The complex, fluctuating dynamics that abounds in nature is now easily monitored and analysed, applying either stochastic or deterministic methods. It has been demonstrated that complex systems far from thermodynamic equilibrium, especially living systems, often exhibit time-varying dynamics. To date they have been usually treated as stochastic. Here we focus on the non-autonomous properties of complex systems and propose a new class of dynamical systems. Namely, we assume that a basic dynamical unit which inherently possesses an internal source of energy, is continuously perturbed by the environment and maintains its stability by adjusting the rate of exchange of energy and matter with the environment. We provide a mathematical formalism for such systems, combining the recent theory of pullback attractors with the theory of self-sustained oscillators. We name the new class of systems as chronotaxic and, based on measured data, show that the heart possesses properties characteristic of chronotaxic systems. This means that its dynamics is largely deterministic, which opens new possibilities for diagnosis and prediction. We expect that many complex systems will be identified as chronotaxic and that their models will become much simpler and more realistic.