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A variety of nonlinear models of biological systems generate complex chaoticbehaviors that contrast with biological homeostasis, the observation that manybiological systems prove remarkably robust in the face of changing external orinternal conditions. Motivated by the subtle dynamics of cell activity in acrustacean central pattern generator (CPG), this paper proposes a refinement ofthe notion of chaos that reconciles homeostasis and chaos in systems withmultiple timescales. We show that systems displaying relaxation cycles whilegoing through chaotic attractors generate chaotic dynamics that are regular atmacroscopic timescales and are thus consistent with physiological function. Wefurther show that this relative regularity may break down through globalbifurcations of chaotic attractors such as crises, beyond which the system mayalso generate erratic activity at slow timescales. We analyze these phenomenain detail in the chaotic Rulkov map, a classical neuron model known to exhibita variety of chaotic spike patterns. This leads us to propose that the passageof slow relaxation cycles through a chaotic attractor crisis is a robust,general mechanism for the transition between such dynamics. We validate thisnumerically in three other models: a simple model of the crustacean CPG neuralnetwork, a discrete cubic map, and a continuous flow.

Reliability and robustness of oscillations in some slow-fast chaotic systems