LORENZ EQUATION AND CHUA’S EQUATION

Abstract

The dynamical properties of two classical paradigms for chaotic behavior are reviewed—the Lorenz and Chua’s Equations—on a comparative basis. In terms of the mathematical structure, the Lorenz Equation is more complicated than Chua’s Equation because it requires two nonlinear functions of two variables, whereas Chua’s Equation requires only one nonlinear function of one variable. It is shown that most standard routes to cbaos and dynamical phenomena previously observed from the Lorenz Equation can be produced in Chua’s system with a cubic nonlinearity. In addition, we show other phenomena from Chua’s system which are not observed in the Lorenz system so far. Some differences in the topological geometric models are also reviewed. We present some theoretical results regarding Chua’s system which are absent for the Lorenz system. For example, it is known that Chua’s system is topologically conjugate to the class of systems with a scalar nonlinearity (except for a measure zero set) and is therefore canonical in this sense. We conclude with some reasons why Chua’s system can be considered superior or more suitable than the Lorenz system for various applications and studies.