The nonlinear local Lyapunov exponent（NLLE） can be used as a quantification of the local predictability limit of chaotic systems. In this study, the phase-spatial structure of the local predictability limit over the...The nonlinear local Lyapunov exponent（NLLE） can be used as a quantification of the local predictability limit of chaotic systems. In this study, the phase-spatial structure of the local predictability limit over the Lorenz-63 system is investigated. It is found that the inner and outer rims of each regime of the attractor have a high probability of a longer than average local predictability limit, while the center part is the opposite. However, the distribution of the local predictability limit is nonuniformly organized, with adjacent points sometimes showing quite distinct error growth.The source of local predictability is linked to the local dynamics, which is related to the region in the phase space and the duration on the current regime.展开更多
In this paper, new approaches for chaotic time series prediction areintroduced. We first summarize and evaluate the existing local prediction models, then proposeoptimization models and new algorithms to modify proced...In this paper, new approaches for chaotic time series prediction areintroduced. We first summarize and evaluate the existing local prediction models, then proposeoptimization models and new algorithms to modify procedures of local approximations. Themodification to the choice of sample sets is given, and the zeroth-order approximation is improvedby a linear programming method. Four procedures of first-order approximation are compared, andcorresponding modified methods are given. Lastly, the idea of nonlinear feedback to raise predictingaccuracy is put forward. In the end, we discuss two important examples, i.e. Lorenz system andRoessler system, and the simulation experiments indicate that the modified algorithms are effective.展开更多
基金supported by the National Natural Science Foundation of China[grant number 41375110]
文摘The nonlinear local Lyapunov exponent（NLLE） can be used as a quantification of the local predictability limit of chaotic systems. In this study, the phase-spatial structure of the local predictability limit over the Lorenz-63 system is investigated. It is found that the inner and outer rims of each regime of the attractor have a high probability of a longer than average local predictability limit, while the center part is the opposite. However, the distribution of the local predictability limit is nonuniformly organized, with adjacent points sometimes showing quite distinct error growth.The source of local predictability is linked to the local dynamics, which is related to the region in the phase space and the duration on the current regime.
文摘In this paper, new approaches for chaotic time series prediction areintroduced. We first summarize and evaluate the existing local prediction models, then proposeoptimization models and new algorithms to modify procedures of local approximations. Themodification to the choice of sample sets is given, and the zeroth-order approximation is improvedby a linear programming method. Four procedures of first-order approximation are compared, andcorresponding modified methods are given. Lastly, the idea of nonlinear feedback to raise predictingaccuracy is put forward. In the end, we discuss two important examples, i.e. Lorenz system andRoessler system, and the simulation experiments indicate that the modified algorithms are effective.
