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A New Fast and Efficient Solution of Chaos Threshold on Dynamical Systems

A novel method is proposed to compute chaos threshold on dynamical systems based on the law of golden section and Lyapunov exponents from limited experimental data range. First, rough region of the system threshold is estimated by Lyapunov exponents with computation precision to be one digit after decimal dot and with a step size 0.1. Second, the exact threshold value is calculated in terms of the law of the golden section. The advantage of the method is low computation cost and faster convergence to expect the threshold at any precision. The test is proved by Duffing equation.