Transient Dynamics of the Lorenz System with a Parameter Drift

Nonautonomous dynamical systems help us to understand the implications of real which are in contact with their environment as it actually occurs nature. Here, we focus on where a parameter changes time at small but non-negligible rates before settling stable value, by using Lorenz system for illustration. This kind commonly show long-term transient dynamics previous sudden transition steady state. can be explained crossing bifurcation associated frozen-in system. We surprisingly uncover scaling law relating duration rate change case chaotic attractor is involved. Additionally, analyze viability recovering reversing its original an alternative control theory drifts. obtain relationship between paramater and number trajectories that tip back initial corresponding