaos for such types of maps are established, and then a criterion of chaos, characterized by snap-back repellers in complete metric spaces, is obtained. All the maps presented in this paper are proved to be chaotic either in the sense of both Li–Yorke and Wiggins or in the sense of both Li–Yorke and Devaney. The results weaken the assumptions in some existing criteria of chaos. Several illustrative examples are provided with computer simulation.