| Mark Edelman |
| Yeshiva University, USA |
Abstract: Regular and chaotic dynamics of nonlinear systems are defined by the structure of periodic points. Fractional systems do not have periodic points except for the fixed points, but they may have asymptotically periodic points. The equations defining asymptotically periodic points in general fractional maps defined as convolutions with power-like kernels (whose particular forms include various known definitions of fractional maps) are quite complicated but can be written in a unified form. Using the fractional logistic map as an example, we demonstrate the current state of the investigation of stability and bifurcations in fractional systems and discuss the possibility of the existence of the fractional Feigenbaum numbers.