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2003•Journal of Xinxiang Teachers CollegeRequires access

Nonlinear Values of Logistic Map in Chaostic Area

Xin Xia Qi

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Abstract

We use several nonlinear means to analysis the nonlinear values of chaostic Logistic map. We use the method of recurrence plot analysis (RPA) and recurrence quantification analysis (RQA) to get the conclusion that the data obeys the deterministic rule. We calculate the correlation dimension (Dc), the largest Lyapunov exponent (λ1) and the approximate entropy (ApEn). It shows that the correlation dimension is between 1 to 2, the largest Lyapunov exponent greater than 0 and the value of approximate entropy is 0. 676460.

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What this paper is about

We use several nonlinear means to analysis the nonlinear values of chaostic Logistic map. We use the method of recurrence plot analysis (RPA) and recurrence quantification analysis (RQA) to get the conclusion that the data obeys the deterministic rule. We calculate the correlation dimension (Dc), the largest Lyapunov exponent (λ1) and the approximate entropy (ApEn). It shows that the correlation dimension is between 1 to 2, the largest Lyapunov exponent greater than 0 and the value of approximate entropy is 0. 676460.

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Available abstract

We use several nonlinear means to analysis the nonlinear values of chaostic Logistic map. We use the method of recurrence plot analysis (RPA) and recurrence quantification analysis (RQA) to get the conclusion that the data obeys the deterministic rule. We calculate the correlation dimension (Dc), the largest Lyapunov exponent (λ1) and the approximate entropy (ApEn). It shows that the correlation dimension is between 1 to 2, the largest Lyapunov exponent greater than 0 and the value of approximate entropy is 0. 676460.

Key concepts: Lyapunov exponent, Correlation dimension, Recurrence plot, Approximate entropy, Recurrence quantification analysis, Nonlinear system, Logistic map, Mathematics

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