Mandelbrot set in coupled logistic maps and in an electronic experiment.
We suggest an approach to constructing physical systems with dynamical characteristics of the complex analytic iterative maps. The idea follows from a simple notion that the complex quadratic map by a variable change may be transformed into a set of two identical real one-dimensional quadratic maps with a particular coupling. Hence, dynamical behavior of similar nature may occur in coupled dissipative nonlinear systems, which relate to the Feigenbaum universality class. To substantiate the feasibility of this concept, we consider an electronic system, which exhibits dynamical phenomena intrinsic to complex analytic maps. Experimental results are presented, providing the Mandelbrot set in the parameter plane of this physical system.
Isaeva
O B
OB
Institute of Radio-Electronics, Russian Academy of Sciences, Zelenaya 38, Saratov 410019, Russian Federation.
Kuznetsov
S P
SP
Ponomarenko
V I
VI