A tutorial and diagnostic tool for chaotic oscillators and time series
Tài liệu tham khảo
Thompson, 1986
Moon, 1992
Barnsley, 1988
Farmer, 1983, The dimension of chaotic attractors, Physica D, 7, 153, 10.1016/0167-2789(83)90125-2
Mandelbrot, 1977
Moon, 1985, The fractal dimension of the two well potential strange attractor, Physica D, 17, 99, 10.1016/0167-2789(85)90137-X
Grebogi, 1986, Metamorphoses of basin boundaries in nonlinear dynamical systems, Physics Review Letters, 56, 1011, 10.1103/PhysRevLett.56.1011
Spitaleri, 1994, Visual numerical environment reference models, methods and tools, Computer Aided Design, 26, 907, 10.1016/0010-4485(94)90056-6
Wolf, 1985, Determining Lyapunov exponents from a time series, Physica D, 16, 285, 10.1016/0167-2789(85)90011-9
Press, 1986
Timoshenko, 1974
Hughes, 1981, Transient algorithm and stability
Ueda, 1979, Randomly transitional phenomena in system governed by Duffing's equation, Journal of Statistical Physics, 20, 181, 10.1007/BF01011512
O'Reilly, 1990
Bryant, 1990, Lyapunov exponents from observed time series, Physics Review Letters, 65, 1523, 10.1103/PhysRevLett.65.1523
Casdagli, 1991, State space reconstruction in the presence of noise, Physica D, 51, 52, 10.1016/0167-2789(91)90222-U
Gibson, 1992, An analytical approach to practical state space reconstruction, Physica D, 57, 1, 10.1016/0167-2789(92)90085-2
Paralitz, 1992, Identification of true and spurious Lyapunov exponents from time series, International Journal of Rifurcation Chaos, 2, 3403
Kennel, 1992, Determining embedding dimension for phase-space reconstruction using a geometrical construction, Physics Review Letters, A45, 185
Eckmann, 1992, Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems, Physica D, 56, 3329, 10.1016/0167-2789(92)90023-G
Zeng, 1991, Estimating the Lyapunov exponent spectrum from short time series of low precision, Physics Review Letters, 66, 349, 10.1103/PhysRevLett.66.3229
Grassberger, 1983, Characterization of strange attractors, Physics Review Letters, 50, 10.1103/PhysRevLett.50.346