The Two Variable Function Constitutes a Necessary Condition of Chaotic Dynamical Systems

Abstract

This article works on the chaotic characteristic of a dynamic system which consists of two variable function. It derives two necessary conditions for this chaotic system based on differential Taylor expansion. Which confirmed the sum of absolute value of the partial derivative on the two variable function in the periodic point of x,y is not greater than 1,and further presents the necessary conditions for product chaos which is described by recursive determinant. The recursive determinant calculation is simple, and it is suitable for a scale to measure as chaotic characteristics.