Noninvasive mechanical ventilation is commonly applied to patients with chronic respiratory failures, mostly at home during night, and using a bilevel positive pressure support mode. The pressure in the ventilatory circuit is controlled by the ventilator. Patient’s inspiratory effort triggers the machine to switch from the low ventilatory pressure (Plv) with which the patient expires to the high ventilatory pressure (Phv). Commonly, Plv < Phv at least by about 5 cmH2O. The synchronyzation between patient breathing cycle and machine cycle is not always optimal and asynchrony events can be common during ventilation in a clinical context. The main asynchrony event is when patient’s inspiratory effort does not trigger the pressurization . It can be observed when the patient’s respiratory muscles are too weak and/or when there are nonintentional leaks , but this is not necessarily the case and it remains an open question to fully explain their occurrence .
In the present study, a group of subjects (Tab. I) was monitored during short sessions of noninvasive ventilation. The resulting data were already investigated in Ref.  but their chaotic nature was not addressed. All subjects were in stable condition during the procedure, as assessed by clinical examination and arterial blood gas. The subjects were ventilated in a quiet seated position using an Smartair ST (Airox, Paris, France) ventilator with an air filter (BB2000APS, Pall, Newquay, UK) to prevent bacterial contamination. It was asked to the subjects to breath as normally as possible. The ventilator was set in a pressure support mode without backup frequency. In most cases, the switch from Phv to Plv was triggered when the flow decreased below 75% of the maximal value of the flow during the running cycle. Pressure Plv was set to 4 cmH2O in the present study. For each Phv value between 10 and 20 cmH2O (with 2 cmH2O increments), a 10 min period was recorded once a stable breathing pattern was observed. During each measurement session, great care was taken to avoid leaks or to estimate them for optimizing the synchronization patients and their ventilators .
All patients used a well-fitting full face mask (Mirage NV, Resmed, North Ride, Australia). A Whisper Swivel ii exhalation port (Respironics, Pittsurgh, PA) was inserted in the ventilatory circuit to avoid CO2 rebreathing. Measurements of the airflow Qt were performed using a pneumotachometer Fleisch #2 (Metabo, Lausanne, Switzerland) connected to a pressure transducer TSD 160A (Biopac Systems, Goletta, CA). The pneumotachometer was inserted between the full face mask and the exhalation port. Airway pressure Pt>/sub> was measured with a differential pressure transducer DP15 (Validyne, Los Angeles, CA) near the pneumotachometer. All signals were sampled at 100 Hz using an acquisition system (MP150, Biopac Systems, Goletta, CA) with the data acquisition software Acqknowledge ACK100. For details of the protocol the reader is referred to . These data were collected by Linda Achour during her Ph.D. Thesis.
Some chaotic global models were recently obtained from some of these data sets 
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