本章参考文献
[1] 朱位秋,蔡国强.随机动力学引论[M].北京:科学出版社,2017.
[2] 朱位秋.非线性随机动力学与控制——Hamilton理论体系框架[M].北京:科学出版社,2003.
[3] Dybiec B,Gudowska-Nowak E,Sokolov I M.Stationary states in Langevin dynamics under asymmetric Lévy noises[J].Phys.Rev.E,2007,76(4 Pt 1):041122.
[4] Chechkin A V,Gonchar V Y,Klafter J,et al.Fundamentals of Lévy flight processes[J].Adv.Chem.Phys.,2006,133:439-496.
[5] Dubkov A A,Spagnolo B,Uchaikin V V.Lévy flight superdiffusion:an introduction[J].Int.J.Bifurcat.Chaos,2008,18(9):2649-2672.
[6] Marquardt T.Fractional Lévy processes with an application to long memory moving average processes[J].Bernoulli,2006,12:1099-1126.
[7] Ditlevsen P D.Observation of α-stable noise induced millennial climate changes from an ice-core record[J].Geophys.Res.Lett.,1999,26(10):1441-1444.
[8] Kong X,Thakor N V.Adaptive estimation of latency changes in evoked potentials[J].IEEE Trans.Biomed.Eng.,1996,43(2):189-197.
[9] Bartumeus F,Luz M G E D,Viswanathan G M,Catalan J M V,Animal search strategies:a quantitative random-walk analysis[J].Ecology,2005,86(11):3078-3087.
[10] Majumdar S N,Ziff R M.Universal record statistics of random walks and Lévy flights[J].Phys.Rev.Lett.,2008,101:050601.
[11] 段金桥.随机动力学系统导论[M].北京:科学出版社,2018.
[12] Leccardi M.Comparison of three algorithms for Lévy noise generation[C].Proceedings of Fifth EUROMECH Nonlinear Dynamics Conference,2005.
[13] Janicki A,Weron A.Simulation and chaotic behavior of alpha-stable stochastic processe[M].New York:Marcel Dekker,Inc.,1994.
[14] Benzi R,Sutera A,Vulpiani A.The Mechanism of stochastic resonance[J].J.Phys.,A:Math.Gen.,1981,14(11):L453-L457.
[15] Benzi R,Parisi G,Sutera A,et al.Stochastic resonance in climatic change[J].Tellus,1982,34(l):10-16.
[16] Fauve S,Heslot F,Stochastic resonance in a bistable system[J].Phys.Lett.,A,1983,97(1-2):5-7.
[17] McNamara B,Wiesenfeld K,Roy R.Observation of stochastic resonance in a ring laser[J].Phys.Rev.Lett.,1988,60(25):2626-2629.
[18] McNamara B,Wiesenfeld K.Theory of stochastic resonance[J].Phys.Rev.A,1989,39(9):4854-4869.
[19] 龚德纯,秦光戎,胡岗,温孝东.由随机共振可获得比最佳线性滤波器更高的信噪比[J].中国科学A辑,1992,35(8):828-833.
[20] Agudov N V,Krichigin A V,Valenti D,Spagnolo B.Stochastic resonance in a trapping overdamped monostable system[J].Phys.Rev.E.,2010,81(5):051123.
[21] Collins J J,Chow C C,Imhoff T T.Aperiodic stochastic resonance in excitable systems[J].Phys.Rev.E.,1995,52(4):3321-3324.
[22] Collins J J,Chow C C,Capela A C,Imhoff T T.Aperiodic stochastic resonance[J].Phys.Rev.E,1996:54(5):5575-5554.
[23] Heneghan C,Chow C C,Collins J J,et al.Information measures quantifying aperiodic stochastic resonance[J].Phys.Rev.E,1996,54(3):R2228-R2231.
[24] Collins J J,Imhoff T T and Grigg P.Noise-enhanced tactile sensation[J].Nature,1996,383(6603):770-770.
[25] Neiman A,Shulgin B,Anishehenko V,Ebeling W,Schimansky-Geier L,et al.Dynamical entropies applied to stochastic resonance[J].Phys.Rev.Lett.,1996,76(23):4299-4302.
[26] Stemmler M.A single spike suffices:the simplest form of stochastic resonance in model neurons[J].Netw.Comput.Neural Syst.,1996,7(4):687-716.
[27] Hlaváčková-Schindler K,Paluš M,Vejmelka M,Bhattacharya J.Causality detection based on information-theoretic approaches in time series analysis[J].Phys.Rep.,2007,441(1):1-46.
[28] Wu J,Xu Y,Wang H Y,Kurths J.Information-based measures for logical stochastic resonance in a synthetic gene network under Lévy flight superdiffusion[J].Chaos,2017,27:63105.
[29] Bulsara A R,Dari A,Ditto W L,Murali K,Sinha S.Logical stochastic resonance[J].Chem.Phys.,2010,375(2-3):424-434.
[30] Spanos P D.Stochastic linearization in structural dynamics[J].Appl.Mech.Rev.,1981,34(1):1-8.
[31] Robert J B,Spanos P D.Random vibration and statistical linearization[M].New York:Wily,1990.
[32] 朱位秋.随机平均法及其应用[J].力学进展,1987,17(3):342-352.
[33] Khasminskii R Z.Stochastic processes defined by differential equations with a small parameter[J].Theory.Probab.Appl.,1966,11(2):211-228.
[34] Khasminskii R Z,Yin G,Zhang Q.Asymptotic expansions of singularly perturbed systems involving rapidly fluctuating Markov chains[J].Appl.Math.,1996,56(1):277-293.
[35] Arnold L,Wihstutz P V.Asymptotic analysis of the lyapunov exponent and rotation Number of the random oscillator and applications[J].SIAM.J.App.Math.,1986,46(3):427-450.
[36] Arnold L.A formula connecting sample and moment stability of linear stochastic systems[J].SIAM J.Appl.Math.,1984,44:793-802.
[37] Oseledets V I.A multiplicative ergodic theorem:Lyapunov characteristic number for dynamical systems[J].Trans.Moscow.Math.Soc,1968,19:197-231.
[38] Arnold L,Wihstutz V.Lyapunov exponents:A survey[M].Springer Berlin Heidelberg,1986.
[39] 刘先斌,陈虬.非线性随机系统的稳定性和分岔研究[J].力学进展,1996,26(4):437-452.
[40] Zhu W Q.Lyapunov exponent and stochastic stability of quasi-non-integrable Hamiltonian systems[J].Nonlin.Mech.,2004,39(4):569-579.
[41] Zhu W Q,Hang Z L.Stochastic stability of quasi-non-integrable-Hamiltonian systems[J].J.Sound.Vib.,1998,218(5):769-789.
[42] Stocks N G.Suprathreshold stochastic resonance in multilevel threshold systems[J].Phys.Rev.Lett.,2000,84(11):2310-2313.
[43] Xu B H,Duan F B,Bao R H,Li J L.Stochastic resonance with tuning system parameters:The application of bistable systems in signal processing[J].Chaos,Soliton Fract.,2002,13(4):633-644.
[44] Mitaim S,Kosko B.Adaptive stochastic resonance[J].Proceedings of the IEEE,1998,86(11):2152-2183.
[45] Mitaim S,Kosko B.Adaptive stochastic resonance and fuzzy approximation[J].Proceedings of the 1998 IEEE International Symposium on Intelligent Control,1998,86(11):471-476.
[46] Murali K,Sinha S,Ditto W L,Bulsara A R.Reliable logic circuit elements that exploit nonlinearity in the presence of a noise floor[J].Phys.Rev.Lett.,2009,102(10):104-107.
[47] 胡岗.随机力与非线性系统[M].上海:上海科技出版社,1994.
[48] Jung P,Hanggi P.Stochastic nonlinear dynamics modulated by external periodic forces[J].Europhys.Lett.,1989,8(6):505-510.
[49] Dykman M I,Luehinsky D G,Mannella R,Mcclintock P V E,et al.Noise-induced linearization[J].Phys.Lett.,A,1994,193:61-66.
[50] Dykman M I,Luehinsky D G,Mannella R,Mcclintock P V E,et al.Stochastic resonance:linear response and giant nonlinearity[J].J.Stat.Phys.1993,70(1-2):463-478.