Piecewise two-dimensional maps and applications to cellular neural networks

Abstract

Of concern is a two-dimensional map T of the form T(x, y) = (y, F(y) - bx). Here F is a three-piece linear map. In this paper, we first prove a theorem which states that a semiconjugate condition for T implies the existence of Smale horseshoe. Second, the theorem is applied to show the spatial chaos of one-dimensional Cellular Neural Networks. We improve a result of Hsu [2000].