  A variety of nonlinear models of biological systems generate complex chaotic
behaviors that contrast with biological homeostasis, the observation that many
biological systems prove remarkably robust in the face of changing external or
internal conditions. Motivated by the subtle dynamics of cell activity in a
crustacean central pattern generator (CPG), this paper proposes a refinement of
the notion of chaos that reconciles homeostasis and chaos in systems with
multiple timescales. We show that systems displaying relaxation cycles while
going through chaotic attractors generate chaotic dynamics that are regular at
macroscopic timescales and are thus consistent with physiological function. We
further show that this relative regularity may break down through global
bifurcations of chaotic attractors such as crises, beyond which the system may
also generate erratic activity at slow timescales. We analyze these phenomena
in detail in the chaotic Rulkov map, a classical neuron model known to exhibit
a variety of chaotic spike patterns. This leads us to propose that the passage
of slow relaxation cycles through a chaotic attractor crisis is a robust,
general mechanism for the transition between such dynamics. We validate this
numerically in three other models: a simple model of the crustacean CPG neural
network, a discrete cubic map, and a continuous flow.
