Chaos linked to memory-term distortions in Rössler and Lorenz systems

Determine whether the chaotic features of the Rössler and Lorenz systems are linked to distortions introduced by the memory terms in the solutions of their respective second-order integro-differential equations.

Background

The authors derive IDE formulations for both the Rössler and Lorenz systems that include memory terms in the frictional and elastic components. They report that, in the chaotic regime, the rate of change of kinetic energy per cycle is positive and irregular, and suggest that memory terms play a central role in the systems’ energy dynamics and self-oscillation.

Based on these observations, they conjecture a direct link between the presence of memory terms and the emergence of chaotic features, specifically through distortions they induce in the solutions of the equations of motion.