If we allow non-smooth or discontinuous functions in definition of an evolution operator for dynamical systems, then situations of quasi-hyperbolic chaotic dynamics often occur like, for example, on attractors in model Lozi map and in Belykh map.
We consider an autonomous system constructed as modification of the logistic differential equation with delay that generates successive trains of oscillations with phases evolving according to chaotic maps. The system contains two feedback loops characterized by two generally distinct retarding time parameters. In the case of their equality, chaotic dynamics is associated with the Smale–Williams attractor that corresponds to the double-expanding circle map for the phases of the carrier of the oscillatory trains.
New computationally efficient model of cardiac activity is introduced. The model is a fourdimensional map based on wellknown Luo–Rudy model. Capabilities of the model in replication of the basic cardiac cells’ properties are shown. Analysis of relationship between changes in individual parameters of the model and biophysical processes in real cardiac cells has been made. The model can reproduce two basic activity modes such as excitable and oscillatory regimes. Bifurcation mechanisms of transitions of between these regimes are investigated using phase space analysis.
