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- Title
A Box-Counting Method for Characteristic Diagnosis of Nonlinear Dynamical Systems.
- Authors
Zhang, Zhengyuan; Dai, Liming
- Abstract
An innovative box-counting method is developed in this research for diagnozing the nonlinear characteristics of dynamical systems. With the method developed, an approach that depicts the evolutionary process on Poincaré maps is established such that the nonlinear dynamical characteristics of the transient and stable process of the system can be graphically and quantitatively identified. A Duffing–van der Pol system is adopted in the research to demonstrate an application of the method. A diagram graphically describing the periodic, quasiperiodic, chaotic, and transient chaotic regions of the system's responses is constructed based on the method. Furthermore, the nature of different box-point curves is explained based on the topology of chaos and quasiperiodicity. The method developed shows innovation and efficiency in diagnozing nonlinear dynamical systems based on the topological properties of general nonlinear systems.
- Subjects
POINCARE maps (Mathematics); NONLINEAR dynamical systems; DIAGNOSIS methods; NONLINEAR systems; TOPOLOGICAL property
- Publication
International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, 2023, Vol 33, Issue 12, p1
- ISSN
0218-1274
- Publication type
Article
- DOI
10.1142/S0218127423501390