Fig. 1. System state transition: (a) System state transition; (b) periodic state.

Fig. 2. Variation of multi-scale entropy in square wave signal detection system.

Fig. 3. Simulation experiment to solve the threshold of square wave signal detection system.

Fig. 4. Variation of multi-scale entropy in sinusoidal signal detection system.

Fig. 5. Simulation experiment to solve the threshold of sinusoidal signal detection system.

Fig. 6. Real underwater acoustic signal.

Fig. 7. Spectrum of real underwater acoustic signals.

Fig. 8. Changes in multi-scale entropy of real signal detection system.

Fig. 9. Simulation experiment to solve the threshold of real underwater acoustic signal detection system.

Fig. 10. Detecting real underwater acoustic signals: (a) The system did not add a real signal; (b) system adds real signal

Fig. 11. Variation of multi-scale entropy in 5 rad/s sinusoidal signal detection system.

Fig. 12. Simulation experiment to solve the threshold of 5 rad/s sinusoidal signal detection system.

Fig. 13. Critical chaotic state of the system.

Fig. 14. Variation of maximum multi-scale entropy of 5 rad/s sinusoidal signal detection system.