| Chunbiao Li |
| Nanjing University of Information Science and Technology, China |
Abstract: A parameter in a dynamical system often introduces different evolutions for bifurcations; Meanwhile, for the reason of multistability, the initial condition also triggers different dynamics. Therefore, typically Lyapunov exponents of the system are applied to detect and manage the dynamical behavior of a system. However, with the study and observation of the dynamics of a system, it has been found that when some parameters in a system change, the Lyapunov exponents may remain unchanged except the amplitude and offset of the attractor are modified; Meanwhile in a multistable system, when the initial value changes, those attractors share different structures such as being of symmetry, or conditional symmetry or other flexible distribution under the same Lyapunov exponents. In this case, the unified Lyapunov exponents cover a great variety of dynamics. In order to apply those dynamical systems to engineering applications reliably, the special complex dynamics should be effectively detected, tracked, and analyzed properly. In this work we aim to demonstrate the complex dynamics under the unified Lyapunov exponents, specifically including amplitude control and offset boosting of a chaotic attractor; And the symmetry and conditional symmetry of a chaotic system and the self-reproducing of chaotic attractor are discussed exhaustively to realize a reliable chaos-based application.