Threshold determination method of Duffing chaotic system based on multi-scale entropy

Entropy is one of the parameters describing the state of matter in thermodynamics, it can be used to measure the degree of confusion. The entropy of the signal can be used to express the complexity of the signal. The threshold for the transition of the Duffing chaotic system from the critical chaotic state to the large-scale periodic state is called the transition threshold. It is an important parameter for the analysis of chaotic systems, and its solution method is one of the problems urgently to be solved in chaos theory. If the jump threshold is smaller than the real threshold of the system, it will affect its detection signal-to-noise ratio. If the jump threshold is larger than the real threshold, it will cause incorrect detection results, so it is very important to accurately determine the jump threshold. In this study, we found that the multiscale sample entropy value of the Duffing system is significantly different when the system is in the chaotic state and the periodic state, when the system is in a chaotic state, the entropy value is larger, when the system is in a periodic state, the entropy value is smaller, and when the system enters the periodic state, the multiscale entropy value tends to be stable, this paper proposes to use this phenomenon to determine the transition threshold by analyzing the relationship between the entropy of the system and the amplitude of the driving force. When the entropy value is obviously smaller and tends to be stable, the corresponding driving force amplitude is the jump threshold. using this method, the jump threshold of the sinusoidal signal and square wave signal detection system is calculated, the results show that the method is fast, accurate and simple to calculate. However, this method may have a problem that the calculated threshold value is smaller than the real threshold value, our analysis is that the random selection of the subsequence used for calculation causes the calculation threshold value to be too small, so the method is improved in conjunction with genetic algorithm, using genetic algorithm to find the most complicated subsequence in the whole sequence, then this subsequence is used to solve the threshold, Through a large number of calculations and analysis, it can be seen that the problem of a small threshold is no longer present, and the improved method can obtain the jump threshold of the Duffing system very accurately.