Chaotic systems exhibit a number of characteristic signatures, from the so-called butterfly effect (a pronounced sensitivity to initial conditions that makes long-term predictions impossible), to the emergence of fractals. Researchers typically study this behavior in systems whose trajectories are permanently evolving: the dynamics are either nondissipative or driven by constantly acting forces. But what would happen in the common case of a dissipative system without energy input from its surroundings, in which all motion eventually dies out? Can such a system be chaotic?
According to a report in Physical Review Letters from Adilson Motter at Northwestern University, Illinois, and colleagues, even dissipative, nondriven systems can exhibit the hallmarks of chaos (the butterfly effect as well as fractals), albeit with key differences. They focus on a model system: a magnetic pendulum subject to the effect of gravity, magnetic forces, and air friction. They find the pendulum has the signatures of what they term “doubly transient chaos,” in which the classical parameters used to describe chaos (such as the rates at which trajectories settle towards an attractor) become time dependent and the trajectories sculpt, in phase space, structures that are fractal-like but not fully invariant upon magnification.
Such behavior may emerge in a broad range of systems, in particular those that would be chaotic if dissipation could be turned off, such as the evolution of chemical reactions toward equilibrium or the coalescence of binary stars as they lose energy to gravitational waves. The emergence of this form of transient chaos would imply these systems are far less predictable than expected. – Matteo Rini