Among the death due to the cardiac problems, the arrhythmias play a major role, particularly the atrial disorders. This alarming situation attracts an intense research, but it is still limited by the availability of experimental models to reproduce the triggering mechanisms of arrhythmias at the cellular level and extensions of these anomalies. Whether they occur on a healthy or pathological heart, or they are benign or potentially dangerous (risk of sudden death), the arrhythmias constitute an important chapter of the cardiology. This thesis is interested in the studying and modeling of the arrhythmias at a cellular scale. Thus the problems of this thesis can be summarized briefly by the following key words: non-linear system, cardiac models, spiral waves, defibrillation.... One of the questions is: how to optimize the defibrillation process with electrical stimulation. In fact, the electrical stimulation can not only terminate the fibrillation but also possibly generate new waves in cardiac tissue. This last effect of stimulation seems inevitable, when the energy of stimulation exceeds certain thresholds. So here arises another question: how to terminate fibrillation by applying stimulation under the threshold to avoid other problems. Among the possible ways, we directed ourselves towards a hybrid strategy of stimulation (combination of sodium channel modification) which makes it possible to achieve this goal. We also worked on an experimental MEA (Multi Electrodes Array) system. This system allows us to acquire electrical signals of cells culture in vitro of new-born rats. As previously mentioned, electrical stimulation can induce new waves in cardiac tissue, this was observed and confirmed in experiments in form of spiral waves. Since the data acquired can be disturbed and erroneous, the wavelet denoising has been used. The wrong signals are eliminated by the "singular value decomposition". Since the nonlinearity of MEA signals is confirmed by "surrogate data analysis", then we construct the bifurcation map for the periods of MEA signals. In the map, a period-doubling phenomenon is observed which is generally considered as the key feature leading to chaos. The Poincaré map showed that there exists an important difference between the normal signals and the arrhythmic ones, which presents some potential diagnostic tools. In the last part of this thesis, in order to retrieve more information from these signals, the method of phase space reconstruction is applied. Their embedding dimension is determined by false nearest neighbor. As for the time lag, three methods have been compared (by autocorrelation function, mutual information and third one is in function of the embedding dimension). In fact, the first one gives a more pertinent time lag. In the reconstructed phase space, the potential attractors projected from 4th and trajectories of the normal signals and the arrhythmic signals are quite different. The next work will be orientated towards the "hybrid stimulation" at the theoretical level. Then we will test this defibrillation strategy of hybrid stimulation on our platform MEA. At the same time, we continue to explore the acquired signals with others nonlinear methods.
