Abstract
Background and Objectives: The basic model of study is the simplest three - dimensional map with two-frequency and three-frequency quasiperiodicity at adding of noise. The main objective is to examine the effect of noise on the quasiperiodic Hopf bifurcation of the 3-torus birth. Materials and Methods: To study the torus map in the presence of noise we use such numerical methods as computing of Lyapunov exponents, calculation of Fourier spectra, drawing of attractor portraits. Results: Quasi-periodic bifurcations under the influence of noise occupy certain intervals in the parameter, but their main classification features (equality or not of the corresponding Lyapunov exponents) are preserved at the qualitative level. Conclusion: We considered the effect of noise on the simplest system with two- and three-frequency quasiperiodicity. The three-frequency quasiperiodicity is preserved at certain noise amplitudes, but then turns into a two-frequency one. In the Fourier spectra, this process develops according to the scenario of "blurring" the noise components of the corresponding spectral components.
Highlights
Background and ObjectivesThe basic model of study is the simplest three - dimensional map with two-frequency and three-frequency quasiperiodicity at adding of noise
The main objective is to examine the effect of noise on the quasiperiodic Hopf bifurcation of the 3-torus birth
We considered the effect of noise on the simplest system with two- and three-frequency quasiperiodicity
Summary
Background and ObjectivesThe basic model of study is the simplest three - dimensional map with two-frequency and three-frequency quasiperiodicity at adding of noise. The main objective is to examine the effect of noise on the quasiperiodic Hopf bifurcation of the 3-torus birth. Materials and Methods: To study the torus map in the presence of noise we use such numerical methods as computing of Lyapunov exponents, calculation of Fourier spectra, drawing of attractor portraits. 1. Карты ляпуновских показателей отображения (2): а – ε = 0, б – ε = 0.01, в – ε = 0.05, г – ε = 0.08 (цвет online)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have