Asymptotic theory for the circuit envelope analysis is developed in this paper.A typical feature of circuit envelope analysis is the existence of two significantly distinct timescales:one is the fast timescale of carr...Asymptotic theory for the circuit envelope analysis is developed in this paper.A typical feature of circuit envelope analysis is the existence of two significantly distinct timescales:one is the fast timescale of carrier wave,and the other is the slow timescale of modulation signal.We first perform pro forma asymptotic analysis for both the driven and autonomous systems.Then resorting to the Floquet theory of periodic operators,we make a rigorous justification for first-order asymptotic approximations.It turns out that these asymptotic results are valid at least on the slow timescale.To speed up the computation of asymptotic approximations,we propose a periodization technique,which renders the possibility of utilizing the NUFFT algorithm.Numerical experiments are presented,and the results validate the theoretical findings.展开更多
The influence of parameter mismatches on multirhythmic patterns in chains of coupled Rossler circuits are explored experimentally. The parameter mismatches in coupled chaotic oscillators are found to help form a kind ...The influence of parameter mismatches on multirhythmic patterns in chains of coupled Rossler circuits are explored experimentally. The parameter mismatches in coupled chaotic oscillators are found to help form a kind of multirhythmic pattern as reported in chains of biological coupled oscillators [Phys. Rev. Lett. 92 228102]. Moreover, a new type of multirhythmic pattern based on the envelope of time series is observed.展开更多
基金supported by the National Key R&D Program of China(Grant Nos.2019YFA0709600,2019YFA0709602)by the Beijing Natural Science Foundation(Grant No.Z220003).
文摘Asymptotic theory for the circuit envelope analysis is developed in this paper.A typical feature of circuit envelope analysis is the existence of two significantly distinct timescales:one is the fast timescale of carrier wave,and the other is the slow timescale of modulation signal.We first perform pro forma asymptotic analysis for both the driven and autonomous systems.Then resorting to the Floquet theory of periodic operators,we make a rigorous justification for first-order asymptotic approximations.It turns out that these asymptotic results are valid at least on the slow timescale.To speed up the computation of asymptotic approximations,we propose a periodization technique,which renders the possibility of utilizing the NUFFT algorithm.Numerical experiments are presented,and the results validate the theoretical findings.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11262006 and 11062002)the Science and Technology Project of Jiangxi Province,China(Grant Nos.GJJ12330 and 2010GQW0021)
文摘The influence of parameter mismatches on multirhythmic patterns in chains of coupled Rossler circuits are explored experimentally. The parameter mismatches in coupled chaotic oscillators are found to help form a kind of multirhythmic pattern as reported in chains of biological coupled oscillators [Phys. Rev. Lett. 92 228102]. Moreover, a new type of multirhythmic pattern based on the envelope of time series is observed.
