The Belousov-Zhabotinski type of chemical reactions was studied. Dynamics of the unperturbed oscillating chemical system and subject to the external perturbations is considered. The system response to the external per...The Belousov-Zhabotinski type of chemical reactions was studied. Dynamics of the unperturbed oscillating chemical system and subject to the external perturbations is considered. The system response to the external periodic perturbation near the Hopf bifurcation point has been monitored. As a response to the external periodic perturbation of system, one obtains the synchronization oscillations, two-, three-and multiperiodic ones as well as obtain two types of chaos. The kinetic of such reactions is analyzed by time series. The Fourier transforms were used to analyze the frequency characteristics of the synchronized and chaotic states giving the different harmonic spectra. As further statistical characteristics the winding numbers and variation values of trajectories are calculated using a rotational model of processes in relation to the coherence parameter joint with perturbation period. For chaotic states the autocorrelation functions and correlation dimensions, which form an approximation of a fractal dimension D, have been calculated. Additionally, Lyapunov exponents were computed. Their positive values confirmed chaotic behavior.展开更多
文摘The Belousov-Zhabotinski type of chemical reactions was studied. Dynamics of the unperturbed oscillating chemical system and subject to the external perturbations is considered. The system response to the external periodic perturbation near the Hopf bifurcation point has been monitored. As a response to the external periodic perturbation of system, one obtains the synchronization oscillations, two-, three-and multiperiodic ones as well as obtain two types of chaos. The kinetic of such reactions is analyzed by time series. The Fourier transforms were used to analyze the frequency characteristics of the synchronized and chaotic states giving the different harmonic spectra. As further statistical characteristics the winding numbers and variation values of trajectories are calculated using a rotational model of processes in relation to the coherence parameter joint with perturbation period. For chaotic states the autocorrelation functions and correlation dimensions, which form an approximation of a fractal dimension D, have been calculated. Additionally, Lyapunov exponents were computed. Their positive values confirmed chaotic behavior.
