Conservative dynamics in a novel class of 3D generalized thermostatted systems

Abstract

This paper reports a method to derive a novel class of 3D generalized thermostatted oscillators from a simple damped harmonic oscillator. Its detailed procedure is obtained through a mathematical derivation. Then, we propose an example system to show the effectiveness of the method. Furthermore, the numerical analysis is performed to investigate its rich conservative dynamics, including chaotic sea, hierarchical invariant tori, and the coexistence of chaotic seas and invariant tori with islands-around-islands hierarchy, even if there are three dissipative terms in the example system. To verify the existence of conservative chaos at the physical level, an analog circuit is presented to observe the existing conservative chaotic flows in National Instruments multisim. We finally provide two systems, which can produce conservative chaotic flows with more complicated topologies, and draw our conclusions.