[1] A. S. Pikovsky, M. Rosenblum, J. Kurths. Synchronization: A Unified Approach to Nolinear Science(2001).

[2] R. Brown, L. Kocarev. A unifying definition of synchronization for dynamical systems. Chaos, 10, 344-349(2000).

[3] L. Glass, M. C. Mackey. From Clocks to Chaos: The Rhythms of Life(1988).

[4] A. T. Winfree. The Geometry of Biological Time(2001).

[5] A. Goldbeter. Biochemical Oscillations and Cellular Rhythms: The Molecular Bases of Periodic and Chaotic Behaviour(1996).

[6] A. F. Taylor, M. R. Tinsley, F. Wang, Z. Y. Huang, K. Showalter. Dynamical quorum sensing and synchronization in large populations of chemical oscillators. Science, 323, 614-617(2009).

[7] S. H. Strogatz. Sync: The Emerging Science of Spontaneous Order(2003).

[8] S. C. Manrubia, A. S. Mikhailov, D. H. Zanette. Emergence of Dynamical Order: Synchronization Phenomena in Complex Systems(2004).

[9] S. Bregni. Synchronization of Digital Telecommunications Networks(2002).

[10] M. Aspelmeyer, T. J. Kippenberg, F. Marquardt. Cavity optomechanics. Rev. Mod. Phys., 86, 1391-1452(2014).

[11] C. A. Holmes, C. P. Meaney, G. J. Milburn. Synchronization of many nanomechanical resonators coupled via a common cavity field. Phys. Rev. E., 85, 066203(2012).

[12] T. Li, T. Y. Bao, Y. L. Zhang, C. L. Zou, X. B. Zou, G. C. Guo. Long-distance synchronization of unidirectionally cascaded optomechanical systems. Opt. Express, 24, 12338-12348(2016).

[13] M. Zhang, G. S. Wiederhecker, S. Manipatruni, A. Barnard, P. McEuen, M. Lipson. Synchronization of micromechanical oscillators using light. Phys. Rev. Lett., 109, 233906(2012).

[14] M. Bagheri, M. Poot, L. Fan, F. Marquardt, H. X. Tang. Photonic cavity synchronization of nanomechanical oscillators. Phys. Rev. Lett., 111, 213902(2013).

[15] S. Y. Shah, M. Zhang, R. Rand, M. Lipson. Master-slave locking of optomechanical oscillators over a long distance. Phys. Rev. Lett., 114, 113602(2015).

[16] N. Yang, A. Miranowicz, Y. C. Liu, K. Xia, F. Nori. Chaotic synchronization of two optical modes in optomechanical systems. Sci. Rep., 9, 15874(2019).

[17] E. Verhagen, S. Deléglise, S. Weis, A. Schliesser, T. J. Kippenberg. Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode. Nature, 482, 63-67(2012).

[18] C. M. Bender, S. Boettcher. Real spectra in non-Hermitian Hamiltonians having PT symmetry. Phys. Rev. Lett., 80, 5243-5246(1998).

[19] A. Mostafazadeh. Pseudo-hermiticity versus PT symmetry: the necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian. J. Math. Phys., 43, 205-214(2002).

[20] C. M. Bender. Making sense of non-Hermitian Hamiltonians. Rep. Prog. Phys., 70, 947-1018(2007).

[21] A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, D. N. Christodoulides. Observation of PT-symmetry breaking in complex optical potentials. Phys. Rev. Lett., 103, 093902(2009).

[22] C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, D. Kip. Observation of parity-time symmetry in optics. Nat. Phys., 6, 192-195(2010).

[23] C. T. West, T. Kottos, T. Prosen. PT-symmetric wave chaos. Phys. Rev. Lett., 104, 054102(2010).

[24] L. Feng, M. Ayache, J. Huang, Y. L. Xu, M. H. Lu, Y. F. Chen, Y. Fainman, A. Scherer. Nonreciprocal light propagation in a silicon photonic circuit. Science, 333, 729-733(2011).

[25] Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, D. N. Christodoulides. Unidirectional invisibility induced by PT-symmetric periodic structures. Phys. Rev. Lett., 106, 213901(2011).

[26] A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, U. Peschel. Parity-time synthetic photonic lattices. Nature, 488, 167-171(2012).

[27] G. S. Agarwal, K. Qu. “Spontaneous generation of photons in transmission of quantum fields in PT-symmetric optical systems. Phys. Rev. A, 85, 031802(2012).

[28] J. Wiersig. Enhancing the sensitivity of frequency and energy splitting detection by using exceptional points: application to microcavity sensors for single-particle detection. Phys. Rev. Lett., 112, 203901(2014).

[29] H. Jing, S. K. Özdemir, X. Y. Lü, J. Zhang, L. Yang, F. Nori. PT-symmetric phonon laser. Phys. Rev. Lett., 113, 053604(2014).

[30] H. Jing, S. K. Özdemir, Z. Geng, J. Zhang, X. Y. Lü, B. Peng, L. Yang, F. Nori. Optomechanically-induced transparency in parity-time-symmetric microresonators. Sci. Rep., 5, 9663(2015).

[31] Z. P. Liu, J. Zhang, S. K. Özdemir, B. Peng, H. Jing, X. Y. Lü, C. W. Li, L. Yang, F. Nori, Y. X. Liu. Metrology with PT-symmetric cavities: enhanced sensitivity near the PT-phase transition. Phys. Rev. Lett., 117, 110802(2016).

[32] D. W. Schönleber, A. Eisfelf, R. El-Ganainy. Optomechanical interactions in non-Hermitian photonic molecules. New J. Phys., 18, 045014(2016).

[33] X. Y. Lü, H. Jing, J. Y. Ma, Y. Wu. PT-symmetry-breaking chaos in optomechanics. Phys. Rev. Lett., 114, 253601(2015).

[34] J. Zhang, P. Bo, S. K. Özdemir, Y. X. H. Jing, X. Y. Lü, Y. L. Liu, L. Yang, F. Nori. Giant nonlinearity via breaking parity-time symmetry: a route to low-threshold phonon diodes. Phys. Rev. B, 92, 115407(2015).

[35] B. Peng, S. K. Özdemir, F. C. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. H. Fan, F. Nori, C. M. Bender, L. Yang. Parity-time-symmetric whispering-gallery microcavities. Nat. Phys., 10, 394-398(2014).

[36] B. Peng, S. K. Özdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, L. Yang. Loss induced suppression and revival of lasing. Science, 346, 328-332(2014).

[37] L. Feng, Z. J. Wong, R. M. Ma, Y. Wang, X. Zhang. Singlemode laser by parity-time symmetry breaking. Science, 346, 972-975(2014).

[38] H. Hodaei, M. A. Miri, M. Heinrich, D. N. Christodoulides, M. Khajavikhan. Parity-time-symmetric microring lasers. Science, 346, 975-978(2014).

[39] L. Chang, X. S. Jiang, S. Y. Hua, C. Yang, J. M. Wen, L. Jiang, G. Y. Li, G. Z. Wang, M. Xiao. Parity-time symmetry and variable optical isolation in active-passive-coupled microresonators. Nat. Photonics, 8, 524-529(2014).

[40] H. Xu, D. Mason, L. Jiang, G. E. Harris. Topological energy transfer in an optomechanical system with exceptional points. Nature, 537, 80-83(2016).

[41] J. Doppler, A. A. Mailybaev, J. Bohm, U. Kuhl, A. Girschik, F. Libisch, T. J. Milburn, P. Rabl, N. Moiseyev, S. Rotter. Dynamically encircling an exceptional point for asymmetric mode switching. Nature, 537, 76-79(2016).

[42] W. Chen, S. K. Özdemir, G. Zhao, J. Wiersig, L. Yang. Exceptional points enhance sensing in an optical microcavity. Nature, 548, 192-196(2017).

[43] H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, M. Khajavikhan. Enhanced sensitivity at higher-order exceptional points. Nature, 548, 187-191(2017).

[44] X. Zhou, Y. D. Chong. PT symmetry breaking and nonlinear optical isolation in coupled imcrocavities. Opt. Express, 24, 6916-6930(2016).

[45] A. U. Hassan, H. Hodaei, M. A. Miri, M. Khajavikhan, D. N. Christodoulides. Nonlinear reversal of PT-symmetric phase transition in a system of coupled semiconductor microring resonators. Phys. Rev. A, 92, 063807(2015).

[46] R. N. Bracewell. The Fourier Transform and Its Applications(1978).

[47] L. R. Rabiner, R. W. Schaefer. Digital Processing of Speech Signals(1978).

[48] N. A. Anstey. Correlation techniques–a review. Can. J. Expl. Geophys., 2, 55-82(1966).

[49] P. H. White. Cross correlation in structural systems: dispersion and nondispersion waves. J. Acoust. Soc. Am., 45, 1118-1128(1969).

[50] M. V. Heel. Similarity measures between images. Ultrmicroscopy, 21, 95-100(1987).

[51] J. P. Lewis. Fast normalized cross-correlation. Proc. Vision Interface, 120(1995).

[52] J. C. Yoo, T. H. Han. Fast normalized cross-correlation. Circuits Syst. Signal Process., 28, 819(2009).

[53] A. Neiman. Synchronization like phenomena in coupled stochastic bistable systems. Phys. Rev. E, 49, 3484-3487(1994).

[54] S. K. Han, T. G. Yim, D. E. Postnov, O. V. Sosnovtseva. Interacting coherence resonance oscillators. Phys. Rev. Lett., 83, 1771-1774(1999).

[55] A. Neiman, L. Schimansky-Geier, A. Cornell-Bell, F. Moss. Noise-enhanced phase synchronization in excitable media. Phys. Rev. Lett., 83, 4896-4899(1999).

[56] H. Nakao, K. Arai, Y. Kawamura. Noise-induced synchronization and clustering in ensembles of uncoupled limit-cycle oscillators. Phys. Rev. Lett., 98, 184101(2007).

[57] K. H. Nagai, H. Kori. Noise-induced synchronization of a large population of globally coupled nonidentical oscillators. Phys. Rev. E, 81, 065202(2010).

[58] Y. M. Lai, M. A. Porter. Noise-induced synchronization, desynchronization, and clustering in globally coupled nonidentical oscillators. Phys. Rev. E, 88, 012905(2013).

[59] C. S. Zhou, J. Kurths. Noise-induced phase synchronization and synchronization transitions in chaotic oscillators. Phys. Rev. Lett., 88, 230602(2002).

[60] D. H. He, P. L. Shi, L. Stone. Noise-induced synchronization in realistic models. Phys. Rev. E, 67, 027201(2003).

[61] H. Schomerus. Quantum noise and self-sustained radiation of PT-symmetric systems. Phys. Rev. Lett., 104, 233601(2010).

[62] S.-Y. Lee, J.-W. Ryu, J.-B. Shim, S.-B. Lee, S. W. Kim, K. An. Divergent Petermann factor of interacting resonances in a stadium-shaped microcavity. Phys. Rev. A, 78, 015805(2008).

[63] G. Yoo, H.-S. Sim, H. Schomerus. Quantum noise and mode nonorthogonality in non-Hermitian PT-symmetric optical resonators. Phys. Rev. A, 84, 063833(2011).

[64] J. Zhang, B. Peng, S. K. Özdemir, S. Rotter, K. Pichler, D. Krimer, G. Zhao, F. Nori, Y.-X. Liu, L. Yang. A phonon laser operating at the exceptional point. Nat. Photonics, 12, 479-484(2018).

[65] H. A. Kramers. Brownian motion in a field of force and the diffusion model of chemical reactions. Physica, 7, 284-304(1940).

[66] G. Klein. Mean first-passage times of Brownian motion and related problems. Proc. R. Soc. London A, 211, 431-443(1952).

[67] H. Hofmann, F. A. Ivanyuk. Mean first passage time for nuclear fission and the emission of light particles. Phys. Rev. Lett., 90, 132701(2003).

[68] H. Risken. The Fokker-Planck Equation: Methods of Solution and Applications(1989).