The coexistence of different dynamical regimes of cardiac cell-model at a fixed set of stimulation parameters, i.e.
multistability, revealed by noise is presented in this paper. Numerical simulations are performed using Luo-Rudy (LR1)
action potential model. Numerical experiments with LR1 model conducted via noisy periodical stimulation showed the
coexistence of several periodic rhythms. Weak noise in period of stimulation causes a hopping process between all the
(meta-) stable rhythms of cell-model. This process is reflected in several parallel branches of the bifurcation diagram:
noise unveils new, invisible before, stable rhythms which could appear in this model at different initial conditions. The
phenomenon of multistability is directly evidenced by other numerical experiments: we have established the
multistability property of a cell consisting in the fact that different initial conditions of stimulation (different extrasystole
application times) lead to different stable periodic rhythms. We have obtained the shaping of attraction basins on the
action potential curves. Such basins of attraction contain a set of initial conditions which determinate a stable periodic
rhythm. We have found a close association between the attraction basins of the complex rhythms on the curves of action
potential and the cardiac vulnerable windows on ECG record, during which extra stimuli can induce life threatening
arrhythmias. Obtained results allow us to make a conclusion that multistability is very important for the electrical
conduction system of the heart from the cell level to the integrated function of the heart.
The signal-to-noise ratio characterizing data transmission using modulation of the parameters of the mapping generating a chaotic sequence is estimated. It is shown that, in systems using a control parameter to introduce information, the output signal-to-noise ratio is reduced as compared to the input value. It is found that noise fluctuations in the information parameter measured depend on signal fluctuations at several adjacent sample points. A multichannel system is considered. It is noted that the increase in the number of channels results in the decrease in the output signal-to-noise ratio due to both addition of the noise components of the adjacent sample elements and exponential growth of errors in the reconstructed parameters of chaotic systems. A decrease in the output signal-to-noise ratio is found to be partly compensated by impeding unauthorized access to the information transmitted.
The possibility of measuring weak noise in nonlinear systems on the basis of the phenomenon of prebifurcation noise amplification is proposed. This phenomenon is shortly outlined with special emphasis on the transition from linear regime to the regime of nonlinear saturation of fluctuation amplification. Estimates of the fluctuation variance are obtained both for the linear (away from the bifurcation threshold) and for the nonlinear regime (in the vicinity of the bifurcation threshold). These estimates have proved to be efficient for two simple bifurcation models: period doubling bifurcation and bifurcation of spontaneous symmetry breaking. Theoretical estimates have proved to be in good agreement with the results of numerical simulation. It is shown, that in the saturation regime, fluctuation variance is proportional to the square root of external noise variance, whereas in linear regime, fluctuation variance is proportional to noise variance. The approach to weak noise measuring is based on comparison of maximal fluctuation variance at the bifurcation threshold with variance away from that threshold. The applicability of this approach is limited by the necessity to perform rather long-term observations.