Conservative chaotic flow generated via a pseudo-linear system

Abstract

Analysis of nonlinear autonomous systems has been a popular field of study in recent decades. As a noticeable nonlinear behavior, chaotic dynamics has been intensively investigated since Lorenz discovered the first physical evidence of chaos in his famous equations. Although many chaotic systems have been ever reported in the literature, a systematic and qualitative approach for chaos generation is still a challenging issue. Recently, we have developed an analysis tool which provides globally valid results about the qualitative behavior of some nonlinear systems based on their pseudolinear form of representation. In this paper, it is applied to generate conservative chaos by focusing on the essential qualitative attribute of conservative chaotic behavior. This feature is the continual stretching and folding of system trajectories which never settle down to a periodic regime. Indeed, it is tried to create this quality of behavior through the aforementioned qualitative analysis tool. The proposed approach helps us to generate a new class of chaotic systems with highly remarkable characteristics. The most elegant one is its almost parameter independency for chaos generation; There is no need for a trial-and-error mechanism to find the exact parameters’ values in order to produce chaotic behavior. It is shown that the system exhibits conservative chaotic dynamics for almost all parameters’ values. The chaotic behavior of the derived system is verified through the analysis of Lyapunov exponents and dimension as well. Besides, the frequency power spectrum analysis is also performed in order to put more emphasis on the chaotic behavior of the system.