Similar articles

Abstract: This study proposes a method for analyzing synchronization in oscillator systems, illustrated by modeling the dynamics of a circuit of two resistively coupled pulse oscillators. The dynamic characteristic of synchronization is the fuzzy entropy (FuzzyEn), which is calculated from a time series composed of the ratios of the number of pulse periods (subharmonic ratio, SHR) at phase-locking intervals. Low and high entropy values indicate strong and weak synchronization between the two oscillators, respectively. The proposed method effectively visualizes synchronized modes of the circuit using entropy maps of synchronization states. In addition, a classification of synchronization states is proposed based on the dependency of FuzzyEn on the embedding vector length of the SHR time series. An extension of this method for analyzing non-pulse (non-spike) signals is demonstrated using the example of phase–phase coupling rhythms of the local field potential of the rat hippocampus. The proposed entropy-statistical approach, using integers and pulse signal forms, is well-suited for signal synchronization analysis and can be implemented on digital mobile platforms.

熵统计法在振荡锁相检测中的应用

[1]Alter O, Brown PO, Botstein D, 2000. Singular value decomposition for genome-wide expression data processing and modeling. Proc Natl Acad Sci USA, 97(18):10101-10106.

[2]Belluscio MA, Mizuseki K, Schmidt R, et al., 2012. Cross-frequency phase-phase coupling between theta and gamma oscillations in the hippocampus. J Neurosci, 32(2):423-435.

[3]Biagi PF, Piccolo R, Ermini A, et al., 2001. Possible earthquake precursors revealed by LF radio signals. Nat Haz Earth Syst Sci, 1(1-2):99-104.

[4]Bonet-Jara J, Quijano-Lopez A, Morinigo-Sotelo D, et al., 2021. Sensorless speed estimation for the diagnosis of induction motors via MCSA. Review and commercial devices analysis. Sensors, 21(15):5037.

[5]Boriskov P, 2024. Chaotic discrete map of pulse oscillator dynamics with threshold nonlinear rate coding. Nonl Dyn, 112(5):3917-3933.

[6]Boriskov P, Putrolaynen V, Velichko A, et al., 2024. Entropy-based detection of synchronization of pulse oscillators: a comparative analysis of entropic measures. Proc SPIE 13217, 3rd Int Conf on Digital Technologies, Optics, and Materials Science, Article 132170Y.

[7]Chen WT, Wang ZZ, Xie HB, et al., 2007. Characterization of surface EMG signal based on fuzzy entropy. IEEE Trans Neur Syst Rehabil Eng, 15(2):266-272.

[8]Chou J, Bramhavar S, Ghosh S, et al., 2019. Analog coupled oscillator based weighted Ising machine. Sci Rep, 9(1):14786.

[9]Cui LL, Wang HB, Zhao DZ, et al., 2024. Synchronous odd symmetric transform for rolling bearing fault diagnosis. Measurement, 226:114184.

[10]Delgado-Bonal A, Marshak A, 2019. Approximate entropy and sample entropy: a comprehensive tutorial. Entropy, 21(6):541.

[11]Ishikawa A, Mieno H, 1979. The fuzzy entropy concept and its application. Fuzzy Sets Syst, 2(2):113-123.

[12]Li H, Zhang CC, Zhang Y, et al., 2023. A fractional-N frequency synthesizer with phase synchronization and programmable phase control capability. Microelectron J, 142:105996.

[13]Lowet E, Roberts MJ, Bonizzi P, et al., 2016. Quantifying neural oscillatory synchronization: a comparison between spectral coherence and phase-locking value approaches. PLoS ONE, 11(1):e0146443.

[14]Mallick A, Bashar MK, Truesdell DS, et al., 2020. Using synchronized oscillators to compute the maximum independent set. Nat Commun, 11(1):4689.

[15]Nikonov DE, Csaba G, Porod W, et al., 2015. Coupled-oscillator associative memory array operation for pattern recognition. IEEE J Explor Sol State Comput Dev Circ, 1:85-93.

[16]Park J, Mackay S, Wright E, 2003. Preface. In: Park J, Mackay S, Wright E (Eds.), Practical Data Communications for Instrumentation and Control. Newnes, Oxford, p.xi-xiii.

[17]Pikovsky A, Rosenblum M, Kurths J, et al., 2002. Synchronization: a universal concept in nonlinear science. Am J Phys, 70(6):655.

[18]Rabiner LR, Gold B, Yuen CK, 1978. Theory and application of digital signal processing. IEEE Trans Syst Man Cybern, 8(2):146.

[19]Ramírez E, Ruipérez-Campillo S, Castells F, et al., 2024. Novel synchronization method for vectorcardiogram reconstruction from ECG printouts: a comprehensive validation approach. Biomed Signal Process Contr, 91:106027.

[20]Romera M, Talatchian P, Tsunegi S, et al., 2018. Vowel recognition with four coupled spin-torque nano-oscillators. Nature, 563(7730):230-234.

[21]Scheffer-Teixeira R, Tort ABL, 2016. On cross-frequency phase-phase coupling between theta and gamma oscillations in the hippocampus. eLife, 5:e20515.

[22]Schüßler HW, Steffen P, 1998. Halfband filters and Hilbert transformers. Circ Syst Signal Process, 17(2):137-164.

[23]Velichko A, 2019. A method for evaluating chimeric synchronization of coupled oscillators and its application for creating a neural network information converter. Electronics, 8(7):756.

[24]Velichko A, Belyaev M, Putrolaynen V, et al., 2018a. Modeling of thermal coupling in VO₂-based oscillatory neural networks. Sol-State Electron, 139:8-14.

[25]Velichko A, Belyaev M, Putrolaynen V, et al., 2018b. Thermal coupling and effect of subharmonic synchronization in a system of two VO₂ based oscillators. Sol-State Electron, 141:40-49.

[26]Wang TS, Roychowdhury J, 2019. OIM: oscillator-based Ising machines for solving combinatorial optimisation problems. Proc 18^th Int Conf on Unconventional Computation and Natural Computation, p.232-256.

[27]Xu XX, Zheng CG, Zhang T, 2013. Reduction in LFP cross-frequency coupling between theta and gamma rhythms associated with impaired STP and LTP in a rat model of brain ischemia. Front Comput Neurosci, 7:27.

[28]Zheng CG, Bieri KW, Hsiao YT, et al., 2016. Spatial sequence coding differs during slow and fast gamma rhythms in the hippocampus. Neuron, 89(2):398-408.