Self-reproducing dynamics in a two-dimensional discrete map
Key Laboratory of Hunan Province on Information Photonics and Freespace Optical Communications, Hunan Institute of Science and Technology, 414006, Yueyang, China
2 School of Physics and Electronics, Central South University, 410083, Changsha, China
Accepted: 4 May 2021
Published online: 5 June 2021
This paper mainly explores the self-reproducing dynamics in discrete-time system by constructing a two-dimension map with infinitely many fixed points. Theoretical analysis shows that the attractor of the map can not only be non-destructively reproduced by the initial values of all state variables along all axis directions, but can also be non-destructively reproduced by the parameter along all axis directions. The numerical simulations of bifurcation diagram, Lyapunov exponent, phase portrait and iterative sequence are carried out to further confirm the theoretical results. The self-reproducing behavior of different type of attractors and the corresponding iterative sequences are also confirmed by the experimental measurements performed on the DSP-based platform. This map is especially suitable for chaos-based engineering applications since the offset can be periodically switched by the initial condition and parameter on the premise of keeping robust dynamical behavior.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2021